psychology research paper using linear regression analysis

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Research Article

Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression

Affiliations Department of Psychology, University of Gothenburg, Gothenburg, Sweden, Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden

Affiliation Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden

Affiliations Department of Psychology, University of Gothenburg, Gothenburg, Sweden, Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden, Department of Psychology, Education and Sport Science, Linneaus University, Kalmar, Sweden

* E-mail: [email protected]

Affiliations Network for Empowerment and Well-Being, University of Gothenburg, Gothenburg, Sweden, Center for Ethics, Law, and Mental Health (CELAM), University of Gothenburg, Gothenburg, Sweden, Institute of Neuroscience and Physiology, The Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden

Ali Al Nima,
Patricia Rosenberg,
Trevor Archer,
Danilo Garcia

Published: September 9, 2013
https://doi.org/10.1371/journal.pone.0073265
Reader Comments

23 Sep 2013: Nima AA, Rosenberg P, Archer T, Garcia D (2013) Correction: Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression. PLOS ONE 8(9): 10.1371/annotation/49e2c5c8-e8a8-4011-80fc-02c6724b2acc. https://doi.org/10.1371/annotation/49e2c5c8-e8a8-4011-80fc-02c6724b2acc View correction

Mediation analysis investigates whether a variable (i.e., mediator) changes in regard to an independent variable, in turn, affecting a dependent variable. Moderation analysis, on the other hand, investigates whether the statistical interaction between independent variables predict a dependent variable. Although this difference between these two types of analysis is explicit in current literature, there is still confusion with regard to the mediating and moderating effects of different variables on depression. The purpose of this study was to assess the mediating and moderating effects of anxiety, stress, positive affect, and negative affect on depression.

Two hundred and two university students (males = 93, females = 113) completed questionnaires assessing anxiety, stress, self-esteem, positive and negative affect, and depression. Mediation and moderation analyses were conducted using techniques based on standard multiple regression and hierarchical regression analyses.

Main Findings

The results indicated that (i) anxiety partially mediated the effects of both stress and self-esteem upon depression, (ii) that stress partially mediated the effects of anxiety and positive affect upon depression, (iii) that stress completely mediated the effects of self-esteem on depression, and (iv) that there was a significant interaction between stress and negative affect, and between positive affect and negative affect upon depression.

The study highlights different research questions that can be investigated depending on whether researchers decide to use the same variables as mediators and/or moderators.

Citation: Nima AA, Rosenberg P, Archer T, Garcia D (2013) Anxiety, Affect, Self-Esteem, and Stress: Mediation and Moderation Effects on Depression. PLoS ONE 8(9): e73265. https://doi.org/10.1371/journal.pone.0073265

Editor: Ben J. Harrison, The University of Melbourne, Australia

Received: February 21, 2013; Accepted: July 22, 2013; Published: September 9, 2013

Copyright: © 2013 Nima et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The authors have no support or funding to report.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Mediation refers to the covariance relationships among three variables: an independent variable (1), an assumed mediating variable (2), and a dependent variable (3). Mediation analysis investigates whether the mediating variable accounts for a significant amount of the shared variance between the independent and the dependent variables–the mediator changes in regard to the independent variable, in turn, affecting the dependent one [1] , [2] . On the other hand, moderation refers to the examination of the statistical interaction between independent variables in predicting a dependent variable [1] , [3] . In contrast to the mediator, the moderator is not expected to be correlated with both the independent and the dependent variable–Baron and Kenny [1] actually recommend that it is best if the moderator is not correlated with the independent variable and if the moderator is relatively stable, like a demographic variable (e.g., gender, socio-economic status) or a personality trait (e.g., affectivity).

Although both types of analysis lead to different conclusions [3] and the distinction between statistical procedures is part of the current literature [2] , there is still confusion about the use of moderation and mediation analyses using data pertaining to the prediction of depression. There are, for example, contradictions among studies that investigate mediating and moderating effects of anxiety, stress, self-esteem, and affect on depression. Depression, anxiety and stress are suggested to influence individuals' social relations and activities, work, and studies, as well as compromising decision-making and coping strategies [4] , [5] , [6] . Successfully coping with anxiety, depressiveness, and stressful situations may contribute to high levels of self-esteem and self-confidence, in addition increasing well-being, and psychological and physical health [6] . Thus, it is important to disentangle how these variables are related to each other. However, while some researchers perform mediation analysis with some of the variables mentioned here, other researchers conduct moderation analysis with the same variables. Seldom are both moderation and mediation performed on the same dataset. Before disentangling mediation and moderation effects on depression in the current literature, we briefly present the methodology behind the analysis performed in this study.

Mediation and moderation

Baron and Kenny [1] postulated several criteria for the analysis of a mediating effect: a significant correlation between the independent and the dependent variable, the independent variable must be significantly associated with the mediator, the mediator predicts the dependent variable even when the independent variable is controlled for, and the correlation between the independent and the dependent variable must be eliminated or reduced when the mediator is controlled for. All the criteria is then tested using the Sobel test which shows whether indirect effects are significant or not [1] , [7] . A complete mediating effect occurs when the correlation between the independent and the dependent variable are eliminated when the mediator is controlled for [8] . Analyses of mediation can, for example, help researchers to move beyond answering if high levels of stress lead to high levels of depression. With mediation analysis researchers might instead answer how stress is related to depression.

