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How to Write the Methods Section of a Research Paper

Writing a research paper is both an art and a skill, and knowing how to write the methods section of a research paper is the first crucial step in mastering scientific writing. If, like the majority of early career researchers, you believe that the methods section is the simplest to write and needs little in the way of careful consideration or thought, this article will help you understand it is not 1 .

We have all probably asked our supervisors, coworkers, or search engines “ how to write a methods section of a research paper ” at some point in our scientific careers, so you are not alone if that’s how you ended up here.  Even for seasoned researchers, selecting what to include in the methods section from a wealth of experimental information can occasionally be a source of distress and perplexity.   

Additionally, journal specifications, in some cases, may make it more of a requirement rather than a choice to provide a selective yet descriptive account of the experimental procedure. Hence, knowing these nuances of how to write the methods section of a research paper is critical to its success. The methods section of the research paper is not supposed to be a detailed heavy, dull section that some researchers tend to write; rather, it should be the central component of the study that justifies the validity and reliability of the research.

Are you still unsure of how the methods section of a research paper forms the basis of every investigation? Consider the last article you read but ignore the methods section and concentrate on the other parts of the paper . Now think whether you could repeat the study and be sure of the credibility of the findings despite knowing the literature review and even having the data in front of you. You have the answer!   

Having established the importance of the methods section , the next question is how to write the methods section of a research paper that unifies the overall study. The purpose of the methods section , which was earlier called as Materials and Methods , is to describe how the authors went about answering the “research question” at hand. Here, the objective is to tell a coherent story that gives a detailed account of how the study was conducted, the rationale behind specific experimental procedures, the experimental setup, objects (variables) involved, the research protocol employed, tools utilized to measure, calculations and measurements, and the analysis of the collected data 2 .

In this article, we will take a deep dive into this topic and provide a detailed overview of how to write the methods section of a research paper . For the sake of clarity, we have separated the subject into various sections with corresponding subheadings.  

Table of Contents

What is the methods section of a research paper ?  

The methods section is a fundamental section of any paper since it typically discusses the ‘ what ’, ‘ how ’, ‘ which ’, and ‘ why ’ of the study, which is necessary to arrive at the final conclusions. In a research article, the introduction, which serves to set the foundation for comprehending the background and results is usually followed by the methods section, which precedes the result and discussion sections. The methods section must explicitly state what was done, how it was done, which equipment, tools and techniques were utilized, how were the measurements/calculations taken, and why specific research protocols, software, and analytical methods were employed.  

Why is the methods section important?  

The primary goal of the methods section is to provide pertinent details about the experimental approach so that the reader may put the results in perspective and, if necessary, replicate the findings 3 .  This section offers readers the chance to evaluate the reliability and validity of any study. In short, it also serves as the study’s blueprint, assisting researchers who might be unsure about any other portion in establishing the study’s context and validity. The methods plays a rather crucial role in determining the fate of the article; an incomplete and unreliable methods section can frequently result in early rejections and may lead to numerous rounds of modifications during the publication process. This means that the reviewers also often use methods section to assess the reliability and validity of the research protocol and the data analysis employed to address the research topic. In other words, the purpose of the methods section is to demonstrate the research acumen and subject-matter expertise of the author(s) in their field.  

Structure of methods section of a research paper  

Similar to the research paper, the methods section also follows a defined structure; this may be dictated by the guidelines of a specific journal or can be presented in a chronological or thematic manner based on the study type. When writing the methods section , authors should keep in mind that they are telling a story about how the research was conducted. They should only report relevant information to avoid confusing the reader and include details that would aid in connecting various aspects of the entire research activity together. It is generally advisable to present experiments in the order in which they were conducted. This facilitates the logical flow of the research and allows readers to follow the progression of the study design.   

It is also essential to clearly state the rationale behind each experiment and how the findings of earlier experiments informed the design or interpretation of later experiments. This allows the readers to understand the overall purpose of the study design and the significance of each experiment within that context. However, depending on the particular research question and method, it may make sense to present information in a different order; therefore, authors must select the best structure and strategy for their individual studies.   

In cases where there is a lot of information, divide the sections into subheadings to cover the pertinent details. If the journal guidelines pose restrictions on the word limit , additional important information can be supplied in the supplementary files. A simple rule of thumb for sectioning the method section is to begin by explaining the methodological approach ( what was done ), describing the data collection methods ( how it was done ), providing the analysis method ( how the data was analyzed ), and explaining the rationale for choosing the methodological strategy. This is described in detail in the upcoming sections.    

How to write the methods section of a research paper  

Contrary to widespread assumption, the methods section of a research paper should be prepared once the study is complete to prevent missing any key parameter. Hence, please make sure that all relevant experiments are done before you start writing a methods section . The next step for authors is to look up any applicable academic style manuals or journal-specific standards to ensure that the methods section is formatted correctly. The methods section of a research paper typically constitutes materials and methods; while writing this section, authors usually arrange the information under each category.

The materials category describes the samples, materials, treatments, and instruments, while experimental design, sample preparation, data collection, and data analysis are a part of the method category. According to the nature of the study, authors should include additional subsections within the methods section, such as ethical considerations like the declaration of Helsinki (for studies involving human subjects), demographic information of the participants, and any other crucial information that can affect the output of the study. Simply put, the methods section has two major components: content and format. Here is an easy checklist for you to consider if you are struggling with how to write the methods section of a research paper .   

• Explain the research design, subjects, and sample details  
• Include information on inclusion and exclusion criteria  
• Mention ethical or any other permission required for the study  
• Include information about materials, experimental setup, tools, and software  
• Add details of data collection and analysis methods  
• Incorporate how research biases were avoided or confounding variables were controlled  
• Evaluate and justify the experimental procedure selected to address the research question  
• Provide precise and clear details of each experiment  
• Flowcharts, infographics, or tables can be used to present complex information     
• Use past tense to show that the experiments have been done   
• Follow academic style guides (such as APA or MLA ) to structure the content  
• Citations should be included as per standard protocols in the field  

Now that you know how to write the methods section of a research paper , let’s address another challenge researchers face while writing the methods section —what to include in the methods section .  How much information is too much is not always obvious when it comes to trying to include data in the methods section of a paper. In the next section, we examine this issue and explore potential solutions.   

What to include in the methods section of a research paper  

The technical nature of the methods section occasionally makes it harder to present the information clearly and concisely while staying within the study context. Many young researchers tend to veer off subject significantly, and they frequently commit the sin of becoming bogged down in itty bitty details, making the text harder to read and impairing its overall flow. However, the best way to write the methods section is to start with crucial components of the experiments. If you have trouble deciding which elements are essential, think about leaving out those that would make it more challenging to comprehend the context or replicate the results. The top-down approach helps to ensure all relevant information is incorporated and vital information is not lost in technicalities. Next, remember to add details that are significant to assess the validity and reliability of the study. Here is a simple checklist for you to follow ( bonus tip: you can also make a checklist for your own study to avoid missing any critical information while writing the methods section ).  

• Structuring the methods section : Authors should diligently follow journal guidelines and adhere to the specific author instructions provided when writing the methods section . Journals typically have specific guidelines for formatting the methods section ; for example, Frontiers in Plant Sciences advises arranging the materials and methods section by subheading and citing relevant literature. There are several standardized checklists available for different study types in the biomedical field, including CONSORT (Consolidated Standards of Reporting Trials) for randomized clinical trials, PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analysis) for systematic reviews and meta-analysis, and STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) for cohort, case-control, cross-sectional studies. Before starting the methods section , check the checklist available in your field that can function as a guide.     
• Organizing different sections to tell a story : Once you are sure of the format required for structuring the methods section , the next is to present the sections in a logical manner; as mentioned earlier, the sections can be organized according to the chronology or themes. In the chronological arrangement, you should discuss the methods in accordance with how the experiments were carried out. An example of the method section of a research paper of an animal study should first ideally include information about the species, weight, sex, strain, and age. Next, the number of animals, their initial conditions, and their living and housing conditions should also be mentioned. Second, how the groups are assigned and the intervention (drug treatment, stress, or other) given to each group, and finally, the details of tools and techniques used to measure, collect, and analyze the data. Experiments involving animal or human subjects should additionally state an ethics approval statement. It is best to arrange the section using the thematic approach when discussing distinct experiments not following a sequential order.  
• Define and explain the objects and procedure: Experimental procedure should clearly be stated in the methods section . Samples, necessary preparations (samples, treatment, and drug), and methods for manipulation need to be included. All variables (control, dependent, independent, and confounding) must be clearly defined, particularly if the confounding variables can affect the outcome of the study.  
• Match the order of the methods section with the order of results: Though not mandatory, organizing the manuscript in a logical and coherent manner can improve the readability and clarity of the paper. This can be done by following a consistent structure throughout the manuscript; readers can easily navigate through the different sections and understand the methods and results in relation to each other. Using experiment names as headings for both the methods and results sections can also make it simpler for readers to locate specific information and corroborate it if needed.   
• Relevant information must always be included: The methods section should have information on all experiments conducted and their details clearly mentioned. Ask the journal whether there is a way to offer more information in the supplemental files or external repositories if your target journal has strict word limitations. For example, Nature communications encourages authors to deposit their step-by-step protocols in an open-resource depository, Protocol Exchange which allows the protocols to be linked with the manuscript upon publication. Providing access to detailed protocols also helps to increase the transparency and reproducibility of the research.  
• It’s all in the details: The methods section should meticulously list all the materials, tools, instruments, and software used for different experiments. Specify the testing equipment on which data was obtained, together with its manufacturer’s information, location, city, and state or any other stimuli used to manipulate the variables. Provide specifics on the research process you employed; if it was a standard protocol, cite previous studies that also used the protocol.  Include any protocol modifications that were made, as well as any other factors that were taken into account when planning the study or gathering data. Any new or modified techniques should be explained by the authors. Typically, readers evaluate the reliability and validity of the procedures using the cited literature, and a widely accepted checklist helps to support the credibility of the methodology. Note: Authors should include a statement on sample size estimation (if applicable), which is often missed. It enables the reader to determine how many subjects will be required to detect the expected change in the outcome variables within a given confidence interval.  
• Write for the audience: While explaining the details in the methods section , authors should be mindful of their target audience, as some of the rationale or assumptions on which specific procedures are based might not always be obvious to the audience, particularly for a general audience. Therefore, when in doubt, the objective of a procedure should be specified either in relation to the research question or to the entire protocol.  
• Data interpretation and analysis : Information on data processing, statistical testing, levels of significance, and analysis tools and software should be added. Mention if the recommendations and expertise of an experienced statistician were followed. Also, evaluate and justify the preferred statistical method used in the study and its significance.  

What NOT to include in the methods section of a research paper  

To address “ how to write the methods section of a research paper ”, authors should not only pay careful attention to what to include but also what not to include in the methods section of a research paper . Here is a list of do not’s when writing the methods section :  

• Do not elaborate on specifics of standard methods/procedures: You should refrain from adding unnecessary details of experiments and practices that are well established and cited previously.  Instead, simply cite relevant literature or mention if the manufacturer’s protocol was followed.  
• Do not add unnecessary details : Do not include minute details of the experimental procedure and materials/instruments used that are not significant for the outcome of the experiment. For example, there is no need to mention the brand name of the water bath used for incubation.    
• Do not discuss the results: The methods section is not to discuss the results or refer to the tables and figures; save it for the results and discussion section. Also, focus on the methods selected to conduct the study and avoid diverting to other methods or commenting on their pros or cons.  
• Do not make the section bulky : For extensive methods and protocols, provide the essential details and share the rest of the information in the supplemental files. The writing should be clear yet concise to maintain the flow of the section.  

We hope that by this point, you understand how crucial it is to write a thoughtful and precise methods section and the ins and outs of how to write the methods section of a research paper . To restate, the entire purpose of the methods section is to enable others to reproduce the results or verify the research. We sincerely hope that this post has cleared up any confusion and given you a fresh perspective on the methods section .

As a parting gift, we’re leaving you with a handy checklist that will help you understand how to write the methods section of a research paper . Feel free to download this checklist and use or share this with those who you think may benefit from it.  

References  

• Bhattacharya, D. How to write the Methods section of a research paper. Editage Insights, 2018. https://www.editage.com/insights/how-to-write-the-methods-section-of-a-research-paper (2018).
• Kallet, R. H. How to Write the Methods Section of a Research Paper. Respiratory Care 49, 1229–1232 (2004). https://pubmed.ncbi.nlm.nih.gov/15447808/
• Grindstaff, T. L. & Saliba, S. A. AVOIDING MANUSCRIPT MISTAKES. Int J Sports Phys Ther 7, 518–524 (2012). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3474299/

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How to Write a Methods Section for a Psychology Paper

Tips and Examples of an APA Methods Section

Verywell / Brianna Gilmartin 

The methods section of an APA format psychology paper provides the methods and procedures used in a research study or experiment . This part of an APA paper is critical because it allows other researchers to see exactly how you conducted your research.

Method refers to the procedure that was used in a research study. It included a precise description of how the experiments were performed and why particular procedures were selected. While the APA technically refers to this section as the 'method section,' it is also often known as a 'methods section.'

The methods section ensures the experiment's reproducibility and the assessment of alternative methods that might produce different results. It also allows researchers to replicate the experiment and judge the study's validity.

This article discusses how to write a methods section for a psychology paper, including important elements to include and tips that can help.

What to Include in a Method Section

So what exactly do you need to include when writing your method section? You should provide detailed information on the following:

• Research design
• Participants
• Participant behavior

The method section should provide enough information to allow other researchers to replicate your experiment or study.

Components of a Method Section

The method section should utilize subheadings to divide up different subsections. These subsections typically include participants, materials, design, and procedure.

Participants 

In this part of the method section, you should describe the participants in your experiment, including who they were (and any unique features that set them apart from the general population), how many there were, and how they were selected. If you utilized random selection to choose your participants, it should be noted here.

For example: "We randomly selected 100 children from elementary schools near the University of Arizona."

At the very minimum, this part of your method section must convey:

• Basic demographic characteristics of your participants (such as sex, age, ethnicity, or religion)
• The population from which your participants were drawn
• Any restrictions on your pool of participants
• How many participants were assigned to each condition and how they were assigned to each group (i.e., randomly assignment , another selection method, etc.)
• Why participants took part in your research (i.e., the study was advertised at a college or hospital, they received some type of incentive, etc.)

Information about participants helps other researchers understand how your study was performed, how generalizable the result might be, and allows other researchers to replicate the experiment with other populations to see if they might obtain the same results.

In this part of the method section, you should describe the materials, measures, equipment, or stimuli used in the experiment. This may include:

• Testing instruments
• Technical equipment
• Any psychological assessments that were used
• Any special equipment that was used

For example: "Two stories from Sullivan et al.'s (1994) second-order false belief attribution tasks were used to assess children's understanding of second-order beliefs."

For standard equipment such as computers, televisions, and videos, you can simply name the device and not provide further explanation.

Specialized equipment should be given greater detail, especially if it is complex or created for a niche purpose. In some instances, such as if you created a special material or apparatus for your study, you might need to include an illustration of the item in the appendix of your paper.

In this part of your method section, describe the type of design used in the experiment. Specify the variables as well as the levels of these variables. Identify:

• The independent variables
• Dependent variables
• Control variables
• Any extraneous variables that might influence your results.

Also, explain whether your experiment uses a  within-groups  or between-groups design.

For example: "The experiment used a 3x2 between-subjects design. The independent variables were age and understanding of second-order beliefs."

The next part of your method section should detail the procedures used in your experiment. Your procedures should explain:

• What the participants did
• How data was collected
• The order in which steps occurred

For example: "An examiner interviewed children individually at their school in one session that lasted 20 minutes on average. The examiner explained to each child that he or she would be told two short stories and that some questions would be asked after each story. All sessions were videotaped so the data could later be coded."

Keep this subsection concise yet detailed. Explain what you did and how you did it, but do not overwhelm your readers with too much information.

Tips for How to Write a Methods Section

In addition to following the basic structure of an APA method section, there are also certain things you should remember when writing this section of your paper. Consider the following tips when writing this section:

• Use the past tense : Always write the method section in the past tense.
• Be descriptive : Provide enough detail that another researcher could replicate your experiment, but focus on brevity. Avoid unnecessary detail that is not relevant to the outcome of the experiment.
• Use an academic tone : Use formal language and avoid slang or colloquial expressions. Word choice is also important. Refer to the people in your experiment or study as "participants" rather than "subjects."
• Use APA format : Keep a style guide on hand as you write your method section. The Publication Manual of the American Psychological Association is the official source for APA style.
• Make connections : Read through each section of your paper for agreement with other sections. If you mention procedures in the method section, these elements should be discussed in the results and discussion sections.
• Proofread : Check your paper for grammar, spelling, and punctuation errors.. typos, grammar problems, and spelling errors. Although a spell checker is a handy tool, there are some errors only you can catch.

After writing a draft of your method section, be sure to get a second opinion. You can often become too close to your work to see errors or lack of clarity. Take a rough draft of your method section to your university's writing lab for additional assistance.

A Word From Verywell

The method section is one of the most important components of your APA format paper. The goal of your paper should be to clearly detail what you did in your experiment. Provide enough detail that another researcher could replicate your study if they wanted.

Finally, if you are writing your paper for a class or for a specific publication, be sure to keep in mind any specific instructions provided by your instructor or by the journal editor. Your instructor may have certain requirements that you need to follow while writing your method section.

Frequently Asked Questions

While the subsections can vary, the three components that should be included are sections on the participants, the materials, and the procedures.

• Describe who the participants were in the study and how they were selected.
• Define and describe the materials that were used including any equipment, tests, or assessments
• Describe how the data was collected

To write your methods section in APA format, describe your participants, materials, study design, and procedures. Keep this section succinct, and always write in the past tense. The main heading of this section should be labeled "Method" and it should be centered, bolded, and capitalized. Each subheading within this section should be bolded, left-aligned and in title case.

The purpose of the methods section is to describe what you did in your experiment. It should be brief, but include enough detail that someone could replicate your experiment based on this information. Your methods section should detail what you did to answer your research question. Describe how the study was conducted, the study design that was used and why it was chosen, and how you collected the data and analyzed the results.

Erdemir F. How to write a materials and methods section of a scientific article ? Turk J Urol . 2013;39(Suppl 1):10-5. doi:10.5152/tud.2013.047

Kallet RH. How to write the methods section of a research paper . Respir Care . 2004;49(10):1229-32. PMID: 15447808.

American Psychological Association.  Publication Manual of the American Psychological Association  (7th ed.). Washington DC: The American Psychological Association; 2019.

American Psychological Association. APA Style Journal Article Reporting Standards . Published 2020.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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The methods section describes actions taken to investigate a research problem and the rationale for the application of specific procedures or techniques used to identify, select, process, and analyze information applied to understanding the problem, thereby, allowing the reader to critically evaluate a study’s overall validity and reliability. The methodology section of a research paper answers two main questions: How was the data collected or generated? And, how was it analyzed? The writing should be direct and precise and always written in the past tense.

Kallet, Richard H. "How to Write the Methods Section of a Research Paper." Respiratory Care 49 (October 2004): 1229-1232.

Importance of a Good Methodology Section

You must explain how you obtained and analyzed your results for the following reasons:

• Readers need to know how the data was obtained because the method you chose affects the results and, by extension, how you interpreted their significance in the discussion section of your paper.
• Methodology is crucial for any branch of scholarship because an unreliable method produces unreliable results and, as a consequence, undermines the value of your analysis of the findings.
• In most cases, there are a variety of different methods you can choose to investigate a research problem. The methodology section of your paper should clearly articulate the reasons why you have chosen a particular procedure or technique.
• The reader wants to know that the data was collected or generated in a way that is consistent with accepted practice in the field of study. For example, if you are using a multiple choice questionnaire, readers need to know that it offered your respondents a reasonable range of answers to choose from.
• The method must be appropriate to fulfilling the overall aims of the study. For example, you need to ensure that you have a large enough sample size to be able to generalize and make recommendations based upon the findings.
• The methodology should discuss the problems that were anticipated and the steps you took to prevent them from occurring. For any problems that do arise, you must describe the ways in which they were minimized or why these problems do not impact in any meaningful way your interpretation of the findings.
• In the social and behavioral sciences, it is important to always provide sufficient information to allow other researchers to adopt or replicate your methodology. This information is particularly important when a new method has been developed or an innovative use of an existing method is utilized.

Bem, Daryl J. Writing the Empirical Journal Article. Psychology Writing Center. University of Washington; Denscombe, Martyn. The Good Research Guide: For Small-Scale Social Research Projects . 5th edition. Buckingham, UK: Open University Press, 2014; Lunenburg, Frederick C. Writing a Successful Thesis or Dissertation: Tips and Strategies for Students in the Social and Behavioral Sciences . Thousand Oaks, CA: Corwin Press, 2008.

Structure and Writing Style

I.  Groups of Research Methods

There are two main groups of research methods in the social sciences:

• The e mpirical-analytical group approaches the study of social sciences in a similar manner that researchers study the natural sciences . This type of research focuses on objective knowledge, research questions that can be answered yes or no, and operational definitions of variables to be measured. The empirical-analytical group employs deductive reasoning that uses existing theory as a foundation for formulating hypotheses that need to be tested. This approach is focused on explanation.
• The i nterpretative group of methods is focused on understanding phenomenon in a comprehensive, holistic way . Interpretive methods focus on analytically disclosing the meaning-making practices of human subjects [the why, how, or by what means people do what they do], while showing how those practices arrange so that it can be used to generate observable outcomes. Interpretive methods allow you to recognize your connection to the phenomena under investigation. However, the interpretative group requires careful examination of variables because it focuses more on subjective knowledge.

II.  Content

The introduction to your methodology section should begin by restating the research problem and underlying assumptions underpinning your study. This is followed by situating the methods you used to gather, analyze, and process information within the overall “tradition” of your field of study and within the particular research design you have chosen to study the problem. If the method you choose lies outside of the tradition of your field [i.e., your review of the literature demonstrates that the method is not commonly used], provide a justification for how your choice of methods specifically addresses the research problem in ways that have not been utilized in prior studies.

The remainder of your methodology section should describe the following:

• Decisions made in selecting the data you have analyzed or, in the case of qualitative research, the subjects and research setting you have examined,
• Tools and methods used to identify and collect information, and how you identified relevant variables,
• The ways in which you processed the data and the procedures you used to analyze that data, and
• The specific research tools or strategies that you utilized to study the underlying hypothesis and research questions.

In addition, an effectively written methodology section should:

• Introduce the overall methodological approach for investigating your research problem . Is your study qualitative or quantitative or a combination of both (mixed method)? Are you going to take a special approach, such as action research, or a more neutral stance?
• Indicate how the approach fits the overall research design . Your methods for gathering data should have a clear connection to your research problem. In other words, make sure that your methods will actually address the problem. One of the most common deficiencies found in research papers is that the proposed methodology is not suitable to achieving the stated objective of your paper.
• Describe the specific methods of data collection you are going to use , such as, surveys, interviews, questionnaires, observation, archival research. If you are analyzing existing data, such as a data set or archival documents, describe how it was originally created or gathered and by whom. Also be sure to explain how older data is still relevant to investigating the current research problem.
• Explain how you intend to analyze your results . Will you use statistical analysis? Will you use specific theoretical perspectives to help you analyze a text or explain observed behaviors? Describe how you plan to obtain an accurate assessment of relationships, patterns, trends, distributions, and possible contradictions found in the data.
• Provide background and a rationale for methodologies that are unfamiliar for your readers . Very often in the social sciences, research problems and the methods for investigating them require more explanation/rationale than widely accepted rules governing the natural and physical sciences. Be clear and concise in your explanation.
• Provide a justification for subject selection and sampling procedure . For instance, if you propose to conduct interviews, how do you intend to select the sample population? If you are analyzing texts, which texts have you chosen, and why? If you are using statistics, why is this set of data being used? If other data sources exist, explain why the data you chose is most appropriate to addressing the research problem.
• Provide a justification for case study selection . A common method of analyzing research problems in the social sciences is to analyze specific cases. These can be a person, place, event, phenomenon, or other type of subject of analysis that are either examined as a singular topic of in-depth investigation or multiple topics of investigation studied for the purpose of comparing or contrasting findings. In either method, you should explain why a case or cases were chosen and how they specifically relate to the research problem.
• Describe potential limitations . Are there any practical limitations that could affect your data collection? How will you attempt to control for potential confounding variables and errors? If your methodology may lead to problems you can anticipate, state this openly and show why pursuing this methodology outweighs the risk of these problems cropping up.

NOTE:   Once you have written all of the elements of the methods section, subsequent revisions should focus on how to present those elements as clearly and as logically as possibly. The description of how you prepared to study the research problem, how you gathered the data, and the protocol for analyzing the data should be organized chronologically. For clarity, when a large amount of detail must be presented, information should be presented in sub-sections according to topic. If necessary, consider using appendices for raw data.

ANOTHER NOTE: If you are conducting a qualitative analysis of a research problem , the methodology section generally requires a more elaborate description of the methods used as well as an explanation of the processes applied to gathering and analyzing of data than is generally required for studies using quantitative methods. Because you are the primary instrument for generating the data [e.g., through interviews or observations], the process for collecting that data has a significantly greater impact on producing the findings. Therefore, qualitative research requires a more detailed description of the methods used.

YET ANOTHER NOTE:   If your study involves interviews, observations, or other qualitative techniques involving human subjects , you may be required to obtain approval from the university's Office for the Protection of Research Subjects before beginning your research. This is not a common procedure for most undergraduate level student research assignments. However, i f your professor states you need approval, you must include a statement in your methods section that you received official endorsement and adequate informed consent from the office and that there was a clear assessment and minimization of risks to participants and to the university. This statement informs the reader that your study was conducted in an ethical and responsible manner. In some cases, the approval notice is included as an appendix to your paper.

III.  Problems to Avoid

Irrelevant Detail The methodology section of your paper should be thorough but concise. Do not provide any background information that does not directly help the reader understand why a particular method was chosen, how the data was gathered or obtained, and how the data was analyzed in relation to the research problem [note: analyzed, not interpreted! Save how you interpreted the findings for the discussion section]. With this in mind, the page length of your methods section will generally be less than any other section of your paper except the conclusion.

Unnecessary Explanation of Basic Procedures Remember that you are not writing a how-to guide about a particular method. You should make the assumption that readers possess a basic understanding of how to investigate the research problem on their own and, therefore, you do not have to go into great detail about specific methodological procedures. The focus should be on how you applied a method , not on the mechanics of doing a method. An exception to this rule is if you select an unconventional methodological approach; if this is the case, be sure to explain why this approach was chosen and how it enhances the overall process of discovery.

Problem Blindness It is almost a given that you will encounter problems when collecting or generating your data, or, gaps will exist in existing data or archival materials. Do not ignore these problems or pretend they did not occur. Often, documenting how you overcame obstacles can form an interesting part of the methodology. It demonstrates to the reader that you can provide a cogent rationale for the decisions you made to minimize the impact of any problems that arose.

Literature Review Just as the literature review section of your paper provides an overview of sources you have examined while researching a particular topic, the methodology section should cite any sources that informed your choice and application of a particular method [i.e., the choice of a survey should include any citations to the works you used to help construct the survey].