In contrast to mediation, moderation investigates the unique conditions under which two variables are related [3] . The third variable here, the moderator, is not an intermediate variable in the causal sequence from the independent to the dependent variable. For the analysis of moderation effects, the relation between the independent and dependent variable must be different at different levels of the moderator [3] . Moderators are included in the statistical analysis as an interaction term [1] . When analyzing moderating effects the variables should first be centered (i.e., calculating the mean to become 0 and the standard deviation to become 1) in order to avoid problems with multi-colinearity [8] . Moderating effects can be calculated using multiple hierarchical linear regressions whereby main effects are presented in the first step and interactions in the second step [1] . Analysis of moderation, for example, helps researchers to answer when or under which conditions stress is related to depression.

Mediation and moderation effects on depression

Cognitive vulnerability models suggest that maladaptive self-schema mirroring helplessness and low self-esteem explain the development and maintenance of depression (for a review see [9] ). These cognitive vulnerability factors become activated by negative life events or negative moods [10] and are suggested to interact with environmental stressors to increase risk for depression and other emotional disorders [11] , [10] . In this line of thinking, the experience of stress, low self-esteem, and negative emotions can cause depression, but also be used to explain how (i.e., mediation) and under which conditions (i.e., moderation) specific variables influence depression.

Using mediational analyses to investigate how cognitive therapy intervations reduced depression, researchers have showed that the intervention reduced anxiety, which in turn was responsible for 91% of the reduction in depression [12] . In the same study, reductions in depression, by the intervention, accounted only for 6% of the reduction in anxiety. Thus, anxiety seems to affect depression more than depression affects anxiety and, together with stress, is both a cause of and a powerful mediator influencing depression (See also [13] ). Indeed, there are positive relationships between depression, anxiety and stress in different cultures [14] . Moreover, while some studies show that stress (independent variable) increases anxiety (mediator), which in turn increased depression (dependent variable) [14] , other studies show that stress (moderator) interacts with maladaptive self-schemata (dependent variable) to increase depression (independent variable) [15] , [16] .

The present study

In order to illustrate how mediation and moderation can be used to address different research questions we first focus our attention to anxiety and stress as mediators of different variables that earlier have been shown to be related to depression. Secondly, we use all variables to find which of these variables moderate the effects on depression.

The specific aims of the present study were:

To investigate if anxiety mediated the effect of stress, self-esteem, and affect on depression.
To investigate if stress mediated the effects of anxiety, self-esteem, and affect on depression.
To examine moderation effects between anxiety, stress, self-esteem, and affect on depression.

Ethics statement

This research protocol was approved by the Ethics Committee of the University of Gothenburg and written informed consent was obtained from all the study participants.

Participants

The present study was based upon a sample of 206 participants (males = 93, females = 113). All the participants were first year students in different disciplines at two universities in South Sweden. The mean age for the male students was 25.93 years ( SD = 6.66), and 25.30 years ( SD = 5.83) for the female students.

In total, 206 questionnaires were distributed to the students. Together 202 questionnaires were responded to leaving a total dropout of 1.94%. This dropout concerned three sections that the participants chose not to respond to at all, and one section that was completed incorrectly. None of these four questionnaires was included in the analyses.

Instruments

Hospital anxiety and depression scale [17] ..

The Swedish translation of this instrument [18] was used to measure anxiety and depression. The instrument consists of 14 statements (7 of which measure depression and 7 measure anxiety) to which participants are asked to respond grade of agreement on a Likert scale (0 to 3). The utility, reliability and validity of the instrument has been shown in multiple studies (e.g., [19] ).

Perceived Stress Scale [20] .

The Swedish version [21] of this instrument was used to measures individuals' experience of stress. The instrument consist of 14 statements to which participants rate on a Likert scale (0 = never , 4 = very often ). High values indicate that the individual expresses a high degree of stress.

Rosenberg's Self-Esteem Scale [22] .

The Rosenberg's Self-Esteem Scale (Swedish version by Lindwall [23] ) consists of 10 statements focusing on general feelings toward the self. Participants are asked to report grade of agreement in a four-point Likert scale (1 = agree not at all, 4 = agree completely ). This is the most widely used instrument for estimation of self-esteem with high levels of reliability and validity (e.g., [24] , [25] ).

Positive Affect and Negative Affect Schedule [26] .

This is a widely applied instrument for measuring individuals' self-reported mood and feelings. The Swedish version has been used among participants of different ages and occupations (e.g., [27] , [28] , [29] ). The instrument consists of 20 adjectives, 10 positive affect (e.g., proud, strong) and 10 negative affect (e.g., afraid, irritable). The adjectives are rated on a five-point Likert scale (1 = not at all , 5 = very much ). The instrument is a reliable, valid, and effective self-report instrument for estimating these two important and independent aspects of mood [26] .