It’s More than Sources of Information! A description of a research study's method should not be confused with a description of the sources of information. Such a list of sources is useful in and of itself, especially if it is accompanied by an explanation about the selection and use of the sources. The description of the project's methodology complements a list of sources in that it sets forth the organization and interpretation of information emanating from those sources.

Azevedo, L.F. et al. "How to Write a Scientific Paper: Writing the Methods Section." Revista Portuguesa de Pneumologia 17 (2011): 232-238; Blair Lorrie. “Choosing a Methodology.” In Writing a Graduate Thesis or Dissertation , Teaching Writing Series. (Rotterdam: Sense Publishers 2016), pp. 49-72; Butin, Dan W. The Education Dissertation A Guide for Practitioner Scholars . Thousand Oaks, CA: Corwin, 2010; Carter, Susan. Structuring Your Research Thesis . New York: Palgrave Macmillan, 2012; Kallet, Richard H. “How to Write the Methods Section of a Research Paper.” Respiratory Care 49 (October 2004):1229-1232; Lunenburg, Frederick C. Writing a Successful Thesis or Dissertation: Tips and Strategies for Students in the Social and Behavioral Sciences . Thousand Oaks, CA: Corwin Press, 2008. Methods Section. The Writer’s Handbook. Writing Center. University of Wisconsin, Madison; Rudestam, Kjell Erik and Rae R. Newton. “The Method Chapter: Describing Your Research Plan.” In Surviving Your Dissertation: A Comprehensive Guide to Content and Process . (Thousand Oaks, Sage Publications, 2015), pp. 87-115; What is Interpretive Research. Institute of Public and International Affairs, University of Utah; Writing the Experimental Report: Methods, Results, and Discussion. The Writing Lab and The OWL. Purdue University; Methods and Materials. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College.

Writing Tip

Statistical Designs and Tests? Do Not Fear Them!

Don't avoid using a quantitative approach to analyzing your research problem just because you fear the idea of applying statistical designs and tests. A qualitative approach, such as conducting interviews or content analysis of archival texts, can yield exciting new insights about a research problem, but it should not be undertaken simply because you have a disdain for running a simple regression. A well designed quantitative research study can often be accomplished in very clear and direct ways, whereas, a similar study of a qualitative nature usually requires considerable time to analyze large volumes of data and a tremendous burden to create new paths for analysis where previously no path associated with your research problem had existed.

To locate data and statistics, GO HERE .

Another Writing Tip

Knowing the Relationship Between Theories and Methods

There can be multiple meaning associated with the term "theories" and the term "methods" in social sciences research. A helpful way to delineate between them is to understand "theories" as representing different ways of characterizing the social world when you research it and "methods" as representing different ways of generating and analyzing data about that social world. Framed in this way, all empirical social sciences research involves theories and methods, whether they are stated explicitly or not. However, while theories and methods are often related, it is important that, as a researcher, you deliberately separate them in order to avoid your theories playing a disproportionate role in shaping what outcomes your chosen methods produce.

Introspectively engage in an ongoing dialectic between the application of theories and methods to help enable you to use the outcomes from your methods to interrogate and develop new theories, or ways of framing conceptually the research problem. This is how scholarship grows and branches out into new intellectual territory.

Reynolds, R. Larry. Ways of Knowing. Alternative Microeconomics . Part 1, Chapter 3. Boise State University; The Theory-Method Relationship. S-Cool Revision. United Kingdom.

Yet Another Writing Tip

Methods and the Methodology

Do not confuse the terms "methods" and "methodology." As Schneider notes, a method refers to the technical steps taken to do research . Descriptions of methods usually include defining and stating why you have chosen specific techniques to investigate a research problem, followed by an outline of the procedures you used to systematically select, gather, and process the data [remember to always save the interpretation of data for the discussion section of your paper].

The methodology refers to a discussion of the underlying reasoning why particular methods were used . This discussion includes describing the theoretical concepts that inform the choice of methods to be applied, placing the choice of methods within the more general nature of academic work, and reviewing its relevance to examining the research problem. The methodology section also includes a thorough review of the methods other scholars have used to study the topic.

Bryman, Alan. "Of Methods and Methodology." Qualitative Research in Organizations and Management: An International Journal 3 (2008): 159-168; Schneider, Florian. “What's in a Methodology: The Difference between Method, Methodology, and Theory…and How to Get the Balance Right?” PoliticsEastAsia.com. Chinese Department, University of Leiden, Netherlands.

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How to Write the Methods Section of an APA Paper

• 3-minute read
• 23rd December 2021

If you’re a researcher writing an APA paper , you’ll need to include a Methods section. This part explains the methods you used to conduct your experiment or research study and is always written in the past tense.

It’s crucial that you include all the relevant information here because other researchers will use this section to recreate your study, as well as judge how valid and accurate your results are.

In this guide, we’ll show you how to write a clear and comprehensive Methods section for your research paper.

Structuring the Methods Section

This section of an APA paper is typically split into three subsections under the following subheadings:

• Participants —who took part in the experiment and why?
• Materials —what tools did you use to conduct the experiment?
• Procedure —what steps were involved in the experiment?

If necessary, you may add further subsections. Different institutions have specific rules on what subsections should be included (for example, some universities require a “Design” subsection), so make sure to check your institution’s requirements before you start writing your Methods section.

Writing the Participants Subsection

In this first subsection, you will need to identify the participants of your experiment or study. You should include:

●  How many people took part, and how many were assigned to the experimental condition

●  How they were selected for participation

●  Any relevant demographic information (e.g., age, sex, ethnicity)

You’ll also need to address whether any restrictions were placed on who was selected and if any incentives were offered to encourage participants to take part.

Writing the Materials Subsection

In this subsection, you should address the materials, equipment, measures, and stimuli used in the study. These might include technology and computer software, tools such as questionnaires and psychological assessments, and, if relevant, the physical setting where the study took place.

You’ll need to describe specialist equipment in detail, especially if it has a niche purpose. However, you don’t need to provide specific information about common or standard equipment (e.g., the type of computer on which participants completed a survey) unless it’s relevant to the experiment.

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In addition, you don’t need to explain a material in depth if it’s well known within your field, such as a famous psychological assessment. Instead, you can provide a citation referring to that material.

If any materials were designed specifically for the experiment, such as a questionnaire, you’ll need to provide such materials in the appendix .

Writing the Procedure Subsection

The procedure subsection should describe what you had participants do in a step-by-step format. It should be detailed but concise and will typically include:

●  A summary of the instructions given to participants (as well as any information that was intentionally withheld)

●  A description of how participants in different conditions were treated

●  How long each step of the process took

●  How participants were debriefed or dismissed at the end of the experiment

After detailing the steps of the experiment, you should then address the methods you used to collect and analyze data.

Proofreading Your Methods Section

Because the Methods section of your paper will help other researchers understand and recreate your experiment, you’ll want your writing to be at its best.

Our expert research paper proofreaders can help your research get the recognition it deserves by making sure your work is clear, concise, and error-free. Why not try our services for free by submitting a trial document ?

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Here's What You Need to Understand About Research Methodology

Table of Contents

Research methodology involves a systematic and well-structured approach to conducting scholarly or scientific inquiries. Knowing the significance of research methodology and its different components is crucial as it serves as the basis for any study.

Typically, your research topic will start as a broad idea you want to investigate more thoroughly. Once you’ve identified a research problem and created research questions , you must choose the appropriate methodology and frameworks to address those questions effectively.

What is the definition of a research methodology?

Research methodology is the process or the way you intend to execute your study. The methodology section of a research paper outlines how you plan to conduct your study. It covers various steps such as collecting data, statistical analysis, observing participants, and other procedures involved in the research process

The methods section should give a description of the process that will convert your idea into a study. Additionally, the outcomes of your process must provide valid and reliable results resonant with the aims and objectives of your research. This thumb rule holds complete validity, no matter whether your paper has inclinations for qualitative or quantitative usage.

Studying research methods used in related studies can provide helpful insights and direction for your own research. Now easily discover papers related to your topic on SciSpace and utilize our AI research assistant, Copilot , to quickly review the methodologies applied in different papers.

The need for a good research methodology

While deciding on your approach towards your research, the reason or factors you weighed in choosing a particular problem and formulating a research topic need to be validated and explained. A research methodology helps you do exactly that. Moreover, a good research methodology lets you build your argument to validate your research work performed through various data collection methods, analytical methods, and other essential points.

Just imagine it as a strategy documented to provide an overview of what you intend to do.

While undertaking any research writing or performing the research itself, you may get drifted in not something of much importance. In such a case, a research methodology helps you to get back to your outlined work methodology.

A research methodology helps in keeping you accountable for your work. Additionally, it can help you evaluate whether your work is in sync with your original aims and objectives or not. Besides, a good research methodology enables you to navigate your research process smoothly and swiftly while providing effective planning to achieve your desired results.

What is the basic structure of a research methodology?

Usually, you must ensure to include the following stated aspects while deciding over the basic structure of your research methodology:

1. Your research procedure

Explain what research methods you’re going to use. Whether you intend to proceed with quantitative or qualitative, or a composite of both approaches, you need to state that explicitly. The option among the three depends on your research’s aim, objectives, and scope.

2. Provide the rationality behind your chosen approach

Based on logic and reason, let your readers know why you have chosen said research methodologies. Additionally, you have to build strong arguments supporting why your chosen research method is the best way to achieve the desired outcome.

3. Explain your mechanism

The mechanism encompasses the research methods or instruments you will use to develop your research methodology. It usually refers to your data collection methods. You can use interviews, surveys, physical questionnaires, etc., of the many available mechanisms as research methodology instruments. The data collection method is determined by the type of research and whether the data is quantitative data(includes numerical data) or qualitative data (perception, morale, etc.) Moreover, you need to put logical reasoning behind choosing a particular instrument.

4. Significance of outcomes

The results will be available once you have finished experimenting. However, you should also explain how you plan to use the data to interpret the findings. This section also aids in understanding the problem from within, breaking it down into pieces, and viewing the research problem from various perspectives.

5. Reader’s advice

Anything that you feel must be explained to spread more awareness among readers and focus groups must be included and described in detail. You should not just specify your research methodology on the assumption that a reader is aware of the topic.  

All the relevant information that explains and simplifies your research paper must be included in the methodology section. If you are conducting your research in a non-traditional manner, give a logical justification and list its benefits.

6. Explain your sample space

Include information about the sample and sample space in the methodology section. The term "sample" refers to a smaller set of data that a researcher selects or chooses from a larger group of people or focus groups using a predetermined selection method. Let your readers know how you are going to distinguish between relevant and non-relevant samples. How you figured out those exact numbers to back your research methodology, i.e. the sample spacing of instruments, must be discussed thoroughly.

For example, if you are going to conduct a survey or interview, then by what procedure will you select the interviewees (or sample size in case of surveys), and how exactly will the interview or survey be conducted.

7. Challenges and limitations

This part, which is frequently assumed to be unnecessary, is actually very important. The challenges and limitations that your chosen strategy inherently possesses must be specified while you are conducting different types of research.

The importance of a good research methodology

You must have observed that all research papers, dissertations, or theses carry a chapter entirely dedicated to research methodology. This section helps maintain your credibility as a better interpreter of results rather than a manipulator.

A good research methodology always explains the procedure, data collection methods and techniques, aim, and scope of the research. In a research study, it leads to a well-organized, rationality-based approach, while the paper lacking it is often observed as messy or disorganized.

You should pay special attention to validating your chosen way towards the research methodology. This becomes extremely important in case you select an unconventional or a distinct method of execution.

Curating and developing a strong, effective research methodology can assist you in addressing a variety of situations, such as:

• When someone tries to duplicate or expand upon your research after few years.
• If a contradiction or conflict of facts occurs at a later time. This gives you the security you need to deal with these contradictions while still being able to defend your approach.
• Gaining a tactical approach in getting your research completed in time. Just ensure you are using the right approach while drafting your research methodology, and it can help you achieve your desired outcomes. Additionally, it provides a better explanation and understanding of the research question itself.
• Documenting the results so that the final outcome of the research stays as you intended it to be while starting.

Instruments you could use while writing a good research methodology

As a researcher, you must choose which tools or data collection methods that fit best in terms of the relevance of your research. This decision has to be wise.

There exists many research equipments or tools that you can use to carry out your research process. These are classified as:

a. Interviews (One-on-One or a Group)

An interview aimed to get your desired research outcomes can be undertaken in many different ways. For example, you can design your interview as structured, semi-structured, or unstructured. What sets them apart is the degree of formality in the questions. On the other hand, in a group interview, your aim should be to collect more opinions and group perceptions from the focus groups on a certain topic rather than looking out for some formal answers.

In surveys, you are in better control if you specifically draft the questions you seek the response for. For example, you may choose to include free-style questions that can be answered descriptively, or you may provide a multiple-choice type response for questions. Besides, you can also opt to choose both ways, deciding what suits your research process and purpose better.

c. Sample Groups

Similar to the group interviews, here, you can select a group of individuals and assign them a topic to discuss or freely express their opinions over that. You can simultaneously note down the answers and later draft them appropriately, deciding on the relevance of every response.

d. Observations

If your research domain is humanities or sociology, observations are the best-proven method to draw your research methodology. Of course, you can always include studying the spontaneous response of the participants towards a situation or conducting the same but in a more structured manner. A structured observation means putting the participants in a situation at a previously decided time and then studying their responses.

Of all the tools described above, it is you who should wisely choose the instruments and decide what’s the best fit for your research. You must not restrict yourself from multiple methods or a combination of a few instruments if appropriate in drafting a good research methodology.

Types of research methodology

A research methodology exists in various forms. Depending upon their approach, whether centered around words, numbers, or both, methodologies are distinguished as qualitative, quantitative, or an amalgamation of both.

1. Qualitative research methodology

When a research methodology primarily focuses on words and textual data, then it is generally referred to as qualitative research methodology. This type is usually preferred among researchers when the aim and scope of the research are mainly theoretical and explanatory.

The instruments used are observations, interviews, and sample groups. You can use this methodology if you are trying to study human behavior or response in some situations. Generally, qualitative research methodology is widely used in sociology, psychology, and other related domains.

2. Quantitative research methodology

If your research is majorly centered on data, figures, and stats, then analyzing these numerical data is often referred to as quantitative research methodology. You can use quantitative research methodology if your research requires you to validate or justify the obtained results.

In quantitative methods, surveys, tests, experiments, and evaluations of current databases can be advantageously used as instruments If your research involves testing some hypothesis, then use this methodology.

3. Amalgam methodology

As the name suggests, the amalgam methodology uses both quantitative and qualitative approaches. This methodology is used when a part of the research requires you to verify the facts and figures, whereas the other part demands you to discover the theoretical and explanatory nature of the research question.

The instruments for the amalgam methodology require you to conduct interviews and surveys, including tests and experiments. The outcome of this methodology can be insightful and valuable as it provides precise test results in line with theoretical explanations and reasoning.

The amalgam method, makes your work both factual and rational at the same time.

Final words: How to decide which is the best research methodology?

If you have kept your sincerity and awareness intact with the aims and scope of research well enough, you must have got an idea of which research methodology suits your work best.

Before deciding which research methodology answers your research question, you must invest significant time in reading and doing your homework for that. Taking references that yield relevant results should be your first approach to establishing a research methodology.

Moreover, you should never refrain from exploring other options. Before setting your work in stone, you must try all the available options as it explains why the choice of research methodology that you finally make is more appropriate than the other available options.

You should always go for a quantitative research methodology if your research requires gathering large amounts of data, figures, and statistics. This research methodology will provide you with results if your research paper involves the validation of some hypothesis.

Whereas, if  you are looking for more explanations, reasons, opinions, and public perceptions around a theory, you must use qualitative research methodology.The choice of an appropriate research methodology ultimately depends on what you want to achieve through your research.

Frequently Asked Questions (FAQs) about Research Methodology

1. how to write a research methodology.

You can always provide a separate section for research methodology where you should specify details about the methods and instruments used during the research, discussions on result analysis, including insights into the background information, and conveying the research limitations.

2. What are the types of research methodology?

There generally exists four types of research methodology i.e.

• Observation
• Experimental
• Derivational

3. What is the true meaning of research methodology?

The set of techniques or procedures followed to discover and analyze the information gathered to validate or justify a research outcome is generally called Research Methodology.

4. Where lies the importance of research methodology?

Your research methodology directly reflects the validity of your research outcomes and how well-informed your research work is. Moreover, it can help future researchers cite or refer to your research if they plan to use a similar research methodology.

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APA Methods Section – How To Write It With Examples

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The APA methods section is a very important part of your academic paper, displaying how you conducted your research by providing a precise description of the methods and procedures you used for the study. This section ensures transparency, allowing other researchers to see exactly how you conducted your experiments. In APA style , the methods section usually includes subsections on participants, materials or measures, and procedures. This article discusses the APA methods section in detail.

Inhaltsverzeichnis

• 1 APA Methods Section – In a Nutshell
• 2 Definition: APA Methods Section
• 3 APA Methods Section: Structure
• 4 APA Methods Section: Participants
• 5 APA Methods Section: Materials
• 6 APA Methods Section: Procedure

APA Methods Section – In a Nutshell

• The APA methods section covers the participants, materials, and procedures.
• Under the ‘Participants’ heading of the APA methods section, you should state the relevant demographic characteristics of your participants.
• Accurately reporting the facts of the study can help other researchers determine how much the results can be generalized.

In what format are you currently required to submit your thesis?

Definition: APA Methods Section

The APA methods section describes the procedures you used to carry out your research and explains why particular processes were selected. It allows other researchers to replicate the study and make their own conclusions on the validity of the experiment.

APA Methods Section: Structure

• The main heading of the APA methods section should be written in bold and should be capitalized. It also has to be centered.
• All subheadings should be aligned to the left and must be boldfaced. You should select subheadings that are suitable for your essay, and the most commonly used include ‘Participants’, ‘Materials’, and ‘Procedure’.

Heading formats:

APA format has certain requirements for reporting different research designs. You should go through these guidelines to determine what you should mention for research using longitudinal designs , replication studies, and experimental designs .

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APA Methods Section: Participants

Under this subheading, you will have to report on the sample characteristics, the procedures used to collect samples, and the sample size selected.

Subject or Participant Characteristics

In academic studies, ‘participants’ refers to the people who take part in a study. If animals are used instead of human beings, the researcher can use the term ‘subjects’. In this subheading of the APA methods section, you have to describe the demographic characteristics of the participants, including their age, sex, race, ethnic group, education level, and gender identity. Depending on the nature of the study, other characteristics may be important. Some of these include:

• Education levels
• Language preference
• Immigration status

By describing the characteristics of the participants, readers will be able to determine how much the results can be generalized. Make sure you use bias-free language when writing this part of the APA methods section.

The study included 100 homosexual men and 100 homosexual women aged between 30 and 50 years from the city of London, UK.

Sampling Procedures

When selecting participants for your study, you will have to use certain sampling procedures. If the study could access all members of the population, you can say that you used random sampling methods. This section of the APA methods section should cover the percentage of respondents who participated in the research, and how they were chosen. You also need to state how participants were compensated and the ethical standard followed.

• Transgender male students from London were invited to participate in a study.
• Invites were sent to the students via email, social media posts, and posters in the schools.
• Each participant received $10 for the time spent in the study.
• The research obtained ethical approval before the participants were recruited.

Sample Size and Statistical Power

In this part of the APA methods section, you should give details on the sample size and statistical power you aimed at achieving. You should mention whether the final sample was the same as the intended sample. This section should show whether your research had enough statistical power to find any effects.

• The study aimed at a statistical power of 75% to detect an effect of 10% with an alpha of .05.
• 200 participants were required, and the study fulfilled these conditions.

APA Methods Section: Materials

Readers also need to know the materials you used for the study. This part of the APA methods section will give other researchers a good picture of the methods used to conduct the study.

Primary and secondary measures

Here, you should indicate the instruments used in the study, as well as the constructs they were meant to measure. Some of these are inventories, scales, tests, software, and hardware. Make sure you cover the following aspects:

• Reliability
• The Traumatic Stress Schedule (TSS) was used to measure the exposure to traumatic events.
• This 10-item chart requires participants to report lifelong exposure to traumatic stress.
• For example, they could indicate whether they suffered the traumatic death of a loved one.
• The Davidson Trauma Scale was also used to assess the symptoms of trauma.

Under this subheading of the APA methods section, you should also mention covariates or additional variables that can explain the outcomes.

Quality of measurements

You can mention the strategies you applied to ensure data integrity and reliability. These may include:

• Training the interviewers
• Establishing clear data nominalization procedures
• Rigorous data handling and analysis processes
• Having multiple people assess the data

If the data was subjectively coded, you should indicate the interrater reliability scores in the APA methods section.

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APA Methods Section: Procedure

This part of the APA methods section indicates the methods you used to carry out the research, process the data, and analyze the results.

Research Design and Data Collection Methods

Data collection is the systematic gathering of observations and measurements, and you have to describe all procedures used in this process. You can use supplementary materials to describe long and complicated data collection methods.

When reporting the research design, you should mention the framework of the study. This could be experimental, longitudinal, correlational, or descriptive. Additionally, you should mention whether you used a between-subjects design or within-subjects design .

In this part of the APA methods section, you should also mention whether any masking methods were used to hide condition assignments from the participants.

• Participants are told the research takes an hour covers their personal experiences in school.
• They were assured that the reports would be confidential and were asked to give consent.
• The participants were asked to fill in questionnaires .
• The control group was given an unrelated filler task, after which they filled a questionnaire.
• It was determined the experiences of homosexual and CIS-gendered students varied.

Data diagnostics

This part of the APA method section outlines the steps taken to process the data. It includes:

• Methods of identifying and controlling outliers
• Data transformation procedures
• Methods of compensating for missing values

Analytic strategies

This subheading of the APA methods section describes the analytic strategies used, but you shouldn’t mention the outcomes. The primary and secondary hypotheses use past studies or theoretical frameworks , while exploratory hypotheses focus on the data in the study.

We started by assessing the demographic differences between the two groups. We also performed an independent samples t-test on the test scores .

What are the parts of an APA methods section?

In this section, you should include the study participants, the methods used, and the procedures.

What is included in the APA methods section?

The methods section covers the participants or subject characteristics, the sampling procedures, the sample size, the measures used, the data collection methods, the research design, the data analysis strategy, and the data processing method.

Should I use the Oxford comma when writing the APA methods section?

Yes, the serial comma is required when writing the APA methods section.

Should I use the first person to write the APA methods section?

Yes, the APA language guidelines encourage researchers to use first-person pronouns when writing the methods section.

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How to Write a Methods Section for a Research Paper

A common piece of advice for authors preparing their first journal article for publication is to start with the methods section: just list everything that was done and go from there. While that might seem like a very practical approach to a first draft, if you do this without a clear outline and a story in mind, you can easily end up with journal manuscript sections that are not logically related to each other. 

Since the methods section constitutes the core of your paper, no matter when you write it, you need to use it to guide the reader carefully through your story from beginning to end without leaving questions unanswered. Missing or confusing details in this section will likely lead to early rejection of your manuscript or unnecessary back-and-forth with the reviewers until eventual publication. Here, you will find some useful tips on how to make your methods section the logical foundation of your research paper.

Not just a list of experiments and methods

While your introduction section provides the reader with the necessary background to understand your rationale and research question (and, depending on journal format and your personal preference, might already summarize the results), the methods section explains what exactly you did and how you did it. The point of this section is not to list all the boring details just for the sake of completeness. The purpose of the methods sections is to enable the reader to replicate exactly what you did, verify or corroborate your results, or maybe find that there are factors you did not consider or that are more relevant than expected. 

To make this section as easy to read as possible, you must clearly connect it to the information you provide in the introduction section before and the results section after, it needs to have a clear structure (chronologically or according to topics), and you need to present your results according to the same structure or topics later in the manuscript. There are also official guidelines and journal instructions to follow and ethical issues to avoid to ensure that your manuscript can quickly reach the publication stage.

Table of Contents:

• General Methods Structure: What is Your Story? 
• What Methods Should You Report (and Leave Out)? 
• Details Frequently Missing from the Methods Section

More Journal Guidelines to Consider 

• Accurate and Appropriate Language in the Methods

General Methods Section Structure: What Is Your Story? 

You might have conducted a number of experiments, maybe also a pilot before the main study to determine some specific factors or a follow-up experiment to clarify unclear details later in the process. Throwing all of these into your methods section, however, might not help the reader understand how everything is connected and how useful and appropriate your methodological approach is to investigate your specific research question. You therefore need to first come up with a clear outline and decide what to report and how to present that to the reader.

The first (and very important) decision to make is whether you present your experiments chronologically (e.g., Experiment 1, Experiment 2, Experiment 3… ), and guide the reader through every step of the process, or if you organize everything according to subtopics (e.g., Behavioral measures, Structural imaging markers, Functional imaging markers… ). In both cases, you need to use clear subheaders for the different subsections of your methods, and, very importantly, follow the same structure or focus on the same topics/measures in the results section so that the reader can easily follow along (see the two examples below).

If you are in doubt which way of organizing your experiments is better for your study, just ask yourself the following questions:

• Does the reader need to know the timeline of your study? 
• Is it relevant that one experiment was conducted first, because the outcome of this experiment determined the stimuli or factors that went into the next?
• Did the results of your first experiment leave important questions open that you addressed in an additional experiment (that was maybe not planned initially)?
• Is the answer to all of these questions “no”? Then organizing your methods section according to topics of interest might be the more logical choice.

If you think your timeline, protocol, or setup might be confusing or difficult for the reader to grasp, consider adding a graphic, flow diagram, decision tree, or table as a visual aid.

What Methods Should You Report (and Leave Out)?

The answer to this question is quite simple–you need to report everything that another researcher needs to know to be able to replicate your study. Just imagine yourself reading your methods section in the future and trying to set up the same experiments again without prior knowledge. You would probably need to ask questions such as:

• Where did you conduct your experiments (e.g., in what kind of room, under what lighting or temperature conditions, if those are relevant)? 
• What devices did you use? Are there specific settings to report?
• What specific software (and version of that software) did you use?
• How did you find and select your participants?
• How did you assign participants into groups?  
• Did you exclude participants from the analysis? Why and how?
• Where did your reagents or antibodies come from? Can you provide a Research Resource Identifier (RRID) ?
• Did you make your stimuli yourself or did you get them from somewhere?
• Are the stimuli you used available for other researchers?
• What kind of questionnaires did you use? Have they been validated?
• How did you analyze your data? What level of significance did you use?
• Were there any technical issues and did you have to adjust protocols?

Note that for every experimental detail you provide, you need to tell the reader (briefly) why you used this type of stimulus/this group of participants/these specific amounts of reagents. If there is earlier published research reporting the same methods, cite those studies. If you did pilot experiments to determine those details, describe the procedures and the outcomes of these experiments. If you made assumptions about the suitability of something based on the literature and common practice at your institution, then explain that to the reader.

In a nutshell, established methods need to be cited, and new methods need to be clearly described and briefly justified. However, if the fact that you use a new approach or a method that is not traditionally used for the data or phenomenon you study is one of the main points of your study (and maybe already reflected in the title of your article), then you need to explain your rationale for doing so in the introduction already and discuss it in more detail in the discussion section .

Note that you also need to explain your statistical analyses at the end of your methods section. You present the results of these analyses later, in the results section of your paper, but you need to show the reader in the methods section already that your approach is either well-established or valid, even if it is new or unusual. 

When it comes to the question of what details you should leave out, the answer is equally simple ‒ everything that you would not need to replicate your study in the future. If the educational background of your participants is listed in your institutional database but is not relevant to your study outcome, then don’t include that. Other things you should not include in the methods section:

• Background information that you already presented in the introduction section.
• In-depth comparisons of different methods ‒ these belong in the discussion section.
• Results, unless you summarize outcomes of pilot experiments that helped you determine factors for your main experiment.

Also, make sure your subheadings are as clear as possible, suit the structure you chose for your methods section, and are in line with the target journal guidelines. If you studied a disease intervention in human participants, then your methods section could look similar to this:

Since the main point of interest here are your patient-centered outcome variables, you would center your results section on these as well and choose your headers accordingly (e.g., Patient characteristics, Baseline evaluation, Outcome variable 1, Outcome variable 2, Drop-out rate ). 

If, instead, you did a series of visual experiments investigating the perception of faces including a pilot experiment to create the stimuli for your actual study, you would need to structure your methods section in a very different way, maybe like this:

Since here the analysis and outcome of the pilot experiment are already described in the methods section (as the basis for the main experimental setup and procedure), you do not have to mention it again in the results section. Instead, you could choose the two main experiments to structure your results section ( Discrimination and classification, Familiarization and adaptation ), or divide the results into all your test measures and/or potential interactions you described in the methods section (e.g., Discrimination performance, Classification performance, Adaptation aftereffects, Correlation analysis ).

Details Commonly Missing from the Methods Section

Manufacturer information.

For laboratory or technical equipment, you need to provide the model, name of the manufacturer, and company’s location. The usual format for these details is the product name (company name, city, state) for US-based manufacturers and the product name (company name, city/town, country) for companies outside the US.

Sample size and power estimation

Power and sample size estimations are measures for how many patients or participants are needed in a study in order to detect statistical significance and draw meaningful conclusions from the results. Outside of the medical field, studies are sometimes still conducted with a “the more the better” approach in mind, but since many journals now ask for those details, it is better to not skip this important step.

Ethical guidelines and approval

In addition to describing what you did, you also need to assure the editor and reviewers that your methods and protocols followed all relevant ethical standards and guidelines. This includes applying for approval at your local or national ethics committee, providing the name or location of that committee as well as the approval reference number you received, and, if you studied human participants, a statement that participants were informed about all relevant experimental details in advance and signed consent forms before the start of the study. For animal studies, you usually need to provide a statement that all procedures included in your research were in line with the Declaration of Helsinki. Make sure you check the target journal guidelines carefully, as these statements sometimes need to be placed at the end of the main article text rather than in the method section.

Structure & word limitations

While many journals simply follow the usual style guidelines (e.g., APA for the social sciences and psychology, AMA for medical research) and let you choose the headers of your method section according to your preferred structure and focus, some have precise guidelines and strict limitations, for example, on manuscript length and the maximum number of subsections or header levels. Make sure you read the instructions of your target journal carefully and restructure your method section if necessary before submission. If the journal does not give you enough space to include all the details that you deem necessary, then you can usually submit additional details as “supplemental” files and refer to those in the main text where necessary.

Standardized checklists

In addition to ethical guidelines and approval, journals also often ask you to submit one of the official standardized checklists for different study types to ensure all essential details are included in your manuscript. For example, there are checklists for randomized clinical trials, CONSORT (Consolidated Standards of Reporting Trials) , cohort, case-control, cross‐sectional studies, STROBE (STrengthening the Reporting of OBservational studies in Epidemiology ), diagnostic accuracy, STARD (STAndards for the Reporting of Diagnostic accuracy studies) , systematic reviews and meta‐analyses PRISMA (Preferred Reporting Items for Systematic reviews and Meta‐Analyses) , and Case reports, CARE (CAse REport) .

Make sure you check if the manuscript uses a single- or double-blind review procedure , and delete all information that might allow a reviewer to guess where the authors are located from the manuscript text if necessary. This means that your method section cannot list the name and location of your institution, the names of researchers who conducted specific tests, or the name of your institutional ethics committee.  

Accurate and Appropriate Language in the Methods Section

Like all sections of your research paper, your method section needs to be written in an academic tone . That means it should be formal, vague expressions and colloquial language need to be avoided, and you need to correctly cite all your sources. If you describe human participants in your method section then you should be especially careful about your choice of words. For example, “participants” sounds more respectful than “subjects,” and patient-first language, that is, “patients with cancer,” is considered more appropriate than “cancer patients” by many journals.

Passive voice is often considered the standard for research papers, but it is completely fine to mix passive and active voice, even in the method section, to make your text as clear and concise as possible. Use the simple past tense to describe what you did, and the present tense when you refer to diagrams or tables. Have a look at this article if you need more general input on which verb tenses to use in a research paper . 

Lastly, make sure you label all the standard tests and questionnaires you use correctly (look up the original publication when in doubt) and spell genes and proteins according to the common databases for the species you studied, such as the HUGO Gene Nomenclature Committee database for human studies .  

Visit Wordvice AI’s AI Text Editor to receive a free grammar check and English editing services (including manuscript editing , paper editing , and dissertation editing ) before submitting your manuscript to journal editors.

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Need editing and proofreading services, research methodology guide: writing tips, types, & examples.

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No dissertation or research paper is complete without the research methodology section. Since this is the chapter where you explain how you carried out your research, this is where all the meat is! Here’s where you clearly lay out the steps you have taken to test your hypothesis or research problem.

Through this blog, we’ll unravel the complexities and meaning of research methodology in academic writing , from its fundamental principles and ethics to the diverse types of research methodology in use today. Alongside offering research methodology examples, we aim to guide you on how to write research methodology, ensuring your research endeavors are both impactful and impeccably grounded!

Ensure your research methodology is foolproof. Learn more

Let’s first take a closer look at a simple research methodology definition:

Defining what is research methodology

Research methodology is the set of procedures and techniques used to collect, analyze, and interpret data to understand and solve a research problem. Methodology in research not only includes the design and methods but also the basic principles that guide the choice of specific methods.

Grasping the concept of methodology in research is essential for students and scholars, as it demonstrates the thorough and structured method used to explore a hypothesis or research question. Understanding the definition of methodology in research aids in identifying the methods used to collect data. Be it through any type of research method approach, ensuring adherence to the proper research paper format is crucial.

Now let’s explore some research methodology types:

Types of research methodology

1. qualitative research methodology.

Qualitative research methodology is aimed at understanding concepts, thoughts, or experiences. This approach is descriptive and is often utilized to gather in-depth insights into people’s attitudes, behaviors, or cultures. Qualitative research methodology involves methods like interviews, focus groups, and observation. The strength of this methodology lies in its ability to provide contextual richness.

2. Quantitative research methodology

Quantitative research methodology, on the other hand, is focused on quantifying the problem by generating numerical data or data that can be transformed into usable statistics. It uses measurable data to formulate facts and uncover patterns in research. Quantitative research methodology typically involves surveys, experiments, or statistical analysis. This methodology is appreciated for its ability to produce objective results that are generalizable to a larger population.

3. Mixed-Methods research methodology

Mixed-methods research combines both qualitative and quantitative research methodologies to provide a more comprehensive understanding of the research problem. This approach leverages the strengths of both methodologies to provide a deeper insight into the research question of a research paper .

Research methodology vs. research methods

The research methodology or design is the overall strategy and rationale that you used to carry out the research. Whereas, research methods are the specific tools and processes you use to gather and understand the data you need to test your hypothesis.

Research methodology examples and application

To further understand research methodology, let’s explore some examples of research methodology:

a. Qualitative research methodology example: A study exploring the impact of author branding on author popularity might utilize in-depth interviews to gather personal experiences and perspectives.

b. Quantitative research methodology example: A research project investigating the effects of a book promotion technique on book sales could employ a statistical analysis of profit margins and sales before and after the implementation of the method.

c. Mixed-Methods research methodology example: A study examining the relationship between social media use and academic performance might combine both qualitative and quantitative approaches. It could include surveys to quantitatively assess the frequency of social media usage and its correlation with grades, alongside focus groups or interviews to qualitatively explore students’ perceptions and experiences regarding how social media affects their study habits and academic engagement.

These examples highlight the meaning of methodology in research and how it guides the research process, from data collection to analysis, ensuring the study’s objectives are met efficiently.

Importance of methodology in research papers

When it comes to writing your study, the methodology in research papers or a dissertation plays a pivotal role. A well-crafted methodology section of a research paper or thesis not only enhances the credibility of your research but also provides a roadmap for others to replicate or build upon your work.

How to structure the research methods chapter

Wondering how to write the research methodology section? Follow these steps to create a strong methods chapter:

Step 1: Explain your research methodology

At the start of a research paper , you would have provided the background of your research and stated your hypothesis or research problem. In this section, you will elaborate on your research strategy. 

Begin by restating your research question and proceed to explain what type of research you opted for to test it. Depending on your research, here are some questions you can consider: 

a. Did you use qualitative or quantitative data to test the hypothesis? 

b. Did you perform an experiment where you collected data or are you writing a dissertation that is descriptive/theoretical without data collection? 

c. Did you use primary data that you collected or analyze secondary research data or existing data as part of your study? 

These questions will help you establish the rationale for your study on a broader level, which you will follow by elaborating on the specific methods you used to collect and understand your data. 

Step 2: Explain the methods you used to test your hypothesis 

Now that you have told your reader what type of research you’ve undertaken for the dissertation, it’s time to dig into specifics. State what specific methods you used and explain the conditions and variables involved. Explain what the theoretical framework behind the method was, what samples you used for testing it, and what tools and materials you used to collect the data. 

Step 3: Explain how you analyzed the results

Once you have explained the data collection process, explain how you analyzed and studied the data. Here, your focus is simply to explain the methods of analysis rather than the results of the study. 

Here are some questions you can answer at this stage: 

a. What tools or software did you use to analyze your results? 

b. What parameters or variables did you consider while understanding and studying the data you’ve collected? 

c. Was your analysis based on a theoretical framework? 

Your mode of analysis will change depending on whether you used a quantitative or qualitative research methodology in your study. If you’re working within the hard sciences or physical sciences, you are likely to use a quantitative research methodology (relying on numbers and hard data). If you’re doing a qualitative study, in the social sciences or humanities, your analysis may rely on understanding language and socio-political contexts around your topic. This is why it’s important to establish what kind of study you’re undertaking at the onset. 

Step 4: Defend your choice of methodology 

Now that you have gone through your research process in detail, you’ll also have to make a case for it. Justify your choice of methodology and methods, explaining why it is the best choice for your research question. This is especially important if you have chosen an unconventional approach or you’ve simply chosen to study an existing research problem from a different perspective. Compare it with other methodologies, especially ones attempted by previous researchers, and discuss what contributions using your methodology makes.  

Step 5: Discuss the obstacles you encountered and how you overcame them

No matter how thorough a methodology is, it doesn’t come without its hurdles. This is a natural part of scientific research that is important to document so that your peers and future researchers are aware of it. Writing in a research paper about this aspect of your research process also tells your evaluator that you have actively worked to overcome the pitfalls that came your way and you have refined the research process. 

Tips to write an effective methodology chapter

1. Remember who you are writing for. Keeping sight of the reader/evaluator will help you know what to elaborate on and what information they are already likely to have. You’re condensing months’ work of research in just a few pages, so you should omit basic definitions and information about general phenomena people already know.

2. Do not give an overly elaborate explanation of every single condition in your study. 

3. Skip details and findings irrelevant to the results.

4. Cite references that back your claim and choice of methodology. 

5. Consistently emphasize the relationship between your research question and the methodology you adopted to study it. 

To sum it up, what is methodology in research? It’s the blueprint of your research, essential for ensuring that your study is systematic, rigorous, and credible. Whether your focus is on qualitative research methodology, quantitative research methodology, or a combination of both, understanding and clearly defining your methodology is key to the success of your research.

Once you write the research methodology and complete writing the entire research paper, the next step is to edit your paper. As experts in research paper editing and proofreading services , we’d love to help you perfect your paper!

Here are some other articles that you might find useful: 

• Essential Research Tips for Essay Writing
• How to Write a Lab Report: Examples from Academic Editors
• The Essential Types of Editing Every Writer Needs to Know
• Editing and Proofreading Academic Papers: A Short Guide
• The Top 10 Editing and Proofreading Services of 2023

Frequently Asked Questions

What does research methodology mean, what types of research methodologies are there, what is qualitative research methodology, how to determine sample size in research methodology, what is action research methodology.

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This is very simplified and direct. Very helpful to understand the research methodology section of a dissertation

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Research Methodology Example

Detailed Walkthrough + Free Methodology Chapter Template

If you’re working on a dissertation or thesis and are looking for an example of a research methodology chapter , you’ve come to the right place.

In this video, we walk you through a research methodology from a dissertation that earned full distinction , step by step. We start off by discussing the core components of a research methodology by unpacking our free methodology chapter template . We then progress to the sample research methodology to show how these concepts are applied in an actual dissertation, thesis or research project.

If you’re currently working on your research methodology chapter, you may also find the following resources useful:

• Research methodology 101 : an introductory video discussing what a methodology is and the role it plays within a dissertation
• Research design 101 : an overview of the most common research designs for both qualitative and quantitative studies
• Variables 101 : an introductory video covering the different types of variables that exist within research.
• Sampling 101 : an overview of the main sampling methods
• Methodology tips : a video discussion covering various tips to help you write a high-quality methodology chapter
• Private coaching : Get hands-on help with your research methodology

PS – If you’re working on a dissertation, be sure to also check out our collection of dissertation and thesis examples here .

FAQ: Research Methodology Example

Research methodology example: frequently asked questions, is the sample research methodology real.

Yes. The chapter example is an extract from a Master’s-level dissertation for an MBA program. A few minor edits have been made to protect the privacy of the sponsoring organisation, but these have no material impact on the research methodology.

Can I replicate this methodology for my dissertation?

As we discuss in the video, every research methodology will be different, depending on the research aims, objectives and research questions. Therefore, you’ll need to tailor your literature review to suit your specific context.

You can learn more about the basics of writing a research methodology chapter here .

Where can I find more examples of research methodologies?

The best place to find more examples of methodology chapters would be within dissertation/thesis databases. These databases include dissertations, theses and research projects that have successfully passed the assessment criteria for the respective university, meaning that you have at least some sort of quality assurance.

The Open Access Thesis Database (OATD) is a good starting point.

How do I get the research methodology chapter template?

You can access our free methodology chapter template here .

Is the methodology template really free?

Yes. There is no cost for the template and you are free to use it as you wish.

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Note: The APA Publication Manual, 7 th Edition specifies different formatting conventions for student  and  professional  papers (i.e., papers written for credit in a course and papers intended for scholarly publication). These differences mostly extend to the title page and running head. Crucially, citation practices do not differ between the two styles of paper.

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Note: For accessibility purposes, we have used "Track Changes" to make comments along the margins of these samples. Those authored by [AF] denote explanations of formatting and [AWC] denote directions for writing and citing in APA 7. 

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This paper should be used only as an example of a research paper write-up. Horizontal rules signify the top and bottom edges of pages. For sample references which are not included with this paper, you should consult the Publication Manual of the American Psychological Association, 4th Edition .

This paper is provided only to give you an idea of what a research paper might look like. You are not allowed to copy any of the text of this paper in writing your own report.

Because word processor copies of papers don’t translate well into web pages, you should note that an actual paper should be formatted according to the formatting rules for your context. Note especially that there are three formatting rules you will see in this sample paper which you should NOT follow. First, except for the title page, the running header should appear in the upper right corner of every page with the page number below it. Second, paragraphs and text should be double spaced and the start of each paragraph should be indented. Third, horizontal lines are used to indicate a mandatory page break and should not be used in your paper.

The Effects of a Supported Employment Program on Psychosocial Indicators for Persons with Severe Mental Illness William M.K. Trochim Cornell University

Running Head: SUPPORTED EMPLOYMENT

This paper describes the psychosocial effects of a program of supported employment (SE) for persons with severe mental illness. The SE program involves extended individualized supported employment for clients through a Mobile Job Support Worker (MJSW) who maintains contact with the client after job placement and supports the client in a variety of ways. A 50% simple random sample was taken of all persons who entered the Thresholds Agency between 3/1/93 and 2/28/95 and who met study criteria. The resulting 484 cases were randomly assigned to either the SE condition (treatment group) or the usual protocol (control group) which consisted of life skills training and employment in an in-house sheltered workshop setting. All participants were measured at intake and at 3 months after beginning employment, on two measures of psychological functioning (the BPRS and GAS) and two measures of self esteem (RSE and ESE). Significant treatment effects were found on all four measures, but they were in the opposite direction from what was hypothesized. Instead of functioning better and having more self esteem, persons in SE had lower functioning levels and lower self esteem. The most likely explanation is that people who work in low-paying service jobs in real world settings generally do not like them and experience significant job stress, whether they have severe mental illness or not. The implications for theory in psychosocial rehabilitation are considered.

The Effects of a Supported Employment Program on Psychosocial Indicators for Persons with Severe Mental Illness

Over the past quarter century a shift has occurred from traditional institution-based models of care for persons with severe mental illness (SMI) to more individualized community-based treatments. Along with this, there has been a significant shift in thought about the potential for persons with SMI to be “rehabilitated” toward lifestyles that more closely approximate those of persons without such illness. A central issue is the ability of a person to hold a regular full-time job for a sustained period of time. There have been several attempts to develop novel and radical models for program interventions designed to assist persons with SMI to sustain full-time employment while living in the community. The most promising of these have emerged from the tradition of psychiatric rehabilitation with its emphases on individual consumer goal setting, skills training, job preparation and employment support (Cook, Jonikas and Solomon, 1992). These are relatively new and field evaluations are rare or have only recently been initiated (Cook and Razzano, 1992; Cook, 1992). Most of the early attempts to evaluate such programs have naturally focused almost exclusively on employment outcomes. However, theory suggests that sustained employment and living in the community may have important therapeutic benefits in addition to the obvious economic ones. To date, there have been no formal studies of the effects of psychiatric rehabilitation programs on key illness-related outcomes. To address this issue, this study seeks to examine the effects of a new program of supported employment on psychosocial outcomes for persons with SMI.

Over the past several decades, the theory of vocational rehabilitation has experienced two major stages of evolution. Original models of vocational rehabilitation were based on the idea of sheltered workshop employment. Clients were paid a piece rate and worked only with other individuals who were disabled. Sheltered workshops tended to be “end points” for persons with severe and profound mental retardation since few ever moved from sheltered to competitive employment (Woest, Klein & Atkins, 1986). Controlled studies of sheltered workshop performance of persons with mental illness suggested only minimal success (Griffiths, 1974) and other research indicated that persons with mental illness earned lower wages, presented more behavior problems, and showed poorer workshop attendance than workers with other disabilities (Whitehead, 1977; Ciardiello, 1981).

In the 1980s, a new model of services called Supported Employment (SE) was proposed as less expensive and more normalizing for persons undergoing rehabilitation (Wehman, 1985). The SE model emphasizes first locating a job in an integrated setting for minimum wage or above, and then placing the person on the job and providing the training and support services needed to remain employed (Wehman, 1985). Services such as individualized job development, one-on-one job coaching, advocacy with co-workers and employers, and “fading” support were found to be effective in maintaining employment for individuals with severe and profound mental retardation (Revell, Wehman & Arnold, 1984). The idea that this model could be generalized to persons with all types of severe disabilities, including severe mental illness, became commonly accepted (Chadsey-Rusch & Rusch, 1986).

One of the more notable SE programs was developed at Thresholds, the site for the present study, which created a new staff position called the mobile job support worker (MJSW) and removed the common six month time limit for many placements. MJSWs provide ongoing, mobile support and intervention at or near the work site, even for jobs with high degrees of independence (Cook & Hoffschmidt, 1993). Time limits for many placements were removed so that clients could stay on as permanent employees if they and their employers wished. The suspension of time limits on job placements, along with MJSW support, became the basis of SE services delivered at Thresholds.

There are two key psychosocial outcome constructs of interest in this study. The first is the overall psychological functioning of the person with SMI. This would include the specification of severity of cognitive and affective symptomotology as well as the overall level of psychological functioning. The second is the level of self-reported self esteem of the person. This was measured both generally and with specific reference to employment.

The key hypothesis of this study is:

• HO: A program of supported employment will result in either no change or negative effects on psychological functioning and self esteem.

which will be tested against the alternative:

• HA: A program of supported employment will lead to positive effects on psychological functioning and self esteem.

The population of interest for this study is all adults with SMI residing in the U.S. in the early 1990s. The population that is accessible to this study consists of all persons who were clients of the Thresholds Agency in Chicago, Illinois between the dates of March 1, 1993 and February 28, 1995 who met the following criteria: 1) a history of severe mental illness (e.g. either schizophrenia, severe depression or manic-depression); 2) a willingness to achieve paid employment; 3) their primary diagnosis must not include chronic alcoholism or hard drug use; and 4) they must be 18 years of age or older. The sampling frame was obtained from records of the agency. Because of the large number of clients who pass through the agency each year (e.g. approximately 500 who meet the criteria) a simple random sample of 50% was chosen for inclusion in the study. This resulted in a sample size of 484 persons over the two-year course of the study.

On average, study participants were 30 years old and high school graduates (average education level = 13 years). The majority of participants (70%) were male. Most had never married (85%), few (2%) were currently married, and the remainder had been formerly married (13%). Just over half (51%) are African American, with the remainder Caucasian (43%) or other minority groups (6%). In terms of illness history, the members in the sample averaged 4 prior psychiatric hospitalizations and spent a lifetime average of 9 months as patients in psychiatric hospitals. The primary diagnoses were schizophrenia (42%) and severe chronic depression (37%). Participants had spent an average of almost two and one-half years (29 months) at the longest job they ever held.

While the study sample cannot be considered representative of the original population of interest, generalizability was not a primary goal – the major purpose of this study was to determine whether a specific SE program could work in an accessible context. Any effects of SE evident in this study can be generalized to urban psychiatric agencies that are similar to Thresholds, have a similar clientele, and implement a similar program.

All but one of the measures used in this study are well-known instruments in the research literature on psychosocial functioning. All of the instruments were administered as part of a structured interview that an evaluation social worker had with study participants at regular intervals.

Two measures of psychological functioning were used. The Brief Psychiatric Rating Scale (BPRS)(Overall and Gorham, 1962) is an 18-item scale that measures perceived severity of symptoms ranging from “somatic concern” and “anxiety” to “depressive mood” and “disorientation.” Ratings are given on a 0-to-6 Likert-type response scale where 0=“not present” and 6=“extremely severe” and the scale score is simply the sum of the 18 items. The Global Assessment Scale (GAS)(Endicott et al, 1976) is a single 1-to-100 rating on a scale where each ten-point increment has a detailed description of functioning (higher scores indicate better functioning). For instance, one would give a rating between 91-100 if the person showed “no symptoms, superior functioning…” and a value between 1-10 if the person “needs constant supervision…”

Two measures of self esteem were used. The first is the Rosenberg Self Esteem (RSE) Scale (Rosenberg, 1965), a 10-item scale rated on a 6-point response format where 1=“strongly disagree” and 6=“strongly agree” and there is no neutral point. The total score is simply the sum across the ten items, with five of the items being reversals. The second measure was developed explicitly for this study and was designed to measure the Employment Self Esteem (ESE) of a person with SMI. This is a 10-item scale that uses a 4-point response format where 1=“strongly disagree” and 4=“strongly agree” and there is no neutral point. The final ten items were selected from a pool of 97 original candidate items, based upon high item-total score correlations and a judgment of face validity by a panel of three psychologists. This instrument was deliberately kept simple – a shorter response scale and no reversal items – because of the difficulties associated with measuring a population with SMI. The entire instrument is provided in Appendix A.

All four of the measures evidenced strong reliability and validity. Internal consistency reliability estimates using Cronbach’s alpha ranged from .76 for ESE to .88 for SE. Test-retest reliabilities were nearly as high, ranging from .72 for ESE to .83 for the BPRS. Convergent validity was evidenced by the correlations within construct. For the two psychological functioning scales the correlation was .68 while for the self esteem measures it was somewhat lower at .57. Discriminant validity was examined by looking at the cross-construct correlations which ranged from .18 (BPRS-ESE) to .41 (GAS-SE).

A pretest-posttest two-group randomized experimental design was used in this study. In notational form, the design can be depicted as:

• R = the groups were randomly assigned
• O = the four measures (i.e. BPRS, GAS, RSE, and ESE)
• X = supported employment

The comparison group received the standard Thresholds protocol which emphasized in-house training in life skills and employment in an in-house sheltered workshop. All participants were measured at intake (pretest) and at three months after intake (posttest).

This type of randomized experimental design is generally strong in internal validity. It rules out threats of history, maturation, testing, instrumentation, mortality and selection interactions. Its primary weaknesses are in the potential for treatment-related mortality (i.e. a type of selection-mortality) and for problems that result from the reactions of participants and administrators to knowledge of the varying experimental conditions. In this study, the drop-out rate was 4% (N=9) for the control group and 5% (N=13) in the treatment group. Because these rates are low and are approximately equal in each group, it is not plausible that there is differential mortality. There is a possibility that there were some deleterious effects due to participant knowledge of the other group’s existence (e.g. compensatory rivalry, resentful demoralization). Staff were debriefed at several points throughout the study and were explicitly asked about such issues. There were no reports of any apparent negative feelings from the participants in this regard. Nor is it plausible that staff might have equalized conditions between the two groups. Staff were given extensive training and were monitored throughout the course of the study. Overall, this study can be considered strong with respect to internal validity.

Between 3/1/93 and 2/28/95 each person admitted to Thresholds who met the study inclusion criteria was immediately assigned a random number that gave them a 50/50 chance of being selected into the study sample. For those selected, the purpose of the study was explained, including the nature of the two treatments, and the need for and use of random assignment. Participants were assured confidentiality and were given an opportunity to decline to participate in the study. Only 7 people (out of 491) refused to participate. At intake, each selected sample member was assigned a random number giving them a 50/50 chance of being assigned to either the Supported Employment condition or the standard in-agency sheltered workshop. In addition, all study participants were given the four measures at intake.

All participants spent the initial two weeks in the program in training and orientation. This consisted of life skill training (e.g. handling money, getting around, cooking and nutrition) and job preparation (employee roles, coping strategies). At the end of that period, each participant was assigned to a job site – at the agency sheltered workshop for those in the control condition, and to an outside employer if in the Supported Employment group. Control participants were expected to work full-time at the sheltered workshop for a three-month period, at which point they were posttested and given an opportunity to obtain outside employment (either Supported Employment or not). The Supported Employment participants were each assigned a case worker – called a Mobile Job Support Worker (MJSW) – who met with the person at the job site two times per week for an hour each time. The MJSW could provide any support or assistance deemed necessary to help the person cope with job stress, including counseling or working beside the person for short periods of time. In addition, the MJSW was always accessible by cellular telephone, and could be called by the participant or the employer at any time. At the end of three months, each participant was post-tested and given the option of staying with their current job (with or without Supported Employment) or moving to the sheltered workshop.

There were 484 participants in the final sample for this study, 242 in each treatment. There were 9 drop-outs from the control group and 13 from the treatment group, leaving a total of 233 and 229 in each group respectively from whom both pretest and posttest were obtained. Due to unexpected difficulties in coping with job stress, 19 Supported Employment participants had to be transferred into the sheltered workshop prior to the posttest. In all 19 cases, no one was transferred prior to week 6 of employment, and 15 were transferred after week 8. In all analyses, these cases were included with the Supported Employment group (intent-to-treat analysis) yielding treatment effect estimates that are likely to be conservative.

The major results for the four outcome measures are shown in Figure 1.

Insert Figure 1 about here

It is immediately apparent that in all four cases the null hypothesis has to be accepted – contrary to expectations, Supported Employment cases did significantly worse on all four outcomes than did control participants.

The mean gains, standard deviations, sample sizes and t-values (t-test for differences in average gain) are shown for the four outcome measures in Table 1.

Insert Table 1 about here

The results in the table confirm the impressions in the figures. Note that all t-values are negative except for the BPRS where high scores indicate greater severity of illness. For all four outcomes, the t-values were statistically significant (p<.05).

Conclusions

The results of this study were clearly contrary to initial expectations. The alternative hypothesis suggested that SE participants would show improved psychological functioning and self esteem after three months of employment. Exactly the reverse happened – SE participants showed significantly worse psychological functioning and self esteem.

There are two major possible explanations for this outcome pattern. First, it seems reasonable that there might be a delayed positive or “boomerang” effect of employment outside of a sheltered setting. SE cases may have to go through an initial difficult period of adjustment (longer than three months) before positive effects become apparent. This “you have to get worse before you get better” theory is commonly held in other treatment-contexts like drug addiction and alcoholism. But a second explanation seems more plausible – that people working full-time jobs in real-world settings are almost certainly going to be under greater stress and experience more negative outcomes than those who work in the relatively safe confines of an in-agency sheltered workshop. Put more succinctly, the lesson here might very well be that work is hard. Sheltered workshops are generally very nurturing work environments where virtually all employees share similar illness histories and where expectations about productivity are relatively low. In contrast, getting a job at a local hamburger shop or as a shipping clerk puts the person in contact with co-workers who may not be sympathetic to their histories or forgiving with respect to low productivity. This second explanation seems even more plausible in the wake of informal debriefing sessions held as focus groups with the staff and selected research participants. It was clear in the discussion that SE persons experienced significantly higher job stress levels and more negative consequences. However, most of them also felt that the experience was a good one overall and that even their “normal” co-workers “hated their jobs” most of the time.

One lesson we might take from this study is that much of our contemporary theory in psychiatric rehabilitation is naive at best and, in some cases, may be seriously misleading. Theory led us to believe that outside work was a “good” thing that would naturally lead to “good” outcomes like increased psychological functioning and self esteem. But for most people (SMI or not) work is at best tolerable, especially for the types of low-paying service jobs available to study participants. While people with SMI may not function as well or have high self esteem, we should balance this with the desire they may have to “be like other people” including struggling with the vagaries of life and work that others struggle with.

Future research in this are needs to address the theoretical assumptions about employment outcomes for persons with SMI. It is especially important that attempts to replicate this study also try to measure how SE participants feel about the decision to work, even if traditional outcome indicators suffer. It may very well be that negative outcomes on traditional indicators can be associated with a “positive” impact for the participants and for the society as a whole.

Chadsey-Rusch, J. and Rusch, F.R. (1986). The ecology of the workplace. In J. Chadsey-Rusch, C. Haney-Maxwell, L. A. Phelps and F. R. Rusch (Eds.), School-to-Work Transition Issues and Models. (pp. 59-94), Champaign IL: Transition Institute at Illinois.

Ciardiello, J.A. (1981). Job placement success of schizophrenic clients in sheltered workshop programs. Vocational Evaluation and Work Adjustment Bulletin, 14, 125-128, 140.

Cook, J.A. (1992). Job ending among youth and adults with severe mental illness. Journal of Mental Health Administration, 19(2), 158-169.

Cook, J.A. & Hoffschmidt, S. (1993). Psychosocial rehabilitation programming: A comprehensive model for the 1990’s. In R.W. Flexer and P. Solomon (Eds.), Social and Community Support for People with Severe Mental Disabilities: Service Integration in Rehabilitation and Mental Health. Andover, MA: Andover Publishing.

Cook, J.A., Jonikas, J., & Solomon, M. (1992). Models of vocational rehabilitation for youth and adults with severe mental illness. American Rehabilitation, 18, 3, 6-32.

Cook, J.A. & Razzano, L. (1992). Natural vocational supports for persons with severe mental illness: Thresholds Supported Competitive Employment Program, in L. Stein (ed.), New Directions for Mental Health Services, San Francisco: Jossey-Bass, 56, 23-41.

Endicott, J.R., Spitzer, J.L. Fleiss, J.L. and Cohen, J. (1976). The Global Assessment Scale: A procedure for measuring overall severity of psychiatric disturbance. Archives of General Psychiatry, 33, 766-771.

Griffiths, R.D. (1974). Rehabilitation of chronic psychotic patients. Psychological Medicine, 4, 316-325.

Overall, J. E. and Gorham, D. R. (1962). The Brief Psychiatric Rating Scale. Psychological Reports, 10, 799-812.

Rosenberg, M. (1965). Society and Adolescent Self Image. Princeton, NJ, Princeton University Press.

Wehman, P. (1985). Supported competitive employment for persons with severe disabilities. In P. McCarthy, J. Everson, S. Monn & M. Barcus (Eds.), School-to-Work Transition for Youth with Severe Disabilities, (pp. 167-182), Richmond VA: Virginia Commonwealth University.

Whitehead, C.W. (1977). Sheltered Workshop Study: A Nationwide Report on Sheltered Workshops and their Employment of Handicapped Individuals. (Workshop Survey, Volume 1), U.S. Department of Labor Service Publication. Washington, DC: U.S. Government Printing Office.

Woest, J., Klein, M. and Atkins, B.J. (1986). An overview of supported employment strategies. Journal of Rehabilitation Administration, 10(4), 130-135.

Figure 1. Pretest and posttest means for treatment (SE) and control groups for the four outcome measures.

The Employment Self Esteem Scale

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Home » Research Methods – Types, Examples and Guide

Research Methods – Types, Examples and Guide

Table of Contents

Research Methods

Definition:

Research Methods refer to the techniques, procedures, and processes used by researchers to collect , analyze, and interpret data in order to answer research questions or test hypotheses. The methods used in research can vary depending on the research questions, the type of data that is being collected, and the research design.

Types of Research Methods

Types of Research Methods are as follows:

Qualitative research Method

Qualitative research methods are used to collect and analyze non-numerical data. This type of research is useful when the objective is to explore the meaning of phenomena, understand the experiences of individuals, or gain insights into complex social processes. Qualitative research methods include interviews, focus groups, ethnography, and content analysis.

Quantitative Research Method

Quantitative research methods are used to collect and analyze numerical data. This type of research is useful when the objective is to test a hypothesis, determine cause-and-effect relationships, and measure the prevalence of certain phenomena. Quantitative research methods include surveys, experiments, and secondary data analysis.

Mixed Method Research

Mixed Method Research refers to the combination of both qualitative and quantitative research methods in a single study. This approach aims to overcome the limitations of each individual method and to provide a more comprehensive understanding of the research topic. This approach allows researchers to gather both quantitative data, which is often used to test hypotheses and make generalizations about a population, and qualitative data, which provides a more in-depth understanding of the experiences and perspectives of individuals.

Key Differences Between Research Methods

The following Table shows the key differences between Quantitative, Qualitative and Mixed Research Methods

Examples of Research Methods

Examples of Research Methods are as follows:

Qualitative Research Example:

A researcher wants to study the experience of cancer patients during their treatment. They conduct in-depth interviews with patients to gather data on their emotional state, coping mechanisms, and support systems.

Quantitative Research Example:

A company wants to determine the effectiveness of a new advertisement campaign. They survey a large group of people, asking them to rate their awareness of the product and their likelihood of purchasing it.

Mixed Research Example:

A university wants to evaluate the effectiveness of a new teaching method in improving student performance. They collect both quantitative data (such as test scores) and qualitative data (such as feedback from students and teachers) to get a complete picture of the impact of the new method.

Applications of Research Methods

Research methods are used in various fields to investigate, analyze, and answer research questions. Here are some examples of how research methods are applied in different fields:

• Psychology : Research methods are widely used in psychology to study human behavior, emotions, and mental processes. For example, researchers may use experiments, surveys, and observational studies to understand how people behave in different situations, how they respond to different stimuli, and how their brains process information.
• Sociology : Sociologists use research methods to study social phenomena, such as social inequality, social change, and social relationships. Researchers may use surveys, interviews, and observational studies to collect data on social attitudes, beliefs, and behaviors.
• Medicine : Research methods are essential in medical research to study diseases, test new treatments, and evaluate their effectiveness. Researchers may use clinical trials, case studies, and laboratory experiments to collect data on the efficacy and safety of different medical treatments.
• Education : Research methods are used in education to understand how students learn, how teachers teach, and how educational policies affect student outcomes. Researchers may use surveys, experiments, and observational studies to collect data on student performance, teacher effectiveness, and educational programs.
• Business : Research methods are used in business to understand consumer behavior, market trends, and business strategies. Researchers may use surveys, focus groups, and observational studies to collect data on consumer preferences, market trends, and industry competition.
• Environmental science : Research methods are used in environmental science to study the natural world and its ecosystems. Researchers may use field studies, laboratory experiments, and observational studies to collect data on environmental factors, such as air and water quality, and the impact of human activities on the environment.
• Political science : Research methods are used in political science to study political systems, institutions, and behavior. Researchers may use surveys, experiments, and observational studies to collect data on political attitudes, voting behavior, and the impact of policies on society.

Purpose of Research Methods

Research methods serve several purposes, including:

• Identify research problems: Research methods are used to identify research problems or questions that need to be addressed through empirical investigation.
• Develop hypotheses: Research methods help researchers develop hypotheses, which are tentative explanations for the observed phenomenon or relationship.
• Collect data: Research methods enable researchers to collect data in a systematic and objective way, which is necessary to test hypotheses and draw meaningful conclusions.
• Analyze data: Research methods provide tools and techniques for analyzing data, such as statistical analysis, content analysis, and discourse analysis.
• Test hypotheses: Research methods allow researchers to test hypotheses by examining the relationships between variables in a systematic and controlled manner.
• Draw conclusions : Research methods facilitate the drawing of conclusions based on empirical evidence and help researchers make generalizations about a population based on their sample data.
• Enhance understanding: Research methods contribute to the development of knowledge and enhance our understanding of various phenomena and relationships, which can inform policy, practice, and theory.

When to Use Research Methods

Research methods are used when you need to gather information or data to answer a question or to gain insights into a particular phenomenon.

Here are some situations when research methods may be appropriate:

• To investigate a problem : Research methods can be used to investigate a problem or a research question in a particular field. This can help in identifying the root cause of the problem and developing solutions.
• To gather data: Research methods can be used to collect data on a particular subject. This can be done through surveys, interviews, observations, experiments, and more.
• To evaluate programs : Research methods can be used to evaluate the effectiveness of a program, intervention, or policy. This can help in determining whether the program is meeting its goals and objectives.
• To explore new areas : Research methods can be used to explore new areas of inquiry or to test new hypotheses. This can help in advancing knowledge in a particular field.
• To make informed decisions : Research methods can be used to gather information and data to support informed decision-making. This can be useful in various fields such as healthcare, business, and education.

Advantages of Research Methods

Research methods provide several advantages, including:

• Objectivity : Research methods enable researchers to gather data in a systematic and objective manner, minimizing personal biases and subjectivity. This leads to more reliable and valid results.
• Replicability : A key advantage of research methods is that they allow for replication of studies by other researchers. This helps to confirm the validity of the findings and ensures that the results are not specific to the particular research team.
• Generalizability : Research methods enable researchers to gather data from a representative sample of the population, allowing for generalizability of the findings to a larger population. This increases the external validity of the research.
• Precision : Research methods enable researchers to gather data using standardized procedures, ensuring that the data is accurate and precise. This allows researchers to make accurate predictions and draw meaningful conclusions.
• Efficiency : Research methods enable researchers to gather data efficiently, saving time and resources. This is especially important when studying large populations or complex phenomena.
• Innovation : Research methods enable researchers to develop new techniques and tools for data collection and analysis, leading to innovation and advancement in the field.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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• Developing clinical...

Developing clinical prediction models: a step-by-step guide

• Related content
• Peer review
• 1 Institute of Primary Health Care (BIHAM), University of Bern, Bern, Switzerland
• 2 Institute of Social and Preventive Medicine (ISPM), University of Bern, Bern, Switzerland
• 3 Department of Clinical Research, University of Bern, Bern, Switzerland
• 4 Smart Data Analysis and Statistics B V, Utrecht, The Netherlands
• 5 Population Health Sciences, Bristol Medical School, University of Bristol, Bristol, UK
• Correspondence to: O Efthimiou orestis.efthimiou{at}unibe.ch (or @oremiou on X)
• Accepted 12 June 2024

Predicting future outcomes of patients is essential to clinical practice, with many prediction models published each year. Empirical evidence suggests that published studies often have severe methodological limitations, which undermine their usefulness. This article presents a step-by-step guide to help researchers develop and evaluate a clinical prediction model. The guide covers best practices in defining the aim and users, selecting data sources, addressing missing data, exploring alternative modelling options, and assessing model performance. The steps are illustrated using an example from relapsing-remitting multiple sclerosis. Comprehensive R code is also provided.

Clinical prediction models aim to forecast future health outcomes given a set of baseline predictors to facilitate medical decision making and improve people’s health outcomes. 1 Prediction models are becoming increasingly popular, with many new ones published each year. For example, a review of prediction models identified 263 prediction models in obstetrics alone 2 ; another review found 606 models related to covid-19. 3 Interest in predicting health outcomes has been heightened by the increasing availability of big data, 4 which has also led to the uptake of machine learning methods for prognostic research in medicine. 5 6

Several resources are available to support prognostic research. The PROGRESS (prognosis research strategy) framework provides detailed guidance on different types of prognostic research. 7 8 9 The TRIPOD (transparent reporting of a multivariable prediction model for individual prognosis or diagnosis) statement gives recommendations for reporting and has recently been extended to address prediction model research in clustered datasets. 10 11 12 13 14 PROBAST (prediction model risk-of-bias assessment tool) provides a structured way to assess the risk of bias in a prediction modelling study. 15 Several papers further outline good practices and provide software code. 16 17 18

Despite these resources, published prediction modelling studies often have severe methodological limitations. For instance, a review of prediction models for cardiovascular disease identified 363 models 19 ; the authors concluded that “the usefulness of most of the models remains unclear owing to methodological shortcomings, incomplete presentation, and lack of external validation and model impact studies.” Another review of 308 prediction models in psychiatry found that most were at high risk of bias. 20 Many biases well known in clinical and epidemiological research also apply to prediction model studies, including inconsistent definitions and measurements of predictors and outcomes or lack of blinding. Some biases are particularly pertinent to prediction modelling; for example, overfitting—estimating many model parameters from few data points—can lead to overestimating the model's performance. 15

This article provides a step-by-step guide for researchers interested in clinical prediction modelling. Based on a scoping review of the literature and discussions in our group, we identified 13 steps. We aim to provide an overview to help numerically minded clinicians, clinical epidemiologists, and statisticians navigate the field. We introduce key concepts and provide references to further reading for each step. We discuss issues related to model inception, provide practical recommendations about selecting predictors, outline sample size considerations, cover aspects of model development, such as handling missing data and assessing performance, and discuss methods for evaluating the model’s clinical usefulness. The concepts we describe and the steps we propose largely apply to statistical and machine learning models. An appendix with code in R accompanies the paper. Although several issues discussed here are also relevant to diagnostic research 21 (which is related but has subtle differences with prediction modelling) and models on predicting treatment effects, 22 23 our focus is primarily on methods for predicting a future health outcome. We illustrate the proposed procedure using an example of a prediction model for relapse in relapsing-remitting multiple sclerosis. The glossary in table 1 summarises the essential concepts and terms used.

Glossary of key terms and concepts used in prediction modelling

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Summary points

Many prediction models are published each year, but they often have methodological shortcomings that limit their internal validity and applicability. A 13 step guide has been developed to help healthcare professionals and researchers develop and validate prediction models, avoiding common pitfalls

In the first step, the objective of the prediction model should be defined, including the target population, the outcome to be predicted, the healthcare setting where the model will be used, the intended users, and the decisions the model will inform

Prediction modelling requires a collaborative and interdisciplinary effort within a team that ideally includes clinicians with content expertise, methodologists, users, and people with lived experiences

Common pitfalls include inappropriate categorising of continuous outcomes or predictors, data driven cut-off points, univariable selection methods, overfitting, and lack of attention to missing data and a sound assessment of performance and clinical benefit

Step 1: Define aims, create a team, review literature, start writing a protocol

Defining aims.

We should start by clearly defining the purpose of the envisaged prediction model. In particular, it is important to clearly determine the following:

The target population—for whom should the model predict? For example, people with HIV in South Africa; people with a history of diabetes; postmenopausal women in western Europe.

The health outcome of interest—what is the endpoint that needs to be predicted? For example, AIDS, overall survival, progression free survival, a particular adverse event.

The healthcare setting—how will the model be used? For example, the model might be used in primary care or be implemented in a clinical decision support system in tertiary care.

The user—who is going to use the model? For example, primary care physicians, secondary care physicians, patients, researchers.

The clinical decisions that the model will inform—how will model predictions be used in the clinical decision making process? For example, a model might be used to identify patients for further diagnostic investigation, to decide on treatment strategies, or to inform a range of personal decisions. 24

Answers to these questions should guide the subsequent steps; they will inform various issues, such as what predictors to include in the model, what data to use for developing and validating the model, and how to assess its clinical usefulness.

Creating a team

When developing a prediction model for clinical use, assembling a group with expertise in the specific medical field, the statistical methodology, and the source data are highly advisable. Including users—that is, clinicians who might use the model and people with lived experiences—is also beneficial. Depending on the model's complexity, it might be necessary to involve software developers at later stages of the project; that is, developing a web application for users to make predictions.

Reviewing the literature

Identifying relevant published prediction models and studies on important risk factors is crucial and can be achieved through a scoping review. Discussing the review's findings with clinicians will help us to understand established predictors and the limitations of existing models. The literature review might also provide information on interactions between predictors, nonlinear associations between predictors and outcomes, reasons for missing data, and the expected distribution of predictors in the target population. In some situations, performing a systematic review might be helpful. Specific guidance on systematic reviews of prediction models has been published. 25 26 27

A study protocol should guide subsequent steps. The protocol can be made publicly available in an open access journal or as a preprint in an online repository (eg, www.medrxiv.org or https://osf.io/ ). In addition to the steps discussed here, the TRIPOD statement 10 14 and the PROBAST tool 15 might be helpful resources when writing the protocol.

Step 2: Choose between developing a new model or updating an existing one

Depending on the specific field, the literature review might show that relevant prediction models already exist. Suppose an existing model has a low risk of bias (according to PROBAST 15 ) and applies to the research question. In that case, assessing its validity for the intended setting might be more appropriate than developing a new model. This approach is known as external validation ( table 1 ). Depending on the validation results, we might decide to update and adapt the model to the population and setting of intended use. Common strategies for updating a prediction model include recalibration (eg, adjustment of the intercept term in a regression model), revision (ie, re-estimation of some model parameters), and extension (ie, addition of new predictors). 28 29 Although updating strategies have mainly been described for regression models, they can also be applied to machine learning. For example, a random forest model was used to predict whether patients with stroke would experience full recovery within 90 days of the event. When tested on an external dataset, the model needed recalibration, which was performed by fitting logistic regression models to the predictions from the random forest. 30 Prediction models for imaging data are often developed by fine tuning previously trained neural networks using a process known as transfer learning. 31

Further guidance on external validation and model updating is available elsewhere, 32 33 34 35 36 including sample size considerations for external validation. 37 In the following steps, we focus on developing a new model; we briefly revisit external validation in step 9.

Step 3: Define the outcome measure

An outcome can be defined and measured in many ways. For example, postoperative mortality can be measured as a binary outcome at 30 days, at 60 days, or using survival time. Using time-to-event instead of binary variables is good practice; a prediction model for time-to-event can better handle people who were followed up for a limited time and did not experience the outcome of interest. Moreover, time-to-event data provide richer information (eg, the survival probability at any time point) than a binary outcome at one time point only. Similarly, we can analyse a continuous health outcome using a continuous scale or after dichotomising or categorising. For example, a continuous depression score at week 8 after starting drug treatment could be dichotomised as remission or non-remission. Categorising a continuous outcome leads to loss of information. 38 39 40 Moreover, the selection of thresholds for categorisation is often arbitrary, lacking biological justification. In some cases, thresholds are chosen after exploring various cut-off points and opting for those that fit the data best or yield statistically significant results. This data driven approach could lead to reduced performance in new data. 38

Step 4: Identify candidate predictors and specify measurement methods

Candidate predictors.

We should identify potential predictors based on the literature review and expert knowledge (step 1). Like the outcomes of interest, they should ideally be objectively defined and measured using an established, reliable method. Understanding the biological pathways that might underpin associations between predictors and the outcome is key. Predictors with proven or suspected causal relationships with the outcome should be prioritised for inclusion; this approach might increase the model's generalisability. On the other hand, the absence of a causal relationship should not a priori exclude potential predictors. Predictors not causally related to the outcome but strongly associated with it might still contribute to model performance, although they might generalise less well to different settings than causal factors. Further, we must include only baseline predictors; that is, information available when making a prognosis. Dichotomising or categorising continuous predictors reduces information and diminishes statistical power and should be avoided. 41 42 Similarly to categorising outcomes, we advise against making data driven, post hoc decisions after testing several categorisation thresholds for predictors. In other words, we should not choose the categories of a continuous outcome based solely on the associated model performance.

Thinking about the user of the prediction model

It is crucial to consider the model's intended use (defined in step 1) and the availability of data. What variables are routinely measured in clinical practice and are available in the database? What are the costs and practical issues related to their measurement, including the degree of invasiveness? 43 For example, the veterans ageing cohort study index (VACS index 2.0) predicts all cause mortality in people with HIV. 44 However, some of its predictors, such as the liver fibrosis index (FIB-4), will not be available in routine practice in many settings with a high prevalence of HIV infection. Similarly, a systematic review of prognostic models for multiple sclerosis found that 44 of 75 models (59%) included predictors unlikely to be measured in primary care or standard hospital settings. 45

Step 5: Collect and examine data

Data collection.

Ideally, prediction models are developed using individual participant data from prospective cohort studies designed for this purpose. 1 In practice, developing prediction models using existing data from cohort studies or other data not collected explicitly for this purpose is much more common. Data from randomised clinical trials can also be used. The quality of trial data will generally be high, but models could have limited generalisability because trial participants might not represent the patients seen in clinical practice. For example, a study found only about 20% of people who have schizophrenia spectrum disorders would be eligible for inclusion in a typical randomised clinical trial. Patients who are ineligible had a higher risk of hospital admission with psychosis than those who are eligible. 46 Therefore, a prediction model based on trial data might underestimate the real world risk of hospital admissions. Registry data offer a simple, low cost alternative; their main advantage is the relatively large sample size and representativeness. However, drawbacks relate to data limitations such as inadequate data on relevant predictors or outcomes, and variability in the timing of measurements. 47

Data errors

Before fitting the model, addressing potential misclassification or measurement errors in predictors and outcomes is crucial. This involves considering the nature of the variables collected and the methods used for measurement or classification. For example, predictors such as physical activity or dietary intake are prone to various sources of measurement error. 48 The extent of these errors can vary across settings, for example, because of differences in the measurement method used. This means that the model's predictive performance and potential usefulness could be reduced. 49 If the risk of measurement error is considered high, we might consider alternative outcome measures or exclude less important, imprecisely measured predictors from the list created in step 4. In particular, if systematic errors in the dataset do not mirror those encountered in clinical practice, the model’s calibration might be poor. While methods for correcting measurement errors have been proposed, they typically require additional data and assumptions. 49

Variable distributions and missing data

After examining their distribution in the dataset, excluding predictors with limited variation is advisable because they will contribute little. For example, if the ages range from 25 to 45 years and the outcomes are not expected to change much within this range, we should remove age from the list of predictors. Similarly, a binary predictor might be present in only a few people. In such cases, we might consider removing it from the model unless there is previous evidence that this is a strong predictor. 47 More complications arise when a variable with low prevalence is known to have meaningful predictive value. For example, a rare genetic mutation could be strongly associated with the outcome. The mutation could be omitted from the model because its effect is difficult to estimate accurately. Alternatively, the few people with the mutation could be excluded, making the model applicable only to people without it. 47 Another issue is incomplete data on predictors and outcomes for some participants. Depending on the prevalence of missing data, we might want to modify the outcome or exclude certain candidate predictors. For example, we might omit a predictor with many missing values, especially if there is little evidence of its predictive power and imputing the missing data is challenging (step 7); that is, when the missing values cannot be reliably predicted using the observed data. Conversely, if the missing information can be imputed, we might decide to retain the variable, particularly when there is existing evidence that the predictor is important.

Step 6: Consider sample size

General considerations about sample size.

A very simple model or a model based on covariates that are not associated with the outcome will perform poorly in the data used to develop it and in new data; this scenario is called underfitting. Conversely, a model with too many predictors developed in a small dataset (overfitting) could perform well in this particular dataset but fail to predict accurately in new data. In practice, overfitting is more common than underfitting because datasets are often small and have few events, and there is the temptation to create models with the best (apparent) performance. Therefore, we must ensure the data are sufficient to develop a robust model that includes the relevant predictors.

Calculating sample size requirements for a specific model

Riley and colleagues 50 provide helpful guidance and code 51 52 on sample size calculations. Users need to specify the overall risk (for binary outcomes) or mean outcome value (for continuous outcomes) in the target population, the number of model parameters, and a measure of expected model performance (eg, the coefficient of determination, R 2 ). Note that the number of parameters can be larger than the number of predictors. For example, we need two parameters when using a restricted cubic spline with three knots to model a nonlinear association of age with the outcome. The sample size calculated this way is the minimum for a standard statistical model. The sample size must be several times larger if we want to use machine learning models. 53 Sample size calculations for such models are considerably more complex and might require simulations. 54

Calculating number of model parameters for fixed sample size

Suppose the sample size is fixed or based on an existing study, as is often the case. Then, we should perform sample size calculations to identify the maximum number of parameters we can include in the model. A structured way to guide model development can be summarised as follows:

Calculate the maximum number of parameters that can be included in the model given the available sample size.

Use the available parameters sequentially by including predictors from the list, starting from the ones that are perceived to be more important. 55

Note that additional parameters will be needed for including nonlinear terms or interactions among the predictors in the list.

Step 7: Deal with missing data

General considerations on missing data.

After removing predictors or outcomes with many missing values, as outlined in step 5, we might still need to address missing values in the retained data. Relying only on complete cases for model development—that is, participants with data for all variables—can dramatically reduce the sample size. To mitigate the loss of valuable information during model development and evaluation, researchers should consider imputing missing data.

Imputation of missing data

Multiple imputation is the approach usually recommended to handle missing data during model development, and appropriately accounts for missing data uncertainty. 56 Several versions of the original dataset are created, each with missing values imputed using an imputation model. The imputation model should be the same (in terms of predictors included, their transformations and interactions) as the final model we will use to make predictions. Additionally, the imputation model might involve auxiliary variables associated with missing data, which can enhance the effectiveness of the imputations. Once we have created the imputed datasets, we must decide whether to include participants with imputed outcomes in the model development. If no auxiliary variables were used in the imputations, people with imputed outcomes can be removed, and the model can be developed based only on people with observed outcomes. 57 However, if imputation incorporates auxiliary variables, including those with imputed outcomes in the model development is advisable. 58 A simpler alternative to multiple imputation is single imputation when each missing value is imputed only once using a regression model. Sisk and colleagues showed that single imputation can perform well, although multiple imputation tends to be more consistent and stable. 59

In step 4, we made the point that a model should include predictors that will be available in practice. However, we might want to make the model available even when some predictors are missing, for example, when using the model in a lower level of care. For example, the QRisk3 tool for predicting cardiovascular disease can be used even if the general practitioner does not enter information on blood pressure variability (the standard deviation of repeated readings). 60 When anticipating missing data during use in clinical practice, we can impute data during the development and implementation phases. In this case, single imputation can be used during model development and model use. 59

Ιmputation methods are not a panacea and might fail, typically when the tendency of the outcome to be missing correlates with the outcome itself. For example, patients receiving a new treatment might be more likely to miss follow-up visits if the treatment was successful, leading to missing data. Developing a prediction model in such cases requires additional modelling efforts 61 that are beyond the scope of this tutorial.

Step 8: Fit the prediction models

Modelling strategies.

The strategies for model development should be specified in the protocol (step 5). Linear regression for continuous outcomes, logistic regression for binary outcomes, and Cox or simple parametric models for survival outcomes are the usual starting points in modelling. If the sample size is large enough (see step 6), models can include nonlinear terms for continuous predictors or interactions between predictors. More advanced modelling strategies, such as machine learning models (eg, random forests, support vector machines, boosting methods, neural networks, etc), can also be used. 62 63 These strategies might add value if there are strong nonlinearities and interactions between predictors, although they are not immune to biases. 64 As discussed under step 10, a final strategy needs to be selected if several modelling strategies are explored.

Dealing with competing events

When predicting binary or time-to-event outcomes, we should consider whether there are relevant competing events. This situation occurs when several possible outcomes exist, but a person can only experience one event. For example, when predicting death from breast cancer, death from another cause is a competing event. In this case, and especially whenever competing events are common, we should use a competing risks model for the analysis, such as a cause specific Cox regression model. 65 A simpler approach would be to analyse a composite outcome.

Data driven variable selection methods

We advise against univariable selection methods—that is, methods that test each predictor separately and retain only statistically significant predictors. These methods do not consider the association between predictors and could lead to loss of valuable information. 55 66 Stepwise methods for variable selection (eg, forward, backwards, or bidirectional variable selection) are commonly used. Again, they are not recommended because they might lead to bias in estimation and worse predictive performance. 55 67 68 If variable selection is desirable—for instance, to simplify the implementation of the model by further reducing the number of predetermined predictors—more suitable methods can be used as described below.

Model estimation

Adding penalty terms to the model (a procedure called penalisation, regularisation, or shrinkage; see table 1 ) is recommended to control the complexity of the model and prevent overfitting. 69 70 71 Penalisation methods such as ridge, LASSO (least absolute shrinkage and selection operator), and elastic net generally lead to smaller absolute values of the coefficients—that is, they shrink coefficients towards zero—compared with maximum likelihood estimation. 72 LASSO and elastic net can be used for variable selection (similar to the methods described above). These models might exclude some predictors by setting their coefficients to zero, leading to a more interpretable and simpler model. Machine learning methods typically also have penalisation embedded. Penalisation is closely related to the bias-variance trade-off depicted in figure 1 , and is a method aiming to bring the model closer to the sweet spot of the bias-variance trade-off curve, where model performance in new data is maximised (note that the figure does not include a description of the double descent phenomenon). 73 Although penalisation methods have advantages, they do not solve all the problems associated with small sample sizes. While these methods typically are superior to standard estimation techniques, they can be unstable in small datasets. Moreover, their application does not ensure improved predictive performance. 74 75

Upper panel: graphical illustration of bias-variance trade-off. The training set is used to develop a model; the testing set is used to test it. A simple, underfitting model leads to high prediction error in training and testing sets. By increasing model complexity, the training set error can be lowered to zero. However, the testing set error (which needs to be minimised) only reduces to a point and then increases as complexity increases. The ideal model complexity is one that minimises the testing set error. An overfitting model might appear to perform well in the training set but might still be worthless—ie, overfitting leads to optimism. Lower three panels: fictional example of three prediction models (lines) developed using a dataset (points). x, y: single continuous predictor and outcome, respectively. The underfitting model has large training error and will also have large testing error; the overfitting model performs perfectly in the development set (ie, zero training error) but will perform poorly in new data (large testing error). The ideal model complexity will perform better than the other two in new data

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Treating multiply imputed data in model development

If multiple imputation was used, we must apply each modelling strategy to every imputed dataset. Consequently, if there are m imputed datasets, m different models will be developed for each modelling strategy. When predicting outcomes, these m models need to be combined. There are two methods to achieve this. The first method uses Rubin’s rule, 76 which is suitable for simple regression models. The estimated parameters from the m models are averaged, resulting in a final set of parameters, which can then be used to predict the outcome for a new person. However, this method is not straightforward for model selection strategies (eg, LASSO) because the m fitted models might have selected different sets of parameters. As a result, combining them becomes more complex. 77 78 Rubin’s rule might not apply to machine learning methods because the m models could have different architectures. Another method for combining the m models is to use them to make predictions for the new person and then average these m predictions, 79 a procedure conceptually similar to stacking in machine learning.

Step 9: Assess the performance of prediction models

General concepts in assessing model performance.

We assess the predictive performance of the modelling strategies explored in step 8. Specifically, we contrast predictions with observed outcomes for people in a dataset to calculate performance measures. For continuous outcomes like blood pressure this is straightforward: observed outcomes can be directly compared with predictions because they are on the same scale. When dealing with binary or survival outcomes, the situation becomes more complex. In these cases, prediction models might give the probability of an event occurring for each individual while observed outcomes are binary (event or no event) or involve time-to-event data with censoring. Consequently, more advanced methods are required.

Dimensions of prediction performance

Prediction performance has two dimensions, and it is essential to assess them both, particularly for binary and survival outcomes (see glossary in table 1 ).

Discrimination—for continuous outcomes, discrimination refers to the model’s ability to distinguish between patients with different outcomes: good discrimination means that patients with higher predicted values also had higher observed outcome values. For binary outcomes, good discrimination means that the model separates people at high risk from those at low risk. For time-to-event outcomes, discrimination refers to the ability of the model to rank patients according to their survival; that is, patients predicted to survive longer survived longer.

Calibration relates to the agreement between observed and predicted outcome values. 80 81 For continuous outcomes, good calibration means that predicted values do not systematically overestimate or underestimate observed values. For binary and survival outcomes, good calibration means the model does not overestimate or underestimate risks.

Discrimination and calibration are essential when evaluating prediction models. A model can have good discrimination by accurately distinguishing between risk levels, but still have poor calibration owing to a mismatch between predicted and observed probabilities. Moreover, a well calibrated model might have poor discrimination. Thus, a robust prediction model should have good discrimination and calibration. Box 1 outlines measures for assessing model performance.

Measures of performance of prediction models for different types of outcomes

Continuous outcomes.

Predicted and observed outcomes can be compared through mean bias, mean squared error, and the coefficient of determination, R 2 , to measure overall performance—ie, combining calibration and discrimination. For discrimination alone, rank correlation statistics between predictions and observations can be used, although this seldom occurs in practice. For calibration, results can be visualised in a scatterplot and an observed versus predicted line fitted. For a perfectly calibrated model, this line is on the diagonal; for an overfit (underfit) model, the calibration line is above (below) the diagonal. A smooth calibration line can assess calibration locally—ie, it can indicate areas where the model underestimates or overestimates the outcome. Smooth calibration lines can be obtained by fitting, for example, restricted cubic splines or a locally estimated scatterplot smoothing line (LOESS) of the predicted versus the observed outcomes.

Binary outcomes

Discrimination can be assessed using the area under the receiver operating characteristic curve (AUC). Mean calibration (calibration in the large, see table 1 ) can be determined by comparing mean observed versus mean predicted event rates. A logistic regression model can be fit to the observed outcome using the log odds of the event from the prediction model as the sole independent variable and then the intercept and slope can be evaluated. Additionally, a calibration curve can be created; for this, participants are grouped according to their predicted probabilities. Calculate the mean predicted probability and the proportion of events for each group; then compare the two in a scatterplot and draw a smooth calibration curve (eg, using splines) to assess calibration locally. The Brier score measures overall performance—it is simply calculated as the mean squared difference between predicted probabilities and actual outcomes. Many additional measures can be used to measure performance, for example, F score, sensitivity-specificity, etc.

Survival outcomes

If focus is on a specific time point, discrimination can be assessed as for binary outcomes (fixed time point discrimination). 18 However, censoring of follow-up times complicates this assessment. Uno and colleagues' inverse probability of censoring weights method can account for censoring. 82 Also, discrimination can be assessed across all time points using Harrell's c statistic. 83 Uno's c statistic can be expanded to a global measure, across all time points. 84 Calibration can be assessed for a fixed time point by comparing the average predicted survival from the model with the observed survival—ie, estimated while accounting for censorship; this can be obtained from a Kaplan-Meier curve by looking at the specific time point (calibration in the large at a fixed time). The Kaplan-Meier curve can be compared with the mean predicted survival across all times. More details can be found elsewhere. 18 Smooth calibration curves can also be used to assess performance of the model across the full range of predicted risks, while additional calibration metrics have also been proposed. 85 86 Similar measures can be used for competing events, with some adjustments. 16

Model validation

What data should we use to assess the performance of a prediction model? The simplest approach is to use the same dataset as for model development; this approach will return the so-called apparent model performance (apparent validation). However, this strategy might overestimate the model’s performance ( fig 1 ); that is, it might lead to erroneous (optimistic) assessments. Optimism is an important issue in prediction modelling and is particularly relevant when sample sizes are small and models complex. Therefore, assessing model performance using a more adequate validation procedure is crucial. Proper validation is essential in determining a prediction model’s generalisability—that is, its reproducibility and transportability. 33 47 Reproducibility refers to the model’s ability to produce accurate predictions in new patients from the same population. Transportability is the ability to produce accurate predictions in new patients drawn from a different but related population. Below, we describe different approaches to model validation.

Internal validation

Internal validation focuses on reproducibility and specifically aims to ensure that assessments of model performance using the development dataset are honest, meaning optimism does not influence them. In an internal validation procedure, we use data on the same patient population as the one used to develop the model and try to assess model performance while avoiding optimism. Validation must follow all steps of model development, including variable selection.

The simplest method is the split sample approach where the dataset is randomly split into two parts (eg, 70% training and 30% testing). However, this method is problematic because it wastes data and decreases statistical power. 55 87 When applied to a small dataset, it might create two datasets that are inadequate for both model development and evaluation. Conversely, for large datasets it offers little benefit because the risk of overfitting is low. Further, it might encourage researchers to repeat the procedure until they obtain satisfactory results. 88 Another approach is to split the data according to the calendar time of patient enrolment. For example, we might develop the model using data from an earlier period and test it in patients enrolled later. This procedure (temporal validation) 35 89 might inform us about possible time trends in model performance. However, the time point used for splitting the data will generally be arbitrary and older data might not reflect current patient characteristics or health care. Therefore, this approach is not recommended for the development phase. 88

A better method is k-fold cross validation. In this approach, we divide the data randomly in k (usually 10) subsets (folds). The model is built using k−1 of these folds and evaluated on the remaining one fold. This process is repeated, cycling through all the folds so that each can be the testing set. The model's performance is measured in each cycle, and the k estimates are then combined and summarised to get a final performance measure. Bootstrapping is another method, 90 which can be used to calculate optimism and optimism corrected performance measures for any model. Box 2 outlines the procedure. 47 Bootstrapping generally leads to more stable and less biased results, 93 and is therefore recommended for internal validation. 47 However, implementation of k-fold cross validation and bootstrapping can be computationally demanding when multiple imputation of missing data is needed. 88

Calculating optimism corrected measures of performance through bootstrapping

Use bootstrapping to correct apparent performance and obtain optimism corrected measures for any model M and any performance measure as follows.

Select a measure X (eg, R 2 , mean squared error, AUC (area under the receiver operating characteristic curve)) and calculate apparent performance (X 0 ) of model M in the original sample.

Create many (at least N B =100) bootstrap samples with the same size as the original dataset by drawing patients from the study population with replacement. Replacement means that some individuals might be included several times in a bootstrap sample, while others might not appear at all.

In each bootstrap sample i (i=1, 2 … N B ) construct model M i by exactly reiterating all steps of developing M, ie, including variable selection methods (if any were used). Determine the apparent performance X i of model M i in sample i.

Apply M i to the original sample and calculate performance, X i *. This performance will generally be worse than X i owing to optimism. Calculate optimism for measure X, sample i, as O i X =X i −X i *.

Average the N B different values of O i X to estimate optimism, O X .

Calculate the optimism corrected value of X as X corrected =X 0 −O i X .

More advanced versions of bootstrapping (eg, the 0.632+ bootstrap 91 ) require slightly different procedures. 92 In practice, we often need to combine bootstrapping with multiple imputation. Ideally, we should first bootstrap and then impute. 92 However, this strategy might be computationally difficult. Instead, we can first impute, then bootstrap, obtain optimism corrected performance measures from each imputed dataset, and finally pool these.

Another method of assessing whether a model’s predictions are likely to be reliable or not is by checking the model’s stability. Model instability means that small changes in the development dataset lead to large changes in the resulting model structure (important differences in estimates of model parameters, included predictors, etc), leading to important changes in predictions and model performance. Riley and Collins described how to assess the stability of clinical prediction models during the model development phase using a bootstrap approach. 94 The model building procedure is repeated in several bootstrap samples to create numerous models. Predictions from these models are then compared with the original model predictions to investigate possible instability.

Internal-external validation

An alternative approach is the internal-external or leave-one-out cross validation. This method involves partitioning the data into clusters based on a specific variable (eg, different studies, hospitals, general practices, countries) and then iteratively using one cluster as the test set while training the model on the remaining clusters. 95 96 Like in k-fold cross validation, this process is repeated for each cluster, and the performance results are summarised at the end. In contrast to k-fold cross validation, internal-external validation can provide valuable insights into how well the model generalises to new settings and populations because it accounts for heterogeneity across different clusters. For example, prediction models for patients with HIV were developed based on data from treatment programmes in Côte d’Ivoire, South Africa, and Malawi and validated using leave-one-country-out cross validation. 97

Note here that although all internal and internal-external validation methods include some form of data splitting, the final model should be developed using data from all patients. This strategy contrasts with the external validation method outlined below.

Εxternal validation

External validation requires testing the model on a new set of patients—that is, those not used for model development. 36 Assuming that the model has shown good internal validity, external validation studies are the next step in determining a model’s transportability before considering its implementation in clinical practice. The more numerous and diverse the settings in which the model is externally validated, the more likely it will generalise to a new setting. An external validation study could indicate that a model requires updating before being used in a new setting. A common scenario is when a model’s discrimination is adequate in new settings and fairly stable over time, but calibration is suboptimal across settings or deteriorates over time (calibration drift). 98 For example, EuroSCORE is a model developed in 1999 for predicting mortality in hospital for patients undergoing cardiac surgery. 99 Using data from 2001 to 2011, EuroSCORE was shown to consistently overestimate mortality and its calibration deteriorated over time. 100 In such situations, model updating (step 2) might be required.

The inclusion of external validation in model development is a topic of debate, with certain journals mandating it for publication. 88 100 One successful external validation, however, does not establish transportability to many other settings, while such a requirement might lead to the selective reporting of validation data. 100 Therefore, our view (echoing recent recommendations 88 ) is that external validation studies should be separated from model development at the moment of model development. External validation studies are ideally performed by independent investigators who were not involved in the original model development. 101 For guidance on methods for external validation, see references cited in step 2.

Step 10: Decide on the final model

Now it is time to choose the final model based on the internal and internal-external validation performance metrics (and possibly on stability assessments). If different modelling strategies perform similarly, we might want to select the simpler model (related to Occam’s razor principle 102 ). For example, logistic regression performed similarly to optimised machine learning models for discriminating between type 1 and type 2 diabetes in young adults. 103 In this case, we would prefer the regression model because it is simpler and easier to communicate and use.

Step 11: Perform a decision curve analysis

A prediction model might strongly discriminate and be well calibrated, but its value depends on how we intend to use it in clinical practice. While an accurate prediction model can be valuable in counselling patients on likely outcomes, determining its utility in guiding decisions is less straightforward. Decision analysis methods can be used to assess whether a prediction model should be used in practice by incorporating and quantifying its clinical impact, considering the anticipated benefits, risks, and costs. 104 For example, the National Institute for Health and Care Excellence (NICE) in the UK recommends cholesterol lowering treatment if the predicted 10 year risk of myocardial infarction or stroke is 10% or higher (the cut-off threshold probability) based on the QRISK3 risk calculator. 60 105 The assumption is that the benefit of treating one patient who would experience a cardiovascular event over 10 years outweighs the harms and costs incurred by treating another nine people who will not benefit. In other words, the harm associated with not treating the one patient who would develop the event is assumed to be nine times greater than the consequences of treating a patient who does not need it.

Net benefit brings the benefits and harms of a decision strategy (eg, to decide for or against treatment based on a prediction model) on the same scale so they can be compared. 104 We can compute the net benefit of using the model at a particular cut-off threshold (eg, 10% risk for the case of QRISK3 risk calculator). The net benefit is calculated as the expected percentage of true positives minus the expected percentage of true negatives, multiplied by a weight determined by the chosen cut-off threshold. We obtain the decision curve by plotting the model's net benefit across a range of cut-off thresholds deemed clinically relevant. 106 107 We can compare the benefit of making decisions based on the model with alternative strategies, such as treating everyone or no one. We can also compare different models. The choice of decision threshold can be subjective, and the range of sensible thresholds will depend on the settings, conditions, available diagnostic tests or treatments, and patient preferences. The lower the threshold, the more unnecessary tests or interventions we are willing to accept. Of note, a decision curve analysis might indicate that a model is not useful in practice despite its excellent predictive ability.

There are several pitfalls in the interpretation of decision curves. 24 Most importantly, the decision curve cannot determine at what threshold probability the model should be used. Moreover, because the model’s predictive performance influences the decision curve, the decision curve can be affected by optimism. Therefore, a model’s good predictive performance (in internal validation and after correction for optimism) should be established before evaluating its clinical usefulness through a decision curve. Additionally, the curve can be obtained using a cross validation approach. 108 Vickers and colleagues provide a helpful step-by-step guide to interpreting decision curve analysis, and a website with a software tutorial and other resources. 107 The multiple sclerosis example below includes a decision curve analysis.

Step 12: Assess the predictive ability of individual predictors (optional step)

In prediction modelling, the primary focus is typically not on evaluating the importance of individual predictors; rather, the goal is to optimise the model’s overall predictive performance. Nevertheless, identifying influential predictors might be of interest, for example, when evaluating the potential inclusion of a new biomarker as a routine measurement. Also, some predictors might be modifiable, raising the possibility that they could play a part in prevention if their association with the outcome is causal. Therefore, as an additional, optional step, researchers might want to assess the predictive capacity of the included predictors.

Looking at estimated coefficients in (generalised) linear regression models is a simple way to assess the importance of different predictors. However, when the assumptions of linear regression are not met, for example, when there is collinearity, these estimates might be unreliable. However, note that multicollinearity does not threaten a model's predictive performance, just at the interpretation of the coefficients. Another method to assess the importance of a predictor, also applicable to machine learning models, is to fit the model with and without this predictor and note the reduction in model performance; omitting more important predictors will lead to a larger reduction in performance. More advanced methods include the permutation importance algorithm 109 and SHAP (Shapley additive explanations) 110 ; we do not discuss these here.

Regardless of the method we choose to assess predictor importance, we should be careful in our interpretations; associations seen in data might not reflect causal relationships (eg, see the “Table 2 fallacy” 111 ). A thorough causal inference analysis is needed to establish causal associations between predictors and outcomes. 112

Step 13: Write up and publish

Congratulations to us! We have developed a clinical prediction model! Now, it is time to write the paper and describe the process and results in detail. The TRIPOD reporting guideline and checklist 10 14 (or, for clustered datasets, TRIPOD cluster 13 ) should be used to ensure all important aspects are covered in the paper. If possible, the article should report the full model equation to allow reproducibility and independent external validation studies. Software code and, ideally, data should be made freely available. Further, we must ensure the model is accessible to the users we defined in step 1. Although this should be self-evident, in practice, there is often no way to use published models to make an actual prediction; for example, Reeve and colleagues found that 52% of published models for multiple sclerosis could not be used in practice because no model coefficients, tools, or instructions were provided. 45

The advantages and disadvantages of different approaches for making the model available to users, including score systems, graphical score charts, nomograms, and websites and smartphone applications have been reviewed elsewhere. 113 Simpler approaches are easier to use, for example, on ward rounds, but might require model simplification by removing some predictors or categorising continuous variables. Online calculators where users input predictor values (eg, a web application using Shiny in R) 114 can be based on the whole model without information loss. However, if publicly accessible, calculators might be misused by people for whom they are not intended, or if the model fails to show any clinical value (eg, in a subsequent external validation). Generally, the presentation and implementation should always be discussed with the users to match their needs (defined in step 1).

Example: relapsing-remitting multiple sclerosis

Multiple sclerosis is a chronic inflammatory disorder of the central nervous system with a highly variable clinical course. 115 Relapsing-remitting multiple sclerosis (RRMS), the most common form, is characterised by attacks of worsening neurological function (relapses) followed by periods of partial or complete recovery (remissions). 116 117 118 These fluctuations pose a major challenge in managing the disease. A predictive tool could inform treatment decisions. Below, we describe the development of a prediction model for RMMS. 119 We briefly outline the procedures followed in the context of our step-by-step guide. Details of the original analysis and results are provided elsewhere. 119

Step-by-step model development

The aim was to predict relapse within two years in patients with RRMS. Such a prediction can help treatment decisions; if the risk of relapsing is high, patients might consider intensifying treatment, for example, by taking more active disease modifying drugs, which might however have a higher risk of serious adverse events, or considering stem cell transplantation. A multidisciplinary team comprising clinicians, patients, epidemiologists, and statisticians was formed. A literature review identified several potential predictors for relapse in RRMS. Additionally, the review showed limitations of existing prediction models, including lack of internal validation, inadequate handling of missing data, and lack of assessment of clinical utility (step 1). These deficiencies compromised the reliability and applicability of existing models in clinical settings. Based on the review, it was decided to pursue the development of a new model, instead of updating an existing one (step 2). The authors chose the (binary) occurrence of at least one relapse within a two year period for people with RRMS (step 3) as the outcome measure.

The following predictors were used based on the literature review and expert opinion: age, expanded disability status scale score, previous treatment for multiple sclerosis, months since last relapse, sex, disease duration, number of previous relapses, and number of gadolinium enhanced lesions. The selection aimed to include relevant predictors while excluding those that are difficult to measure in clinical practice (step 4). The model was developed using data from the Swiss Multiple Sclerosis Cohort, 120 a prospective cohort study that closely monitors patients with RRMS. Data included a total of 1752 observations from 935 patients followed up every two years, with 302 events observed (step 5). Sample size calculations 50 indicated a minimum sample of 2082 patients, which is larger than the available sample, raising concerns about possible overfitting issues (step 6). Multiple imputations were used to impute missing covariate data. The authors expected no missing data when using the model in practice (step 7).

A Bayesian logistic mixed effects prediction model was developed, which accounted for several observations within patients. Regression coefficients were penalised through a Laplace prior distribution to address possible overfitting (step 8). Model calibration was examined in a calibration plot ( fig 2 , upper panel), and discrimination was assessed using the AUC (area under the receiver operating characteristic curve). Both assessments were corrected for optimism through a bootstrap validation procedure (described in box 2 ), with 500 bootstrap samples created for each imputed dataset. The optimism corrected calibration slope was 0.91, and the optimism corrected AUC was 0.65—this value corresponds to low to moderate discriminatory ability, comparable to or exceeding previous RRMS models (steps 9 and 10). A decision curve analysis was performed to assess the clinical utility of the model ( fig 2 , lower panel). The analysis indicated that deciding to intensify or not intensify the treatment using information from the model is preferable to simpler strategies—do not intensify treatment, and intensify treatment for all—for thresholds between 15% and 30%. Therefore, the model is useful to guide decisions in practice only if we value the avoidance of relapse 3.3–6.6 times more than the risks and inconveniences of more intensive treatments (step 11). Among the included predictors, younger age, higher expanded disability status scale scores, and shorter durations since the last relapse were associated with higher odds of experiencing a relapse in the next two years according to the estimated regression coefficients. However, none of the predictors were modifiable factors (step 13). The model was implemented in a freely available R-shiny 114 web application, where patients, doctors, and decision makers can estimate the probability of experiencing at least one relapse within the next two years ( https://cinema.ispm.unibe.ch/shinies/rrms/ ) . To enable reproducibility, all code was made publicly available at https://github.com/htx-r/Reproduce-results-from-papers/tree/master/PrognosticModelRRMS (step 13).

Results from a model predicting the probability of a patient with relapsing-remitting multiple sclerosis experiencing a relapse in the next two years. Figures adapted from Chalkou et al. 119 Upper panel: calibration plot. Solid blue line shows calibration using a LOESS (locally estimated scatterplot smoothing line), and shaded area shows 95% confidence intervals. Dotted blue line corresponds to perfect calibration. Maximum predicted probability was around 60% for this example. The model is well calibrated for predicted probabilities lower than 35%. Lower panel: decision curve analysis comparing net benefit of three strategies deciding on whether to intensify treatment in patients with relapsing-remitting multiple sclerosis (from no treatment to first line treatment, or from first line to second line treatment, etc). The strategies are to continue current treatment (do not intensify), to intensify treatment for all, or to intensify treatment according to predictions from model considering probability of experiencing a relapse in next two years—ie, if predicted probability is higher than a threshold (shown on x axis), then the treatment can be intensified

Our appendix is available online at https://github.com/esm-ispm-unibe-ch/R-guide-to-prediction-modelling , where we provide R code covering many aspects of the development of prediction models. The code uses simulated datasets and describes the case of continuous, binary, time-to-event, and competing risk outcomes. The code covers the following aspects: sample size calculations, multiple imputation, modelling nonlinear associations, assessing apparent model performance, performing internal validation using bootstrap, internal-external validation, and decision curve analysis. Readers should note that the appendix does not cover all possible modelling methods, models, and performance measures that can be used. Moreover, parts of the code are based on previous publications. 16 18 Additional code is provided elsewhere, for example, by Zhou and colleagues. 17

Conclusions

This tutorial provides a step-by-step guide to developing and validating clinical prediction models. We stress that this is not a complete and exhaustive guide, and it does not aim to replace existing resources. Our intention is to introduce essential aspects of clinical prediction modelling. Figure 3 provides an overview of the proposed steps.

Graphical overview of 13 proposed steps for developing a clinical prediction model. TRIPOD=transparent reporting of a multivariable prediction model for individual prognosis or diagnosis

In principle, most steps we have described apply to traditional statistical and machine learning approaches, 14 with some exceptions. For example, the structure of a machine learning model is often defined during model development and so will not be known a priori. Consequently, using the final model for multiple imputations, as we discussed in step 7, might not be possible. Further, bootstrapping, which we recommended as the method of choice for internal validation, might not be computationally feasible for some machine learning approaches. Moreover, some machine learning approaches might require additional development steps to ensure calibration. 94 121 122

We trust that our presentation of the key concepts and discussion of topics relevant to the development of clinical prediction models will help researchers to choose the most sensible approach for the problem at hand. Moreover, the paper will hopefully increase awareness among researchers of the need to work in diverse teams, including clinical experts, methodologists, and future model users. Similar to guidance on transparent reporting of research, adopting methodological guidance to improve the quality and relevance of clinical research is a responsibility shared by investigators, reviewers, journals, and funders. 123

Contributors: OE conceived the idea of the project and wrote the first draft of the manuscript. KC performed the analysis of the real example in relapsing-remitting multiple sclerosis. MS and OE prepared the online supplement. ME and GS contributed concepts and revised the manuscript. All authors contributed to the final manuscript. OE is the guarantor of the article. ME and GS contributed equally to the manuscript as last authors. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted.

Funding: OE and MS were supported by the Swiss National Science Foundation (SNSF Ambizione grant 180083). ME was supported by special project funding from the SNSF (grant 32FP30-189498) and funding from the National Institutes of Health (5U01-AI069924-05, R01 AI152772-01). KC and GS were supported by the HTx project, funded by the European Union's Horizon 2020 research and innovation programme, 825162. The funders had no role in considering the study design or in the collection, analysis, interpretation of data, writing of the report, or decision to submit the article for publication.

Competing interests: All authors have completed the ICMJE uniform disclosure form at www.icmje.org/disclosure-of-interest/ and declare support from the Swiss National Science Foundation, National Institutes of Health, and European Union's Horizon 2020 research and innovation programme for the submitted work; no financial relationships with any organisations that might have an interest in the submitted work in the previous three years; no other relationships or activities that could appear to have influenced the submitted work.

Provenance and peer review: Not commissioned; externally peer reviewed.

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0/ .

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Article  

• Volume 15, issue 2
• MS, 15, 515–529, 2024
• Related articles

Task-driven geometric synthesis method of a bistable compliant mechanism for the rigid guidance problem

Jingyu jiang, hanchao wang.

Compliant bistable mechanisms are specialized mechanisms that have specific self-locking characteristics in two positions. They are widely used in aerospace, micro-electromechanical systems, and high-precision manufacturing. The coupling of kinematic with elastomechanical behaviors of compliant mechanisms, known as kinetostatics, increases the difficulty of synthesizing compliant mechanisms. Currently, most research relies on optimization approaches to find compliant mechanisms that meet motion requirements. To address this challenge, this paper proposes a geometric synthesis method for compliant bistable mechanisms to solve the rigid guidance problem. The pole similarity transformation characteristics of planar beams and the static equilibrium characteristic of bistable mechanisms at stable positions are utilized to decouple the kinematic synthesis and static analysis. The proposed method introduces a task-driven synthesis process, where the critical structural parameters in compliant mechanisms are determined based on the desired guidance positions of motion tasks. This approach eliminates the need for a tedious and time-consuming iterative optimization process. The resulting bistable mechanisms have two stable positions that correspond to the desired guidance positions of the motion task. To illustrate the effectiveness of the geometric synthesis method, a two-position problem of a compliant bistable mechanism is provided as an example.

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Jiang, J., Lin, S., and Wang, H.: Task-driven geometric synthesis method of a bistable compliant mechanism for the rigid guidance problem, Mech. Sci., 15, 515–529, https://doi.org/10.5194/ms-15-515-2024, 2024.

The synthesis of mechanisms has long been a topic of study in the field of rigid mechanisms. One classic problem in this area is the rigid guidance problem, which has been extensively researched for hundreds of years. Various efficient and accurate synthesis methods, such as the geometric method, analytical method, and atlas method, have been proposed to address this problem ( McCarthy and Soh ,  2010 ) . However, when it comes to compliant mechanisms, the situation is different. The motion transmission in compliant mechanisms primarily relies on the deformation of compliant components (usually planar beams) under external forces. This unique characteristic makes it challenging to independently figure out kinematic design and static analysis, posing significant challenges in the synthesis of compliant mechanisms ( Howell et al. ,  2013 ; Lobontiu ,  2002 ) .

If the length of the compliant components is similar to the length of the rigid components, the geometric nonlinearity caused by large deformation must be considered ( Kimball and Tsai ,  2002 ) . At present, many method have developed to analyze the large deflection of planar beams, such as the elliptical integral method, pseudo-rigid-body model (PRBM) and beam constraint model (BCM). The elliptic integral method is a classic solution for high-precision large deformation problems of planar beams. This method originated from the elastica problem and was introduced into the analysis of compliant mechanisms to solve the large deflection problem under different tip loads ( Shoup and McLarnan ,  1971 ) . Zhang and Chen ( 2013 ) have extended this method and provided a comprehensive solution of elliptic integrals for large deflection problems, which can solve the problem of multiple inflection points in compliant beam deformation. Holst et al. ( 2011 ) and others improved the accuracy of the elliptic integral method by in troducing axial deflection and applying it to fixed-guidance beams. Although the final results of the elliptic integral method need to be obtained through elliptic integral tables, as an analytical solution for large deflection problems, the method provides the most accurate results for compliant beam deformation. Based on the elliptic integral method, Wang and Xu ( 2017 ) conducted an analysis of the kinetostatics of an XY micro-positioning stage with negative stiffness. Based on the results of the elliptic integral method, Midha et al. ( 2000 ) proposed a pseudo-rigid-body model (PRBM), which approximates compliant beams as a rigid link mechanism with torsion springs and decouples the kinematics and static analysis of planar beams. Howell and Midha ( 1994 ) created a synthesis approach based on PRBM, which can provide a practical means for analyzing and designing the compliant mechanisms. PRBM simplifies the geometric nonlinearity problem of compliant beams down to a very intuitive rigid mechanism model but at the cost of reducing the accuracy of motion analysis. Furthermore, several improved model, including PRBM with axial springs ( Saxena and Kramer ,  1998 ) , PRBM with variable parameters ( Dado ,  2001 ) , 2R PRBM ( Yu et al. ,  2012 ) , 3R PRBM ( Su ,  2009 ; Lin et al. ,  2021 ) , and 5R PRBM ( Yu and Zhu ,  2017 ) , were proposed and applied in the design of compliant mechanisms with large deflection. Various compliant mechanisms with special characteristics, including compliant beams with inflection points ( Zhu and Yu ,  2017 ) , compliant beams with contact ( Jin et al. ,  2020 ) , three-dimensional (3D​​​​​​​) compliant beam deformation ( Chase et al. ,  2011 ) , and initially curved compliant beam deformation ( Kalpathy Venkiteswaran and Su ,  2017 ) , can be analyzed and designed using PRBM. Another widely used method for modeling compliant mechanism is the beam constraint model (BCM). BCM, proposed by Awtar et al. ( 2006 ) , provides a closed-form model of planar beam within an intermediate deformation range. Ma and Chen ( 2015 ) proposed a chain-beam constraint model (CBCM) to solve large deformation problems based on the BCM. CBCM can obtain the displacement at each node on the planar beam, making it more suitable for general compliant mechanism design problems. Besides, the energy-minimization-based kinetostatic solutions are also used in the design of compliant mechanism. For example, Turkkan and Su ( 2017 ) , Turkkan et al. ( 2018 ) , and Jiang et al. ( 2023 ) have all proposed design methods for compliant mechanisms based on the principle of minimum potential energy combined with optimization methods. Chen et al. ( 2017 ) also proposed a design method for compliant mechanisms based on the Crotti–Engesser theorem.

Bistable mechanisms are a type of compliant mechanism with special energy characteristics. Within their range of motion, there are positions or deformed states with local minima of strain energy, which are referred to as the stable positions or stable equilibrium positions of the mechanism. The mechanism can remain in a stable equilibrium position without relying on external forces and can return to the stable equilibrium position after being disturbed by external forces. This self-sustaining characteristic of compliant bistable mechanisms makes them highly valuable in specific rigid guidance problems. Currently, the most common design method for bistable mechanisms is to utilize the buckling characteristic of planar beams. Sönmez and Tutum ( 2008 ) and Zhao et al. ( 2008 ) established models of bistable mechanisms with hinged and fixed connections at both ends of a buckled beam. To avoid higher-order buckling states during deformation, Qiu et al. ( 2004 ) , Hussein et al. ( 2019 ) , Hussein et al. ( 2020 ) , and Haddab et al. ( 2018 ) proposed buckling models of curved beams and used them to create linear bistable mechanisms. In order to provide more adjustable parameters for the design of bistable mechanisms, scholars such as Parkinson et al. ( 2000 ) , Chen et al. ( 2021 ) , Todd et al. ( 2010 ) , and Tran and Wang ( 2017 ) proposed multi-segment planar beam bistable mechanisms. Another method to obtain the desired mechanical performance of bistable mechanism is using the planar beams with special shapes based on topology optimization ( Chen et al. ,  2019 ) or other optimization method ( Chi et al. ,  2019 ) . Building upon this, to address the issue of axial stiffness reduction after buckling of planar beams, Nathan and Howell ( 2003 ) , Wilcox and Howell ( 2005 ) , Han et al. ( 2017 ) , and others proposed bending-torsion planar beam configurations for designing planar bistable mechanisms with linear motion. Additionally, Jiang et al. ( 2024 ) proposed a synthesis method of series-based bistable compliant mechanisms for the rigid-body guidance problem based on the geometrical similarity transformation. Sargent et al. ( 2020 ) proposed a bistable mechanism used in medical support systems based on origami. Huang et al. ( 2020 ) designed a special linear bistable mechanism which only need one actuator to switch between two stable positions.

As mentioned above, a large number of compliant mechanism design methods have proposed and successfully applied in the design of various compliant mechanisms. Most of these methods still start from the analysis of mechanisms and find the optimal mechanisms that meet the motion task requirements through numerical optimization, especially in the field of bistable mechanism design. It is still difficult to simultaneously consider the accuracy and efficiency in large-deformation compliant mechanism design, and it is even more difficult to adjust the structural parameters of the mechanism with purpose based on motion tasks. Therefore, this paper proposes a synthesis method for the compliant bistable mechanism based on the pole similarity transformation. This method utilizes the special properties in the geometric transformation process of planar beams and the static equilibrium characteristics of stable positions in bistable compliant mechanism to directly select and determine the structural parameters in compliant mechanisms according to the given motion tasks. The synthesis of compliant mechanism rigid guidance problems with two stable positions is completed through this method.

The organization of paper is as follows: Sect.  2 presents the basic theories involved in this paper, including the deformation behavior of planar beams, the solution of the poles of planar beams, and the similarity transformation characteristics of planar beams. Section  3 introduces the synthesis method for two-position bistable mechanisms, including the description of motion tasks, the solution of the mechanism's structural parameters, and the general process of bistable mechanism synthesis. Sections  4 and  5 provide a specific synthesis case, and the design results were validated through simulations and experiments. In Sect.  6 , we discuss the experimental results and propose future research directions.

Planar beams are the primary elements in compliant mechanisms that transmit motion and force. This study initially determines the deformation behavior of planar beams. The motion of the beam’s tip is then described using the pole and pole angle. Lastly, the study presents the similarity transformation characteristics of the pole, which establishes the relationship between the structural parameters of planar beams and the motion of the beams' tips.

2.1  Analysis of planar beam's deformation behavior

The deformation of the planar beam in this paper is based on the Bernoulli–Euler beam theory, in which the relationship between the sectional bending moment and the beam curvature of the planar beam is as follows:

where M b represents the bending moment of the cross section, d θ / d s represents the angular deformation rate (curvature) along the beam, E represents Young’s modulus of the material, and I represents the moment of inertia of the beam. The curvature, κ , can be further calculated by the deformation of a flexible beam as follows:

As shown in Fig.  1 , for a planar beam subjected to concentrated loads and bending moments at the beam's tip, the sectional bending moment on the beam can be calculated using loads and the coordinates of the deformed beam as follows:

where F x = F cos ( φ ) represents the component of the load in the x direction and F y = F sin ( ϕ ) represents the component of the load in the y direction. ϕ is the angle between the load F and the x direction. ( a , b ) represents the coordinates of the end of the beam after deformation. In addition, as shown in Fig.  1 , an equivalent action line of force, ℓ F , can be found, which is at distance d e from the end of the beam, where d e = M e / F .

Figure 1 The deformation and bending moment diagram of the planar beam under the loads.

By substituting Eq. ( 3 ) into Eq. ( 1 ) and differentiating both sides of the equation, we obtain the following:

Since d x / d s = cos θ and d y / d s = sin θ , Eq. ( 4 ) can be further simplified as follows:

After applying the chain rule of differentiation, the left side of Eq. ( 5 ) can be written as follows:

By substituting d θ / d s = κ into Eq. ( 6 ), we obtain

By substituting Eq. ( 7 ) into Eq. ( 5 ) and integrating both sides of the equation, we obtain the following:

At θ = θ e , we can establish the boundary condition – that is, κ e = M e / ( E I ) ; therefore, we can obtain the following:

By substituting Eq. ( 9 ) into Eq. ( 8 ), we obtain the following:

We define the first term of Eq. ( 11 ) as the load ratio, η , of the planar beam as follows:

When φ ∈ [ 0 , π ] , with α 2 = F L 2 sin φ / ( E I ) , Eq. ( 10 ) can be rewritten as

By separating variables and integrating Eq. ( 13 ), we can obtain the relationship between α and the rotational angle, θ e , as follows:

When the angle of loads, φ ∈ [ 0 , π ] ; the rotational angle, θ e ; and the load ratio, η , are provided, the load of the planar beam, F , can be calculated as follows:

The coordinates of the beam's tip can be calculated as follows:

Similarly, when the angle of loads is φ ∈ ( π , 2 π ] , with α 2 = - F L 2 sin φ / ( E I ) , we have

2.2  Position changes of the beam's tip described by the pole

As shown in Fig.  2 , the relative positional relationship between the beam's tip positions, B 1 and B 2 , can be described by pole P and its corresponding rotation angle, ϑ . According to the definition of the pole, the position coordinates of pole P and the rotation angle, ϑ , can be calculated by the following formulas:

where B 1 = L + i 0 represents the tip position of the planar beam in its natural state and B 2 = a + i b represents the tip position of the planar beam carrying the tip loads F and M e . Expanding this formula yields the coordinates of the pole as follows:

Moment M O of the planar beam at frame O is

where M e = 2 F η E I sin φ . The position of the equivalent load line, ℓ F , can be determined by its intersection point with the x  axis, R , as follows:

The distance, d P , between pole P and the equivalent load line, ℓ F can be calculated by the vector product of the vector R P and equivalent load line, ℓ F , as follows:

Figure 2 The pole of the deformed planar beam.

2.3  The similarity transformation characteristics of planar beams

Pole P of the planar beam completely describes the relative position of the beam's tip. For any planar beam, the rotation direction of the beam's tip, the position of the pole, the distance between the pole and equivalent load line, and the rotation angle of the equivalent load line can be adjusted by the similarity transformation.

2.3.1  Changing the rotation direction through mirror transformation

Planar beams can change the rotation direction by mirroring the load along the x  axis. As shown in Fig.  3 a, to change the rotation direction of the planar beam, the equivalent force line of the planar beam, ℓ F ′ , needs to flipped along the x  axis. In this scenario, the load angle is φ ′ = - φ , the pole position ( x P ′ , y P ′ ) = ( x P , - y P ) , and the pole angle ϑ ′ = - ϑ .

Figure 3 The similarity transformation of deformed planar beam: (a)  mirror transformation, (b)  translation transformation, (c)  rotation transformation, and (d)  scale transformation.

2.3.2  Changing the pole position through translation transformation

Planar beams can adjust the pole position by translating the frame, O . As shown in Fig.  3 b, when pole P of the beam is translated along vector τ , its tip position, ( a ′ , b ′ ) ; equivalent force line, ℓ F ′ ; and frame, O ′ , also undergo the same translation motion. After translation, the magnitude of the load, F ′ ; the angle of the equivalent force line, φ ′ ; and the distance from pole to the equivalent force line, d P ′ , all remain unchanged.

2.3.3  Changing the angle of equivalent force line through rotation transformation

Planar beams can adjust the angle of the equivalent force line by rotating the frame O . As shown in Fig.  3 c, when the frame O rotates around the pole by an angle, γ , its tip position, ( a ′ , b ′ ) , and the equivalent force line, ℓ F ′ , also undergo the same rotational motion. After rotation, the magnitude of load F ′ and the distance from the pole to the equivalent force line d P ′ remain unchanged. The angle between the equivalent force line and the positive direction of the x  axis changes to φ ′ = φ + γ .

2.3.4  Changing the distance from pole to the equivalent force line through scale transformation

The planar beam can adjust the distance from pole to the equivalent force line by proportionally changing the beam's length, L . As shown in Fig.  3 d, when the beam's length is scaled by proportion μ , according to Eqs. ( 16 ), ( 15 ), and ( 19 ), the scaled beam's tip position is ( a ′ , b ′ ) = ( μ a , μ b ) , the scaled pole position ( x P ′ , y P ′ ) = ( μ x P , μ y P ) , and the scaled loads F ′ = F / μ 2 . On this basis, by substituting scaled parameters ( a ′ , b ′ ) , ( x P ′ , y P ′ ) , and F ′ into Eqs. ( 20 ), ( 21 ), and ( 22 ), it can be concluded that the scaled distance from the pole to equivalent force line is d P ′ = μ d P .

Through the analysis of the deformation behavior of the planar beam, the load required for achieving a given beam's tip rotation is determined. The relative positional relationship between the two positions of the beam's tip is described using the pole. Through the pole similarity transformation, the pole position and the equivalent force line of the beam can be flexibly adjusted within the motion plane. In order to ensure that the rigid components of the compliant mechanism are in a stable state at specified positions, it is necessary to arrange the planar beams of the compliant mechanism into suitable positions. This paper utilizes the characteristics of the similarity transformation to adjust the pole position of the planar beams, ultimately establishing a synthesis method for the rigid-body guidance problem of compliant bistable mechanisms.

3.1  The motion task and structural characteristic of the designed compliant mechanism

Figure  4 shows two stable positions of the bistable mechanism that needs to be designed in this paper, which consists of three planar beams and two rigid components. In the natural state, the flexible beams are located at O a B 1 a , O b B 1 b , and O c B 1 c , respectively. The three beams are connected to the rigid components B 1 a D 1 a C 1 a O c and B 1 b D 1 b C 1 b B 1 c . O a B 2 a , O b B 2 b , and O c ′ B 2 c ′ represent the deformation states of the three planar beams when B 2 a D 2 a C 2 a O c ′ and B 2 b D 2 b C 2 b B 2 c ′ are the rigid components at the second stable position. In this paper, the two given positions of first rigid component are D 1 a C 1 a and D 2 a C 2 a , while the two given positions of the second rigid component are D 1 b C 1 b and D 2 b C 2 b , respectively. The motion task of the rigid guidance problem can be described by the poles. As shown in Fig.  5 , the pole of first component, P a , can be calculated by

while the pole of second component, P b , can be calculated by

Figure 4 The illustration of the stable positions of the compliant bistable mechanism.

Figure 5 The pole of the two different positions in the rigid-body guidance problem.

3.2  Determination of structural parameters of the designed compliant mechanism

3.2.1  the poles of planar beams in the designed compliant mechanism.

In the compliant mechanism, two planar beams, O a B 1 a and O b B 1 b , are connected to the frame on one tip and to the rigid components on the other tip, so their poles should be consistent with the poles of the motion task, P a ( ϑ a ) and P b ( ϑ b ) . The two tips of the third planar beam, O c B 1 c , are connected to two rigid components, respectively; thus, there are two poles, P c and P c ′ , that correspond to two stable equilibrium positions. As shown in Fig.  6 , pole P c ′ can be viewed as the result of rotating P c around P a by ϑ a or as the result of rotating P c around P b by ϑ b . Therefore, P c and P c ′ are symmetric in relation to the line P a P b . When we know the poles of two rigid components, we connect the poles P a and P b , rotate P a P b around P a by ϑ a , and then rotate P a P b around P b by ϑ b . The intersection of the two lines is the first pole of the third beam, P c . Similarly, when P a P b is rotated around P a and P b by − ϑ a and − ϑ b , respectively, the intersection is the second pole of the third beam P c ′ . The pole of third beam represents the relative angle between two rigid components, which is known from the characteristic of the polar triangle, i.e., the rotation angle ϑ c = - ϑ a + ϑ b .

Figure 6 The pole of the three planar beams of the compliant mechanism in the motion generation problem.

3.2.2  The structural parameters of the designed compliant mechanism

After determining the poles of each planar beam, it is necessary to determine the dimensional parameters and installation positions of the planar beams in the compliant mechanism. The process is as follows:

Determination of the load balance line. The first stable position of the bistable compliant mechanism is the natural state of the mechanism, in which the planar beams are not subjected to external forces. When the compliant mechanism is in the second stable position, the equilibrium of the mechanism is achieved through the interaction forces between the beams. Therefore, in order to ensure that the compliant mechanism maintains balance in the second stable position, the equivalent instances of the force line of the three compliant beams, ℓ F k , need to coincide, and the coinciding position is the load balance line, ℓ B .

As shown in Fig.  7 , due to the opposite rotation directions of the two planar beams connected to the frame, the directions of their loads, F a and F b , are also opposite. In order to ensure the balance of forces on the rigid components, load F c on the third beam has the same direction as F a . The position and angle of the load balance line can be arbitrarily given, but it needs to ensure that the load balance line, ℓ B , passes through two edges, P a P c ′ and P b P c ′ , of the pole triangle P a P b P c ′ . After the load balance line is selected, the load directions of each beam in the x O y coordinate system are already determined – that is, the directions of F a and F c are ϕ a = ϕ c = ϕ , and the direction of F b is ϕ b = ϕ - π . Based on this, the distances d PB a , d PB b , and d PB c between the poles of planar beams and the load balance line are also determined.

The initial solution of planar beams. The rotation angle of the beam's tip, θ e k , is determined by the pole angle of each beam. To avoid negative curvature, a mirror transformation is required for the planar beam with negative pole rotation. Taking Fig.  6 as an example, beams b and c need to be reversed using a mirror transformation. The rotation angle of the planar beams can be calculated by

The elastic modulus, E , of the planar beam needs to be determined based on the selected material, and the section height, h 0 k ; section width, b 0 k ; beam length, L 0 k ; load ratio, η 0 k ; and load angle, φ 0 k , of each planar beam can be arbitrarily chosen. After parameter selection, as shown in Fig.  8 , the position of the pole, P 0 k , the load magnitude, F 0 k , and the distance from the equivalent force line to the pole of the planar beam, d 0 k , can be calculated according to the procedures in Sect. 2.1 and 2.2. The calculated result is the initial solution of the planar beam.

The similarity transformation of planar beam. To meet the requirements of the motion task, pole P 0 k and the equivalent force line of the planar beams, ℓ F k , need to be transformed to the suitable positions ( P k and ℓ B ) in the compliant mechanism. For each planar beam, four steps of the pole similarity transformation are required.

Translation transformation. Pole P 0 k of the planar beam k is moved to the origin, and the translation vector τ 1 k = - P 0 k , where k ∈ { a , b , c } .

Scale transformation. In order to ensure that d P k = d PB k , planar beam k is subjected to a scale transformation with a scaling factor, μ k = d PB k / d 0 k , where k ∈ { a , b , c } . After the scaling transformation, the load magnitude of the planar beam also changes to F 1 k = F 0 k / ( μ k ) 2 .

Rotation transformation. In order to make ℓ F k parallel to ℓ B , planar beam k needs to undergo a rotation transformation with an angle of γ k = ϕ k - φ 0 k , where k ∈ { a , b , c } .

Translation transformation. The rotated planar beam, k , needs to be translated back to the pole of the compliant mechanism, and the translation vector is τ 2 k = P k , where k ∈ { a , b , c } .

Determination of the beams' width. After the similarity transformation, the load position and motion of the planar beam already satisfy the requirements of the compliant bistable mechanism. In order to ensure that the static equilibrium condition is satisfied at the second stable position, it is necessary to adjust the width of the planar beam b k to unify the load magnitude, F k . According to the scaled load, F 1 k , of each planar beam k , the equilibrium load at the second stable position of the compliant mechanism, F m , is selected. According to Eq. ( 15 ), the tip load of the planar beam is proportional to the inertia moment, I . For the rectangular cross section, the inertia moment, I , is proportional to the width of the cross section. Therefore, the cross-section width of each planar beam k is adjusted in proportion to the load magnitude, F 1 k , and equilibrium load F m – that is, b k = v k b 0 k , where v k = F m / F 1 k .

Figure 7 The loads balanced line of compliant bistable mechanism.

Figure 8 The initial solutions of three planar beams in compliant bistable mechanism.

3.3  The synthesis process of the bistable compliant mechanism

Based on the pole similarity transformation, the synthesis process of the bistable compliant mechanism is shown in Fig.  9 . First, the poles and corresponding pole angles of the rigid components and planar beams in the compliant mechanism are determined based on the given positions of the motion task. Second, the load balance line and the magnitude of the equilibrium load for the compliant mechanism are selected. Then, the initial solution of the planar beams based on the geometric and mechanical features is obtained, and so are the compliant mechanism solution that satisfies the motion task requirements and static equilibrium conditions through similarity transformation. Finally, output the relevant parameters of the planar beams and rigid components in the compliant mechanism for the specific design of the compliant mechanism. After defining the input and output of the program, this synthesis process can be automatically completed using MATLAB software.

Figure 9 General synthesis process of compliant bistable mechanism.

This section takes the planar two-position rigid-body guidance mechanism as an example and designs a bistable compliant mechanism based on the proposed synthesis process. The guidance positions of the rigid components are D 1 a C 1 a , D 2 a C 2 a and D 1 b C 1 b , D 2 b C 2 b . Table  1 shows the motion task parameters.

Table 1 Parameters of motion task.

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According to the proposed synthesis process, the geometric features of the motion task and the compliant mechanism are first extracted. Poles P a and P b are determined according to Eqs. ( 23 ) and ( 24 ). Poles P c and P c ′ are obtained by rotation and pole angle of ϑ c = - ϑ a + ϑ b . The specific results are shown in Table  2 .

Table 2 Geometric features of the motion task and the compliant mechanism.

The position of the load balance line is selected according to the position of the poles. The load balance line passes through points (0.5 cm, 2.5 cm) and (8.5 cm, 4.5 cm), and ϕ   =  194.04°. The magnitude of equilibrium load is F m   =  0.5 N. The distance from poles P a , P b , and P c ′ to the load balance line, ℓ B , is determined to be d PB a   =  0.606 cm, d PB b   =  0.606 cm, and d PB c   =  0.666 cm, respectively. The material selected for the planar beams is 65Mn spring steel, with an elastic modulus of E   =  210 000 MPa.

The initial parameters of the planar beams need to be selected, including the initial length, L 0 k   =  1 cm; initial width, b 0 k   =  0.1 cm; and initial height, h 0 k   =  0.005 cm. The load ratio, η 0 k , and angle of equivalent force line, ϕ 0 k , are shown in Table  3 . Based on these parameters, the initial solutions of the planar beams are determined. As shown in Table  4 , the similarity transformation parameters of the three beams are calculated according to Sect.  3.2.2 . After transforming the planar beams to the corresponding pole positions, all parameters of the compliant mechanism can be determined. The specific result can be found in Table  5 and Fig.  10 .

Table 3 Parameters for the initial solution of compliant mechanism.

Table 4 Similarity transformation parameters of compliant mechanism.

Table 5 Parameters of final solution of compliant mechanism.

Figure 10 The synthesis results of compliant bistable mechanism and their comparison with finite-element analysis (FEA).

The synthesis process of bistable compliant mechanism for the rigid-body guidance problem is completed. The designed compliant mechanism is modeled in finite-element analysis (FEA) software to verify the motion accuracy and bistable characteristics. As shown in Fig.  11 a, the models of planar beams are imported into the FEA software and establish rigid constraints between the beams to simulate the connection of rigid components in the compliant mechanism. Two reference points are established at D 1 a and D 1 b , and they are fixed to the tips of slender beams a and b . The rotation constraint is applied at the reference points of D 1 a , and the first rigid component is driven to rotate counterclockwise by Δ β a   =  35°, indicating that the mechanism will reach and surpass the second stable position. The deformation of the mechanism at the initial position and the second stable position is shown in Fig.  11 b. The strain energy of the mechanism and the second rigid component's motion during the movement are shown in Fig.  12 . It can be observed that in the simulation, the strain energy of the mechanism reaches a local minimum when the rotation angle of the first rigid component reaches 30°. At this point, the rotation angle of the second rigid component is − 40°, and the coordinates of reference points D 1 a and D 1 b are (1.87 cm, 2.50 cm) and (8.23 cm, 4.64 cm), respectively, indicating that the designed mechanism meets the requirement of stable positions in the motion task. The beam's shape of the second stable position in the simulation is shown in Fig.  10 .

Figure 11 The FEA results regarding the strain energy of the compliant mechanism.

Figure 12 The FEA results regarding the strain energy of the compliant mechanism and second rigid component's motion.

The prototype is manufactured according to the synthesis results. As shown in Fig.  13 , the frame and rigid components in the mechanism are manufactured through 3D printing. The planar beams are made of spring steel (65Mn). The planar beams and rigid components are securely fastened together using bolted connections. Three yellow markers are added to the frame and rigid components using 3D printing. The second stable position of the prototype is shown in Fig.  13 . The red markers in the figure represent the results from the finite-element analysis at the second stable position, and it can be observed that the deformation of the planar beams in the prototype is consistent with the simulation results.

Figure 13 The prototype and the comparison of the beams' shape at the second stable position with FEA results.

We utilize monocular ranging algorithm to calculate the stable position of the rigid components in the prototype. As shown in Fig.  14 , image-processing techniques are employed to identify the markers on the frame and rigid components. The three markers on the frame are used to determine the origin and orientation of the coordinate system for the prototype. The positions of the markers on the rigid components can be calculated through coordinate transformation. The pole angles and the location of the poles are calculated by the markers. Any two markers on the same rigid component can form a directed line segment. By utilizing the positional relationship of directed line segments between two stable positions, a pole and its corresponding pole angle can be determined. The results are presented in Table  6 . The maximum error for the location of the pole is 3.82 %, and the maximum error for the pole angle is 4.92 %.

Figure 14 The marker detection results of the two stable positions.

Table 6 The pole angles and location of poles of the prototype.

Due to the self-holding characteristic of the bistable mechanism, the driving force or torque of the mechanism has significant features. There are three states with zero driving force between the two stable positions, which corresponds to the positions of minimum and maximum strain energy. To measure the driving torque of the prototype, an experimental platform is set up as shown in Fig.  15 . The first rigid component is made to rotate using a servo motor in position mode. The driving torque is recorded using a torque sensor. The experiment is repeated three times, and the comparison between the experimental results and the simulation is shown in Fig.  16 . It can be seen that the results of the three experiments show good consistency. Throughout the motion process, the driving torque has three intersections with the x  axis, verifying the bistable characteristic of the mechanism. The first intersection is located at the initial position with a driving angle of Δ β a   =  0°, and the third intersection is located at the second stable position with a driving angle of approximately Δ β a   =  30°, which is consistent with the design goal. The second intersection is located at a driving angle of Δ β a   =  26°, which is greater than the simulated result of 25°. This is mainly caused by manufacturing and assembly errors in the prototype.

Figure 15 The platform of the driving torque experiment.

Figure 16 The comparison of the driving torque between experiments and simulation.

Poles are a geometric tool that can accurately describe multiple planar positions, and they can reveal the relationship between guidance mechanisms and given design tasks. Based on the similarity transformation of poles, this paper proposes a novel synthesis method for compliant bistable mechanisms. The synthesis example and results of simulation and prototype experiments have demonstrated the effectiveness of the proposed method. Regarding the proposed design method, future research can focus on the following two aspects:

Study on the energy and mechanical characteristics of the intermediate states in bistable mechanisms . The proposed method can design the stable positions of the mechanism based on the motion task. However, the maximum strain energy and maximum driving force between the two stable positions of the mechanism also have important research value. How to incorporate the calculations of these intermediate characteristics into the overall process of mechanism synthesis will be a key issue for future research.

Research on integrated manufacturing methods for mechanisms . One important advantage of compliant mechanisms is their ability to be manufactured in an integrated manner, eliminating the assembly process. In the proposed method, the planar beams have different widths, which requires us to manufacture and assemble the components separately. The assembly process not only limits the size of the prototype but also introduces significant assembly errors. Exploring miniaturized integrated manufacturing methods is also one of the important research topics for future studies.

This paper proposes a novel geometrical approach to bistable compliant mechanism synthesis based on the similarity transformation of poles. The study demonstrates the feasibility of decoupling the kinematic design and static analysis processes in the synthesis of bistable compliant mechanisms. At the method level, a general synthesis process for bistable compliant mechanisms is provided, simplifying the iterative process in the design of compliant mechanisms and offering an efficient synthesis tool for general compliant bistable mechanisms. In addition, this study illustrates the synthesis approach with an example, and a prototype was made.

All the code and data used in this paper can be obtained from the corresponding author upon request.

JJ and SL proposed the methodology. HW took part in the discussion of the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The authors would like to thank anonymous reviewers for their valuable comments and suggestions that enabled them to revise the paper.

This research has been supported by the Natural Science Foundation of Fujian Province (grant no. 2022J05246).

This paper was edited by Engin Tanık and reviewed by two anonymous referees.

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• Introduction
• Theoretical basis
• Synthesis method
• Synthesis example
• Simulation and experiments
• Conclusions
• Code and data availability
• Author contributions
• Competing interests
• Acknowledgements
• Financial support
• Review statement

• Systematic Review
• Open access
• Published: 30 August 2024

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Stroke is a leading cause of mortality and disability. In higher-income countries, mortality and disability have been reduced with advances in stroke care and early access to rehabilitation services. However, access to such services and the subsequent impact on stroke outcomes in the Philippines, which is a lower- and middle-income countries (LMIC), is unclear. Understanding gaps in service delivery and underpinning research from acute to chronic stages post-stroke will allow future targeting of resources.

This scoping review aimed to map available literature on stroke services in the Philippines, based on Arksey and O’Malley’s five-stage-process.

Summary of review

A targeted strategy was used to search relevant databases (Focused: MEDLINE (ovid), EMBASE (ovid), Cumulative Index to Nursing and Allied Health Literature (CINAHL), PsycINFO (ebsco); broad-based: Scopus; review-based: Cochrane Library, International Prospective Register of Systematic Reviews (PROSPERO), JBI (formerly Joanna Briggs Institute) as well as grey literature (Open Grey, Google scholar). The searches were conducted between 12/2022-01/2023 and repeated 12/2023. Literature describing adults with stroke in the Philippines and stroke services that aimed to maximize well-being, participation and function were searched. Studies were selected if they included one or more of: (a) patient numbers and stroke characteristics (b) staff numbers, qualifications and role (c) service resources (e.g., access to a rehabilitation unit) (d) cost of services and methods of payment) (e) content of stroke care (f) duration of stroke care/rehabilitation and interventions undertaken (g) outcome measures used in clinical practice.

A total of 70 papers were included. Articles were assessed, data extracted and classified according to structure, process, or outcome related information. Advances in stroke services, including stroke ready hospitals providing early access to acute care such as thrombectomy and thrombolysis and early referral to rehabilitation coupled with rehabilitation guidelines have been developed. Gaps exist in stroke services structure (e.g., low number of neurologists and neuroimaging, lack of stroke protocols and pathways, inequity of stroke care across urban and rural locations), processes (e.g., delayed arrival to hospital, lack of stroke training among health workers, low awareness of stroke among public and non-stroke care workers, inequitable access to rehabilitation both hospital and community) and outcomes (e.g., low government insurance coverage resulting in high out-of-pocket expenses, limited data on caregiver burden, absence of unified national stroke registry to determine prevalence, incidence and burden of stroke). Potential solutions such as increasing stroke knowledge and awareness, use of mobile stroke units, TeleMedicine, TeleRehab, improving access to rehabilitation, upgrading PhilHealth and a unified national long-term stroke registry representing the real situation across urban and rural were identified.

This scoping review describes the existing evidence-base relating to structure, processes and outcomes of stroke services for adults within the Philippines. Developments in stroke services have been identified however, a wide gap exists between the availability of stroke services and the high burden of stroke in the Philippines. Strategies are critical to address the identified gaps as a precursor to improving stroke outcomes and reducing burden. Potential solutions identified within the review will require healthcare government and policymakers to focus on stroke awareness programs, primary and secondary stroke prevention, establishing and monitoring of stroke protocols and pathways, sustainable national stroke registry, and improve access to and availability of rehabilitation both hospital and community.

What is already known?

Stroke services in the Philippines are inequitable, for example, urban versus rural due to the geography of the Philippines, location of acute stroke ready hospitals and stroke rehabilitation units, limited transport options, and low government healthcare insurance coverage resulting in high out-of-pocket costs for stroke survivors and their families.

What are the new findings?

The Philippines have a higher incidence of stroke in younger adults than other LMICs, which impacts the available workforce and the country’s economy. There is a lack of data on community stroke rehabilitation provision, the content and intensity of stroke rehabilitation being delivered and the role and knowledge/skills of those delivering stroke rehabilitation, unmet needs of stroke survivors and caregiver burden and strain,

What do the new findings imply?

A wide gap exists between the availability of stroke services and the high burden of stroke. The impact of this is unclear due to the lack of a compulsory national stroke registry as well as published data on community or home-based stroke services that are not captured/published.

What does this review offer?

This review provides a broad overview of existing evidence-base of stroke services in the Philippines. It provides a catalyst for a) healthcare government to address stroke inequities and burden; b) development of future evidence-based interventions such as community-based rehabilitation; c) task-shifting e.g., training non-neurologists, barangay workers and caregivers; d) use of digital technologies and innovations e.g., stroke TeleRehab, TeleMedicine, mobile stroke units.

Peer Review reports

Introduction

In the Philippines, stroke is the second leading cause of death, with a prevalence of 0·9% equating to 87,402 deaths per annum [ 1 , 2 ]. Approximately 500,000 Filipinos will be affected by stroke, with an estimated US$350 million to $1·2 billion needed to meet the cost of medical care [ 1 ]. As healthcare is largely private, the cost is borne out-of-pocket by patients and their families. This provides a major obstacle for the lower socio-demographic groups in the country.

Research on implementation of locally and regionally adapted stroke-services and cost-effective secondary prevention programs in the Philippines have been cited as priorities [ 3 , 4 ]. Prior to developing, implementing, and evaluating future context-specific acute stroke management services and community-based models of rehabilitation, it was important to map out the available literature on stroke services and characteristics of stroke in the Philippines.

The scoping review followed a predefined protocol, established methodology [ 5 ] and is reported according to the Preferred Reporting Items for Systematic Review and Meta-Analyses Extension for Scoping Reviews Guidelines (PRISMA-ScR) [ 6 , 7 ]. Healthcare quality will be described according to the following three aspects: structures, processes, and outcomes following the Donabedian model [ 8 , 9 ].The review is based on Arksey and O'Malley’s five stages framework [ 5 ].

Stage 1: The research question:

What stroke services are available for adults within the Philippines? The objective was to systematically scope the literature to describe the availability, structure, processes, and outcome of stroke services for adults within the Philippines.

Stage 2: Identifying relevant studies:

The following databases were searched. Focused: MEDLINE, EMBASE, Cumulative Index to Nursing and Allied Health Literature (CINAHL), PsycINFO; broad-based: Scopus; review-based: Cochrane Library, Prospero, JBI (formerly Joanna Briggs Institute); Grey literature: Herdin, North Grey, Grey matters, MedRxiv, NIHR health technology assessment, Department of Health Philippines, The Kings Fund, Ethos, Carrot2. Additionally, reference lists of full text included studies were searched.

The targeted search strategy, developed in consultation with an information scientist, was adapted for each database (see supplemental data). Search terms were peer reviewed using the PRESS (Peer Review of Electronic Search Strategies) checklist [ 10 ].

The key search concepts from the Population, Concept and Context (PCC) framework were ≥ 18 years with a stroke living in the Philippines ( population ), stroke services aiming to maximize well-being, participation and function following a stroke ( concept ) and stroke services from acute to chronic including those involving healthcare professionals, non-healthcare related personnel or family or friends ( context ). Search tools such as medical subject headings (MESH) and truncation to narrow or expand searches were used. Single and combined search terms were included (see supplemental data). The search was initially conducted over two weeks in December 2022 and re-run in December 2023.

Studies were selected if they described stroke care in the Philippines in terms of one or more of the following: (a) patient numbers and stroke characteristics (b) staff numbers, qualifications and role (c) service resources (e.g., number of beds/access to a rehabilitation unit, equipment used) (d) cost of services and methods of payment (UHC, Insurance, private) (e) content of stroke care (f) duration of stroke care (hours of personnel contact e.g., Therapy hours per day); interventions undertaken (g) outcome measures used in clinical practice.

Additional criteria:

Context: all environments (home, hospital, outpatients, clinic, academic institute).

Date limits: published between 2002 onwards. This is based on the Philippines Community Rehabilitation Guidelines published in 2009 that would suggest that papers earlier than 2002 may not reflect current practice [ 11 ].

Qualitative and quantitative studies including grey literature.

Language: reported in English or Filipino only.

Publication status: no limit because the level of rigor was not assessed.

Type of study: no limit which included conference abstracts, as the level of rigor was not assessed.

Studies were excluded if they were in non-stroke populations or the full text article could not be obtained. Conference abstracts were excluded if there were insufficient data about methods and results.

Searches of databases were performed by one researcher (JM) and searches of grey literature were performed by one researcher (AO). All retrieved articles were uploaded into Endnote X9 software™, and duplicates identified and removed before transferring them to Rayyan [ 12 ] for screening.

Stage 3: study selection

The title and abstract were selected using eligibility criteria. Two pairs of researchers independently screened abstracts and titles;(Databases: JM and AL and grey literature by AO and LF). Where a discrepancy existed for title and abstract screening, the study was automatically included for full text review and discussed among reviewers.

Two reviewers (JM and AL) undertook full-text screening of the selected studies. Discrepancies were resolved through consensus discussions without the need for a third reviewer. There were no discrepancies that required a third reviewer. Reason for exclusion were documented according to pre-determined eligibility criteria. References of included full text articles were screened by each reviewer independently and identified articles were subjected to the same screening process as per the PRISMA-ScR checklist (Fig.  1 ).

PRISMA-ScR flow diagram

Stage 4: Charting the data

Two reviewers independently extracted the data using a piloted customized and standardized data extraction form including (1) Structure: financial (e.g., costs, insurance, government funding), resources (structure and number of stroke facilities, staff (number, profession/specialism, qualifications etc.), stroke characteristics (2) Process: duration of care, content of stroke care within acute, secondary care, community, outcome measures used; (3) Outcome: survival, function, patient satisfaction, cost (admission and interventions), and (4) year of publication, geographical location (including if Philippines only or multiple international locations) and type of evidence (e.g., policy, review, observational, experimental, clinical guidelines). Critical appraisal of included studies was not undertaken because the purpose of the review was to map available evidence on stroke services available within the Philippines.

Stage 5: Collating, summarising and reporting the results

The search identified 351 records from databases and registers. A total of 70 records are included and reasons for non-inclusion are summarized in Fig.  1 .

Study descriptors

The characteristics of included studies are shown in Supplementary Material Table 1. Of the 70 included studies, 36 were observational with most being based on a retrospective review of case notes ( n  = 31), two were audits, eight were surveys or questionnaires, four were consensus opinion and/or guideline development, three were randomized controlled trial (RCT) or feasibility RCT, 1 was a systematic review, two were policy and guidelines, 11 were narrative reviews or opinion pieces, two were case series or reports and one was an experimental study.

Of the 70 studies, 32 (45.7%) were based in a single tertiary hospital site. There were only three papers based in the community (4.3%). Papers that were opinion pieces or reviews were classified as having a national focus. Of the 22 papers classified as having a national focus, 10 (45.5%) were narrative reviews/ opinion pieces (Table 1 ).

The primary focus of the research studies (excluding the 11 narrative reviews and 2 policy documents) were classified as describing structure ( n  = 8, 14%); process ( n  = 21,36.8%) or outcomes ( n  = 29, 49.2%). The structure of acute care was described in seven studies out of eight studies ( n  = 7/8 87.5%) whilst neurosurgery structures were described in one out of eight studies (12.5%). Acute care processes were described in 11 out of 21 studies ( n  = 11/21 52.3%) whilst rehabilitation processes were described in six out of 21 studies (28.6%), with three out of 21 studies primarily describing outcome measurement (14.3%). The primary focus of the outcomes were stroke characteristics (25 out of 28 papers, 89.2%) in terms of number of stroke (prevalence), mortality or severity of stroke. Measures of stroke quality of life were not reported. Healthcare professional knowledge was described in two studies ( n  = 2/28 7.1%) whilst risk factors for stroke were described in one study ( n  = 1/28, 3.6%). Carer burden was described in one study ( n  = 1/28, 3.6%).

A summary of the findings is presented in Table 2 .

This scoping review describes the available literature on stroke services within the Philippines across the lifespan of an adult (> 18 years) with a stroke. The review has identified gaps in information about structures, processes and outcomes as well as deficits in provision of stroke services and processes as recommended by WHO. These included a low number of specialist clinicians including neurologists, neuro-radiographers and neurosurgeons. The high prevalence of stroke suggests attention and resources need to focus on primary and secondary prevention. Awareness of stroke is low, especially in terms of what a stroke is, the signs/symptoms and how to minimize risk of stroke [ 25 ]. Barriers exist, such as lack of healthcare resources, maldistribution of health facilities, inadequate training on stroke treatment among health care workers, poor stroke awareness, insufficient government support and limited health insurance coverage [ 22 ].

The scoping review also highlighted areas where further work is needed, for example, descriptions and research into the frequency, intensity, and content of rehabilitation services especially in the community setting and the outcome measures used to monitor recovery and impairment. PARM published stroke rehabilitation clinical practice guidelines in 2012, which incorporated an innovative approach to contextualize Western clinical practice guidelines for stroke care to the Philippines [ 42 ]. Unfortunately, availability and equitable access to evidence-based rehabilitation for people with stroke in the Philippines pose significant challenges because of multiple factors impacting the country (e.g., geographical, social, personal, environmental, educational, economic, workforce) [ 25 , 40 , 43 ].

The number of stroke survivors with disability has not been reported previously, thus, the extent and burden of stroke from acute to chronic is unknown. The recent introduction of a national stroke registry across public and private facilities may provide some of this data [ 82 ]. The project started in 2021 and captures data on people hospitalized for transient ischemic attack or stroke in the Philippines. National stroke registries have been identified as a pragmatic solution to reduce the global burden of stroke [ 83 ] through surveillance of incidence, prevalence, and outcomes (e.g., death, disability) of, and quality of care for, stroke, and prevalence of risk factors. For the Philippine government to know the full impact and burden of stroke nationally, identify areas for improvement and make meaningful changes for the benefit of Filipinos, the registry would need to be compulsory for all public and private facilities and include out of hospital data. This will require information technology, trained workforces for data capture, monitoring and sharing, as well as governance and funding [ 83 ].

This scoping review has generated a better understanding of the published evidence focusing on availability of stroke services in the Philippines, as well as the existing gaps through the lens of Donabedian’s Structure , Process and Outcome framework. The findings have helped to inform a wider investigation of current stroke service utilization conducted using survey and interview methods with stroke survivors, carers and key stakeholders in the Philippines, and drive forward local, regional and national policy and service changes.

Conclusions

This scoping review describes the existing evidence-based relating to structure, processes and outcomes of stroke services for adults within the Philippines. The review revealed limited information in certain areas, such as the impact of stroke on functional ability, participation in everyday life, and quality of life; the content and intensity of rehabilitation both in the hospital or community setting; and the outcome measures used to evaluate clinical practice. Developments in stroke services have been identified however, a wide gap exists between the availability of stroke services and the high burden of stroke in the Philippines. Strategies are critical to address the identified gaps as a precursor to improving stroke outcomes and reducing burden. Potential solutions identified within the review will require a comprehensive approach from healthcare policymakers to focus on stroke awareness programs, primary and secondary prevention, establishing and monitoring of stroke protocols and pathways, implementation of a compulsory national stroke registry, use of TeleRehab, TeleMedicine and mobile stroke units and improve access to and availability of both hospital- and community-based stroke rehabilitation. Furthermore, changes in PhilHealth coverage and universal credit to minimize catastrophic out-of-pocket costs.

Limitations

Although a comprehensive search was undertaken, data were taken from a limited number of located published studies on stroke in the Philippines. This, together with data from databases and grey literature, may not reflect the current state of stroke services in the country.

Availability of data and materials

Not applicable.

Data availability

No datasets were generated or analysed during the current study.

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Acknowledgements

We acknowledge the TULAY collaborators: Dr Roy Francis Navea, Dr Myrna Estrada, Dr Elda Grace Anota, Dr Maria Mercedes Barba, Dr June Ann De Vera, Dr Maria Elena Tan, Dr Sarah Buckingham and Professor Fiona Jones. We are grateful to Lance de Jesus and Dr Annah Teves, Research Assistants on the TULAY project, for their contribution to some of the data extraction.

This research was funded by the NIHR Global Health Policy and Systems Research Programme (Award ID: NIHR150244) in association with UK aid from the UK Government to support global health research. The views expressed in this publication are those of the authors and not necessarily those of the NIHR or the UK’s Department of Health and Social Care.

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Investigating landslide data balancing for susceptibility mapping using generative and machine learning models

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• Published: 05 September 2024

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• Yuhang Jiang 1 , 2 ,
• Wei Wang 1 , 2 ,
• Lifang Zou 3 ,
• Yajun Cao 1 , 2 &
• Wei-Chau Xie 4  

With the development and application of machine learning, significant advances have been made in landslide susceptibility mapping. However, due to challenges in actual field landslide investigations, current landslide susceptibility mapping is usually characterized by insufficient landslide samples (positive samples) and low reliability of non-landslide samples (negative samples). Considering Lianghe County in Yunnan Province, China, as an example, this paper aims to research the effectiveness of three oversampling models in generating positive samples for landslides: Conditional Tabular Generative Adversarial Networks (CTGAN), Generative Adversarial Networks (GAN), and the traditional Synthetic Minority Oversampling Technique (SMOTE) algorithms. Additionally, three machine learning methods, including 1D Convolutional Neural Network-Long Short-Term Memory Neural Network (CNN-LSTM), Random Forest (RF), and Gradient Boosting Decision Tree (GBDT) classifiers, are used for landslide susceptibility assessment. We also devise a non-landslide data (negative samples) screening method utilizing a self-trained support vector machine within a semi-supervised framework. The results show that by training on the dataset after negative sample screening, the AUC values for the 1D-CNN-LSTM, RF, and GBDT models have shown significant improvement, increasing from (0.778, 0.869, 0.849) to (0.837, 0.936, 0.877). Compared with the original training set, the prediction accuracy of the three machine learning models is improved after training on the augmented data by CTGAN, GAN, and SMOTE models. The RF model, augmented with 200 positive samples generated by CTGAN, achieves the highest prediction accuracy in the study (AUC = 0.962). The 1D CNN-LSTM model achieves its highest prediction accuracy (AUC = 0.953) when augmented with 200 positive samples from GAN. Similarly, the GBDT model reaches its highest prediction accuracy (AUC = 0.928) when augmented with 200 positive samples created by SMOTE. In addition, the spatial distribution of data indicates that the data generated by the generative adversarial model exhibits higher diversity, which can be used for landslide susceptibility assessment.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12072102, 12102129), the Six talent peaks project in Jiangsu Province, and the Program to Cultivate Middle-aged and Young Science Leaders of Colleges and Universities of Jiangsu Province, China.

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• Published: 02 September 2024

Fault diagnosis method for oil-immersed transformers integrated digital twin model

• Haiyan Yao 1 ,
• Xin Zhang 2 ,
• Qiang Guo 1 ,
• Yufeng Miao 1 &
• Shan Guan 3  

Scientific Reports volume  14 , Article number:  20355 ( 2024 ) Cite this article

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• Electrical and electronic engineering
• Mechanical engineering

To address the problems of low accuracy in fault diagnosis of oil-immersed transformers, poor state perception ability and real-time collaboration during diagnosis feedback, a fault diagnosis method for transformers based on the integration of digital twins is proposed. Firstly, fault sample balance is achieved through Iterative Nearest Neighbor Oversampling (INNOS), Secondly, nine-dimensional ratio features are extracted, and the correlation between dissolved gases in oil and fault types is established. Then, sparse principal component analysis (SPCA) is used for feature fusion and dimensionality reduction. Finally, the Aquila Optimizer (AO) is introduced to optimize the parameters of the Kernel Extreme Learning Machine (KELM), establishing the optimal AO-KELM diagnosis model. The final fault diagnosis accuracy reaches 98.1013%. Combining transformer digital twin models, real-time interaction mapping between physical entities and virtual space is achieved, enabling online diagnosis of transformer faults. Experimental results show that the method proposed in this paper has high diagnostic accuracy and strong stability, providing reference for the intelligent operation and maintenance of transformers.

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Introduction.

The transformer, as the hub of power systems, its health status directly impacts the stability and reliability of the electrical system's operation. Therefore, the precise management of a transformer's health status is paramount to ensuring the steadfast and secure operation of the power grid 1 .

Presently, the technology of Dissolved Gas Analysis (DGA) is extensively employed in the monitoring and identification of faults within oil-insulated transformers 2 , 3 , primarily encompassing: the IEC triad ratio method 4 , the Rogers quadruple ratio method 5 , and the DUVAL triangle technique 6 . Despite their simplicity of operation, these approaches lack the depth of representation for fault characteristics and are limited by their capabilities, resulting in a blurred and indistinct encoding boundary, thereby leading to a low accuracy rate in fault recognition 7 . With the rapid advancement of artificial intelligence, eminent scholars have integrated machine learning with DGA technology, achieving notable results in the field of transformer fault detection. The literature 8 optimizes the support vector machine parameters through the refinement of the scalar search algorithm, thereby augmenting both the convergence velocity and the diagnostic precision of the methodology. The literature 9 proffers an SE-ELM diagnostic method, whose efficacy was validated through the verification across various datasets. The literature 10 enhances the particle swarm optimization algorithm through the dynamic adjustment of inertial weights and acceleration factors, iteratively optimizing the parameters of XGBoost, thereby augmenting the model's classification acumen. Additionally, methods such as Convolutional Neural Networks 11 , 12 , Long Short-Term Memory Networks 13 , 14 , 15 , LightGBM 16 , and the Capsule Network 17 are extensively employed.

With the advancement of big data and the Internet of Things (IoT) technologies, the Digital Twin (DT) 18 technology has paved a new path for enhancing the efficiency of equipment health management. The core concept is to construct a holographic virtual twin model in the digital realm, utilizing advanced technologies such as intelligent sensing and data transmission, which accurately, comprehensively, and in real-time reflect the evolution of physical devices, achieving intelligent control over entities 19 , 20 , 21 . This technology has been extensively utilized in various sectors including aerospace, manufacturing, and healthcare.

In the field of transformer fault diagnosis, scholars both domestically and internationally have carried out extensive research. Referencing 22 , the study proposed a method for constructing a dual-driving twin model integrating data and models, focusing on 10 kv oil-immersed transformers. This approach enables the synchronization between the actual operating conditions of the transformer and the digital twin center. Referencing 23 , a digital twin fault diagnosis model was constructed based on the mechanism model and data model of transformers. Five characteristic gases extracted from DGA data were selected as input feature vectors for a CNN. Experimental results showed that the 1D-CNN model established in this study responded rapidly, had a short training time, and achieved high accuracy, thus validating the effectiveness of the model. Referencing 24 , a fault diagnosis model based on digital twin was constructed for transformers, taking into account their structural characteristics and operational traits. By optimizing the smoothing factor δ in a probabilistic neural network through differential evolution algorithm, the diagnostic accuracy reached an impressive 96.7%, enabling precise monitoring of the transformer's actual operating state. Reference 25 conducts a statistical analysis of the operating data and state information quantity of power transformers, proposes a framework for a state evaluation system and fault detection system based on GCA-CNN, and verifies with 2000 real data cases that the model has higher accuracy and evaluation and detection effects. The literature 26 establishes a high-fidelity simulation model of transformers to accurately simulate winding currents and the temperatures of different components, which can be used for the identification of early faults. However, the aforementioned research is only focused on a single dissolved gas in oil or vibration signal as the basis for fault diagnosis, but there are many factors affecting transformer faults. In the future, it may be possible to combine multi-source data for comprehensive judgment.

In light of the above context, this paper proposes a fault diagnosis method for oil-immersed transformers that integrates a digital twin model. The main contributions of the paper are divided into several parts. Part 1 mainly elaborates on the research background of the paper and the future research direction. Part 2 establishes a transformer digital twin framework, based on geometric, physical, behavioral, and rule models, to achieve interaction mapping between the virtual entity and the physical entity. Part 3 introduces the methods used in the paper, providing theoretical support for the establishment of an accurate and efficient fault diagnosis model. Part 4 addresses the issue of imbalanced small sample data that can easily lead to misjudgment of minority class samples, deeply explores the correlation between dissolved gases in oil and fault types, and eliminates the 'dimensionality catastrophe' problem, using instance data to obtain diagnostic results. Part 5 discusses and analyzes different sampling methods, different features, and different diagnostic models. Part 6 summarizes the entire paper.

Transformer fault diagnosis model fusing digital twin

Transformer digital twin framework.

This article takes a 400kV oil-immersed transformer as the research object and establishes a transformer digital twin integrated digital twin technology. The constructed digital twin framework mainly includes: physical space, twin body, twin data layer and application service layer 27 , as shown in Fig.  1 .

Transformer digital twin framework.

In the process of building a digital twin, the geometric model is the foundation for creating the digital twin model. Three-dimensional software such as UG and SolidWorks are used to comprehensively describe the solid model in terms of geometric dimensions, material properties, and assembly relationships. Based on prior knowledge, physical properties, and operating mechanisms, the geometric model is analyzed and tested for magnetic field, structure, and other modeling aspects, fully reflecting the intrinsic nature and operating mechanism of the transformer. Heterogeneous data from multiple sources, such as dissolved gas in oil and acoustic vibration signals, are collected using state-aware devices. Artificial intelligence algorithms integrated in the behavior model are used for processing and analysis. The derived data generated from simulation calculations are fed back to the mechanism model in real-time. At the same time, simulation data, state-aware data, as well as transformer's full life cycle process data, maintenance records, and computed derived data collectively form the twin database. Through data communication protocols and interfaces, real-time updates and interactive control between the physical entity and the digital twin are achieved, enabling visual description, real-time monitoring, analysis, diagnosis, and intelligent decision-making for the physical transformer. This provides new ideas for improving the safety and reliable operation of power transmission and transformation equipment.

The five-dimensional model of digital twin

The present work is founded on the five-dimensional model proposed by Tao Fei from Beijing Aerospace University 28 , culminating in the creation of a digital twin for transformers, as exemplified by Eq. ( 1 ).

where: PE denotes the physical entity of the transformer, VE represents the virtual entity, SS signifies data, algorithms and models of the digital twin, DD stands for the twinning data of the transformer, and CN symbolizes the interaction and communication among the various components.

The acronym PE stands for transformer physical entity, an ensemble of components including the core, windings, tap-changer, and cooling equipment, it caters to the perception of contact or non-contact by state-sensing devices, embodying the interactive and responsive essence of an objective presence.

The SS represents the process of integrating data and models generated by the digital twin transformer system, thereby facilitating comprehensive monitoring of entities, diagnostic analysis of equipment failures, and predictive maintenance.

VE represents the twin model of the virtual realm, establishing the fundamental groundwork for mapping the virtual to the real. The specific composition is delineated by the formula ( 2 ) shown:

where: Gv represents the geometric model, which uses 3D modeling software to create a comprehensive description of the geometric features of physical entities; Pv represents the physical model, which describes the physical properties and operating mechanisms of electrical equipment; Bv represents the behavior model, which combines artificial intelligence algorithms to create Bv; Rv represents the rule model, which mainly includes expert experience and rule inference based on processed historical data for optimization and deduction.

DD represents twin data, which dynamically stores relevant data of PE/VE/SS, and is an important prerequisite for ensuring intelligent operation and maintenance of transformers. The specific representation is shown in formula ( 3 ):

where: Dp refers to the dynamic factor data collected through the state-aware device; Dv refers to the running parameters in the virtual model; Ds mainly refers to the functional and business service data; Dk includes expert experience, industry rules in the transformer field, and usage guidelines, etc. Df refers to the integrated transformation, interactive fusion, and other derived data of the above-mentioned data.

CN represents the data connection part, which is crucial for ensuring the interaction and updating of the elements in the digital twin model. Through data interfaces, communication protocols, etc., efficient transmission and utilization of data in the digital twin system can be achieved, enabling seamless communication and connectivity among different parts of the model. The interactive relationships of the five dimensions in the digital twin model are shown in Fig.  2 .

Transformer digital twin five-dimensional model connection relationship.

Transformer fault diagnosis model based on optimized extreme learning machine

Iterative nearest neighbor oversampling algorithm.

The iterative neighborhood oversampling 29 algorithm is a sampling method designed to tackle class imbalance issues, with its principal tenet being the selection of a multitude of class-specific samples as neighbors, and then traversing all k data points within this category, scouring for the most recent unlabeled instance within each label data subset of said category until the dataset balances out or approaches close to it. Here follow the specific steps:

Assume the samples in the dataset for each tag to be \({\text{r}} = \left\{ {r_{1} ,r_{2} , \cdots ,r_{j} , \cdots ,r_{a} } \right\}\) , with \(r_{j} \left( {j = 1,2, \cdots a} \right)\) denoting the number of samples contained within category j . Define the sample set's imbalance factor, utilizing the standard deviation \({\text{var}} \left( r \right)\) to symbolize the dispersal of various types of samples within the dataset, as illustrated in Eq. ( 4 ):

where: \(\mathop r\limits^{ - } = \frac{1}{a}\sum\limits_{j = 1}^{a} {r_{j} }\) .

Based on the philosophy of greedy search, endeavor to identify a multitude of particular sub-samples, with the process detailed in formula ( 5 ):

where: \(x_{j}\) represents the labeled data in category j . If \(x_{\max k}\) is the classification boundary, remove it and select the next nearest neighbor. Then, label it as category j , remove it from the unlabeled data set \(X_{U}\) , add it to the labeled data set \(X_{L}\) , and set \(r_{j} = r_{j} + 1\) . Recalculate the imbalance degree until the preset value is reached, and stop iterating.

Extreme learning machine algorithm

The Kernel Extreme Learning Machine (KELM) 30 is based on a single hidden layer feedforward neural network. It introduces a kernel function on top of the ELM algorithm, which maps low-dimensional data to a high-dimensional feature space, resulting in a model with stronger generalization and robustness. The specific steps are as follows:

Assume we are provided with N samples represented as \(\left\{ {\left( {{\text{x}}_{{\text{i}}} ,t_{i} } \right)} \right\}_{i = 1}^{N}\) , where \(x_{i} = \left[ {x_{i1} ,x_{i2} , \cdots ,x_{in} } \right]^{T} \in R^{n}\) and \(t_{i} = \left[ {t_{i1} ,t_{i2} , \cdots ,t_{im} } \right]^{T} \in R^{n}\) denote the input vector and output function of the model respectively. In the context of a neural network with k hidden layers and an activation function \(g\left( x \right)\) , the number of hidden nodes is L , and the ELM model can be articulated by the formula shown in Eq. ( 6 ):

where: \(\beta_{j} = \left[ {\beta_{j1} ,\beta_{j2} , \cdots ,\beta_{jL} } \right]^{T} \left( {j = 1,2, \cdots ,L} \right)\) denotes the output weight value connecting the j th implicit layer node with the output layer node. Among these, \(H = \left\{ {h_{ij} } \right\}\left( {i = 1,2, \cdots ,N;j = 1,2, \cdots ,L} \right)\) represents the output matrix of the hidden layer, and H denotes the jth column of the input \(x_{1} ,x_{2} , \cdots ,x_{n}\) corresponding to the jth hidden layer node. Within H, the jth row corresponds to the output vector of \(x_{i}\) .

Using the least squares method to obtain the output weight values, as shown in formula ( 7 ):

In the formula, \(H{\prime}\) represents the generalized inverse matrix of the hidden layer output matrix H .

Introducing the kernel function mitigates the issue of randomly generated input weights and bias values, exemplified by the KELM weight output formula ( 8 ):

The KELM output function as expressed in formula ( 9 ):

When \(h\left( x \right)\) remains unknown, the kernel function matrix is represented by formula ( 10 ):

In the equation, \(K\left( {x_{i} ,x_{j} } \right)\) denotes the nuclear function, represented as:

The KELM model's output function expression is delineated in formula ( 12 ):

Sparse principal component analysis

The sparse principal component analysis 31 is a method that builds upon the principal component analysis algorithm by incorporating the LASSO penalty term, thereby enabling the matrix to be sparsely populated. By solving the regression coefficient matrix, it further transforms PCA into an optimization problem aimed at finding the optimal set of coefficients for regression. Compared to traditional PCA, SPCA excels in effectively managing the sparsity within high-dimensional data, yielding results that are more interpretative.

The SPCA algorithm is resolve into two segments: the first entails calculating the principal components via PCA; the second entails enhancing the LASSO penalty term to render the obtained solution sparse. Here follow the specific steps:

Given a \({\text{n}} \times m\) -variant dataset X, the feature decomposition upon normalization treatment, as expounded upon in formula ( 13 ):

In the equation, \(\Lambda \in R^{m \times m}\) represents a diagonal matrix of eigenvalues, arranged in descending order. \(\Lambda \in R^{m \times m}\) is a unitary matrix with column vectors as load vectors.

Select the first k columns of the load matrix \(P \in R^{m \times k}\) , compute the score matrix T , as shown in Eq. ( 14 ):

Projecting T onto X yields a new matrix \(\mathop X\limits^{ \wedge }\) that encompasses information from the corresponding principal component; the difference with X is denoted as E , as illustrated in formula ( 15 ), ( 16 ):

The solution of the SPCA first reverts to the PCA model. The formula ( 15 – 16 ) yields the expression ( 17 ):

Ensure the main component is as near to the original data as possible, that is,it mandates E'sminimalism. Therefore, the principal component seeks resolution through formula ( 18 ):

In the equation, \(\mathop P\limits^{ \wedge }\) is the solution to the minimum value of the principal matrix P .

The vectors sought by PCA are all non-zero; thus, the sparse solution is achieved by incorporating the LASSO penalty term, thereby mitigating the overfitting issue in PCA. The solution formula for sparse principal components, as displayed in formula ( 19 ), is illustrated:

In this equation, matrix A denotes the expected demand matrix to be sought, while matrix B represents the demand matrix expected under the regression problem. A and B represent the \(m \times k\) matrix, \(\mathop A\limits^{ \wedge }\) and \(\mathop B\limits^{ \wedge }\) the matrices to be solved for minimizing values of A and B; they are subject to the constraints \(b_{j} \propto P_{j}\) , \(\lambda\) and \(\lambda_{1,j}\) being the penalty coefficients, and must adhere to \(\lambda > 0\) . The adjusted variance, as expressed in formula ( 20 ), is indicative of:

In the equation, the diagonal matrix interpreting variance is delineated, with \(\mathop P\limits^{ \wedge }\) representing the load matrix following the coefficients. Model contribution lies articulated in formula ( 21 ):

Transformer fault diagnosis model process

This article, established on the premise of transformer fault imbalance within small sample sets, aims at achieving real-time and precise diagnosis through the establishment of a diagnostic model and a determined diagnostic process. The specific diagnostic process is illustrated in Fig.  3 . The article employs the AO-KELM model as the diagnostic model, erecting a diagnostic process that integrates offline model training with online fault identification.

Transformer fault diagnosis model based on optimized kernel extreme learning machine.

⑴ Train the model offline

The article delves into the offline model training segment from three perspectives: data preprocessing, feature extraction, and model recognition.

Step 1: the preprocessing segment encompasses data INNOS's oversampling and normalization treatment. Collect the gathered DGA samples through INNOS for augmenting the minority class samples, followed by normalization treatment.

Step 2: the feature extraction section encompasses the establishment of ratio signature generation and the integration of SPCA for fusion dimensionality reduction. First, construct a multidimensional discriminant signature, delving deeply into the correlation between the ratio of dissolved gas content in oil and the type of fault. Subsequently, employ SPCA for feature fusion to acquire the optimal principal component, thereby removing redundant information, and divide the training set, validation set, and test set proportionally.

Step 3: the model identification segment encompasses the training and validation of the model. Utilizing the AO algorithm to optimize the regularization parameters C and the kernel functions within the KELM model, one verifies the model's accuracy through validation set on each iteration. Should the discrepancy between consecutive training sessions fall beneath 5%, the model training continues; otherwise, the model retraining commences anew until the prerequisite conditions are met. The ultimate establishment of the AO-KELM optimal diagnostic model.

⑵ Online fault diagnosis

Normalize the samples collected in real-time to handle and construct multi-dimensional features, employing an unencoded ratio method to input into an optimal diagnosis model directly following optimal principal component projection, thereby achieving swift recognition of transformer fault. Although the computational time for offline model training is accordingly elevated, it is merely necessary to undergo training once, with the aim of achieving online recognition and diagnosis of transformer faults as data from real-time monitoring continues to be inputted.

Case study analysis

Data source and normalization processing.

Transformer insults are exacerbated by thermal electrochemical action, causing the decomposition of internal insulating materials and the dissolution of various hydrocarbon gases within the insulation oil. Distinct characteristics of gas dissolved in oil under varying fault types exist; research has demonstrated that diagnostic and classification of faults can be achieved through the use of DGA techniques 32 . Consequently, these five gas contents are utilized as a basis for transformer fault diagnosis in this article.

The article selected a comprehensive sample of 337 monitoring data from a particular power supply company, dividing the operating status of transformers into categories such as normal, moderate heat overload, high temperature overload, high energy discharge, low energy discharge, and local discharge, each represented by labels 1 through 6. Each type of fault is augmented with specific characteristic gases including H 2 , CH 4 , C 2 H 4 , C 2 H 6 , and C 2 H 2 ; the exact number of samples for each category is detailed in Table 1 . The data reveals that the majority of samples fall into the category of normal, comprising 35.63% of the total. Low-energy discharge and local discharge types account for 5.55% and 9.78% respectively, with a maximum disparity reaching 5.1:1. Such imbalanced data is prone to misidentifying samples of the minority class as normal, thereby impacting recognition accuracy. Therefore, this paper employs the INNOS algorithm to augment the minority class samples, achieving a balance in sample categories.

To manifest the disparities between data prior to and after sampling, a principal component analysis is conducted upon the sample data from before and after said sampling process. Subsequently, the first two principal components are selected for visualizing the data of various types both before and after said sampling, as illustrated in Fig.  4 . In Fig.  4 , it becomes apparent that the data distribution trends for various types of faults, prior to and after the adoption of the INNOS sampling method, are identical, thereby underscoring the viability of the INNOS sampling approach.

Scatter plot of INNOS samples.

Transformer malfunction signature composition

Considering the substantial disparities among the various volatile gases, a preliminary normalization is required for each gas's abundance, as illustrated in Eq. ( 22 ):

In the equation: \(x_{i}\) and \(x_{{\text{i}}}^{*}\) represent features pre-normalized; \({\text{x}}_{{{\text{i}}\max }}\) and \({\text{x}}_{{{\text{i}}\min }}\) indicate the original minimal and maximum values.

The method of unencoded ratio analysis 33 is but one among numerous techniques widely employed, utilizing the percentage ratio of key gases to either the total gas or the hydrocarbon concentration can profoundly illustrate the interconnectedness between characteristic gases and types of failures. For instance, the ratio of a singular gas to the total hydrocarbon concentration provides a more conclusive indicator of the interplay between diverse fault types; the concentrations of C 2 H 4 and CH 4 can effectively demarcate local discharge from discharge with overheating diagnosis; the percentage composition of C 2 H 2 can determine whether a transformer has experienced thermal failure, among other determinations. The construction of this paper is predicated on the integration of pertinent literature, establishing a nine-dimensional candidate ratio signature for transformer fault diagnosis 31 , as delineated in Table 2 , wherein THC = CH 4  + C 2 H 4  + C 2 H 6  + C 2 H 2 , and ALL = H 2  + CH 4  + C 2 H 4  + C 2 H 6  + C 2 H 2 .

Dimensionality reduction through feature parameter fusion

To avoid the redundancy of fault-related feature information within the samples and to enhance the efficiency and precision of the diagnostic model, the SPCA method was employed for the integration of the derived rational features. The cumulative explicable variance contribution rate of each principal component is depicted in Fig.  5 . It is evident from Fig.  5 that the cumulative variance contribution rate for the first six principal components reaches 90.4419%, indicating that the first five principal components can achieve more than 90% of the ability expressed by all the principal components. Hence, selecting these five principal components as inputs for the transformer fault diagnosis model is warranted.

Cumulative variance contribution rate.

Transformer malfunction diagnosis outcomes

The fused features derived from the SPCA extraction are delineated in a ratio of 6:2:2 to be divided into training, testing, and validation datasets. The regularization parameters C within KELM determine the learning capacity of the model and its diagnostic precision; in this paper, we employ the AO optimization algorithm to optimize C, with an introduction of the AO algorithm as delineated in literature 34 , 35 , culminating in the establishment of a diagnostic model based on SPCA-AO-KELM. Figure  6 delineates the confusion matrix diagram of the transformer fault diagnosis. It is evident from Fig.  6 that within the test set of 158 samples, 155 were correctly diagnosed, representing a total correct rate of 98.1013%. The accuracy rates for normal, high-temperature overheating, and low-energy discharge diagnoses are 100%, one case of misjudgment was found in medium–low temperature overheating, high-energy discharge, and partial discharge.

Transformer fault diagnosis results.

However, the precision of diagnostic accuracy alone cannot comprehensively nor efficaciously evaluate the impact of rare class faults on classification performance 36 , 37 . In this paper, we introduce classification model performance evaluation metrics derived from confusion matrices, employing accuracy (R), precision (P), and F1-score as the core components of our evaluation system. The veracity of diagnostic models for identifying various faults is assessed by the accuracy rate, the sensitivity of the model in recognizing a variety of faults is evaluated by the coverage rate, while the F1 score derived from the amalgamation of precision and recall reflects the model's classification performance amidst sample imbalance, with specific formulas denoted in the literature displayed here. The model's precision, recall, and F1-score derived from the computed graph in Fig.  6 respectively stand at 0.9816, 0.9825, and 0.9820, further underscoring the model's high fault detection accuracy and its stable nature.

Results and discussions

Comparison and analysis of different sampling methods.

To verify the effectiveness of the new samples synthesized based on INNOS in improving the accuracy of transformer fault diagnosis, this paper uses unbalanced data set, random oversampling, SMOTE, and ADASYN oversampling algorithms for sample augmentation, and the diagnostic results are shown in Fig.  7 . The red dots in the figure represent the samples that are correctly classified in the test set, while the circles represent the samples of the true class, and the scattered dots represent the samples that are misclassified as other classes. The more scattered sample points, the higher the misclassification rate. In Fig.  7 d, the diagnostic accuracy of the original unbalanced data set without balancing processing is only 88.4058%, indicating that due to the imbalance of data in each fault category, the training of the diagnostic model is insufficient, and it is easy to misclassify minority class samples as majority class samples during classification recognition. After balancing the data set using different sampling methods, the misclassification rate of the samples decreases. The sampling method used in this paper improves the diagnostic accuracy by 7.7967%, 2.5316%, and 1.8987% compared to ADASYN, SMOTE, and random oversampling, respectively, indicating that the INNOS sampling method can effectively solve the problem of low diagnostic accuracy caused by data imbalance.

Diagnostic results under different sampling methods.

Qualitative and quantitative analysis with integrated features

To demonstrate the effectiveness of the SPCA feature fusion method, this study conducted analysis from two perspectives: qualitative observation and quantitative analysis. Firstly, PCA, KPCA, and SPCA were used to extract features from the constructed ratio signs. The cumulative variance contribution rate threshold was set at 90%, and the obtained principal component information is detailed in Table 3 . LASSO penalty term was introduced based on PCA to constrain some loading vectors to zero, resulting in a loss of variance contribution rate. From the data in the table, it can be seen that the contribution rate of SPCA principal components is slightly lower than that of PCA and KPCA, effectively removing redundant information in the ratio features and providing a valid data foundation for subsequent classification and recognition.

Furthermore, for the above feature extraction methods, quantitative calculations were performed. The fused features extracted by the 9-dimensional joint feature, PCA, KPCA, and SPCA were input into the diagnostic model for comparative analysis, as shown in Fig.  8 . From Fig.  8 a–d, it can be observed that the diagnostic accuracy is significantly improved after feature extraction. Figure  8 a has a higher accuracy compared to Fig.  8 b and c, which validates the superiority of the SPCA feature extraction method.

Diagnostic outcomes under various characteristics.

Analysis of contrastive diagnostic models

To explore the diagnostic performance of the models, three diagnostic models, ELM, KELM, and AO-ELM, were constructed for horizontal comparison. The diagnostic results are shown in Table 4 . From the perspective of a single model, the introduction of a kernel function improved the diagnostic accuracy and evaluation indicators of ELM. From the perspective of optimization algorithms, the diagnostic capability of fault recognition was effectively improved after parameter optimization using the AO algorithm.

On the other hand, the extracted integration features are respectively inputted into the POA-SVM model proposed in Literature 38 , the SSA-ELM model suggested in Literature 39 , and the PSO-BiLSTM model introduced in Literature 40 for longitudinal comparison. To circumvent the chances of chance, each model is subjected to ten-fold cross-validation, as manifested in Table 5 . It is evident from Table 5 that, under conditions where the input features remain identical, the AO-KELM outperforms both the POA-SVM and POA-SVM by elevating the average accuracy by 3.23% and 2.64%, respectively, while the PSO-BiLSTM lags behind with a mere 1.8% increase in accuracy. This clearly signifies the robust stability of the AO-KELM model and its formidable classification capabilities.

The paper introduces an oil-immersed transformer fault diagnosis method that integrates digital twin models, providing validation through case studies, leading to the conclusions below:

Build a twin mechanism model based on geometric, physical, rule, and behavior models, use real-time data to drive the fusion of data and mechanism models, complete real-time mapping between physical entities and virtual entities, and use visualization technology to express the twin in multiple dimensions, achieve intelligent diagnosis, health monitoring, and optimization decision-making for the transformer entity.

Proposed a transformer fault diagnosis model based on optimized kernel extreme learning machine, which solves the problem of misjudgment of minority class samples caused by unbalanced small samples, effectively extracts fusion features, establishes the optimal AO-KELM classifier, and achieves an accuracy of 98.1013%. By comparing with different diagnostic models, the classification performance and stability of the proposed method are verified.

Data availability

The datasets generated and/or analysed during the currentstudy are not publicly availabledue [REASON WHY DATA ARENOT PUBLlC] but are availablefrom the corresponding authoron reasonable request. E-mail:[email protected].

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Acknowledgements

Project supported by Jilin Provincial Development and Reform Commission innovation capacity construction fund (2020C022-6).

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Haiyan Yao, Qiang Guo & Yufeng Miao

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Haiyan Y designed the experiments and contributedmaterials/analysis tools; Xin Zhang analyzed the data and its visualization; Qiang Guo and Yufeng Miao M guided the data analysis; Shan Guan wrote the paper; All authors have reviewed the manuscript.

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Yao, H., Zhang, X., Guo, Q. et al. Fault diagnosis method for oil-immersed transformers integrated digital twin model. Sci Rep 14 , 20355 (2024). https://doi.org/10.1038/s41598-024-71107-w

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Received : 20 May 2024

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DOI : https://doi.org/10.1038/s41598-024-71107-w

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