Questionnaires were distributed to the participants on several different locations within the university, including the library and lecture halls. Participants were asked to complete the questionnaire after being informed about the purpose and duration (10–15 minutes) of the study. Participants were also ensured complete anonymity and informed that they could end their participation whenever they liked.

Correlational analysis

Depression showed positive, significant relationships with anxiety, stress and negative affect. Table 1 presents the correlation coefficients, mean values and standard deviations ( sd ), as well as Cronbach ' s α for all the variables in the study.

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https://doi.org/10.1371/journal.pone.0073265.t001

Mediation analysis

Regression analyses were performed in order to investigate if anxiety mediated the effect of stress, self-esteem, and affect on depression (aim 1). The first regression showed that stress ( B = .03, 95% CI [.02,.05], β = .36, t = 4.32, p <.001), self-esteem ( B = −.03, 95% CI [−.05, −.01], β = −.24, t = −3.20, p <.001), and positive affect ( B = −.02, 95% CI [−.05, −.01], β = −.19, t = −2.93, p = .004) had each an unique effect on depression. Surprisingly, negative affect did not predict depression ( p = 0.77) and was therefore removed from the mediation model, thus not included in further analysis.

The second regression tested whether stress, self-esteem and positive affect uniquely predicted the mediator (i.e., anxiety). Stress was found to be positively associated ( B = .21, 95% CI [.15,.27], β = .47, t = 7.35, p <.001), whereas self-esteem was negatively associated ( B = −.29, 95% CI [−.38, −.21], β = −.42, t = −6.48, p <.001) to anxiety. Positive affect, however, was not associated to anxiety ( p = .50) and was therefore removed from further analysis.

A hierarchical regression analysis using depression as the outcome variable was performed using stress and self-esteem as predictors in the first step, and anxiety as predictor in the second step. This analysis allows the examination of whether stress and self-esteem predict depression and if this relation is weaken in the presence of anxiety as the mediator. The result indicated that, in the first step, both stress ( B = .04, 95% CI [.03,.05], β = .45, t = 6.43, p <.001) and self-esteem ( B = .04, 95% CI [.03,.05], β = .45, t = 6.43, p <.001) predicted depression. When anxiety (i.e., the mediator) was controlled for predictability was reduced somewhat but was still significant for stress ( B = .03, 95% CI [.02,.04], β = .33, t = 4.29, p <.001) and for self-esteem ( B = −.03, 95% CI [−.05, −.01], β = −.20, t = −2.62, p = .009). Anxiety, as a mediator, predicted depression even when both stress and self-esteem were controlled for ( B = .05, 95% CI [.02,.08], β = .26, t = 3.17, p = .002). Anxiety improved the prediction of depression over-and-above the independent variables (i.e., stress and self-esteem) (Δ R 2 = .03, F (1, 198) = 10.06, p = .002). See Table 2 for the details.

https://doi.org/10.1371/journal.pone.0073265.t002

A Sobel test was conducted to test the mediating criteria and to assess whether indirect effects were significant or not. The result showed that the complete pathway from stress (independent variable) to anxiety (mediator) to depression (dependent variable) was significant ( z = 2.89, p = .003). The complete pathway from self-esteem (independent variable) to anxiety (mediator) to depression (dependent variable) was also significant ( z = 2.82, p = .004). Thus, indicating that anxiety partially mediates the effects of both stress and self-esteem on depression. This result may indicate also that both stress and self-esteem contribute directly to explain the variation in depression and indirectly via experienced level of anxiety (see Figure 1 ).

Changes in Beta weights when the mediator is present are highlighted in red.

https://doi.org/10.1371/journal.pone.0073265.g001

For the second aim, regression analyses were performed in order to test if stress mediated the effect of anxiety, self-esteem, and affect on depression. The first regression showed that anxiety ( B = .07, 95% CI [.04,.10], β = .37, t = 4.57, p <.001), self-esteem ( B = −.02, 95% CI [−.05, −.01], β = −.18, t = −2.23, p = .03), and positive affect ( B = −.03, 95% CI [−.04, −.02], β = −.27, t = −4.35, p <.001) predicted depression independently of each other. Negative affect did not predict depression ( p = 0.74) and was therefore removed from further analysis.

The second regression investigated if anxiety, self-esteem and positive affect uniquely predicted the mediator (i.e., stress). Stress was positively associated to anxiety ( B = 1.01, 95% CI [.75, 1.30], β = .46, t = 7.35, p <.001), negatively associated to self-esteem ( B = −.30, 95% CI [−.50, −.01], β = −.19, t = −2.90, p = .004), and a negatively associated to positive affect ( B = −.33, 95% CI [−.46, −.20], β = −.27, t = −5.02, p <.001).

A hierarchical regression analysis using depression as the outcome and anxiety, self-esteem, and positive affect as the predictors in the first step, and stress as the predictor in the second step, allowed the examination of whether anxiety, self-esteem and positive affect predicted depression and if this association would weaken when stress (i.e., the mediator) was present. In the first step of the regression anxiety ( B = .07, 95% CI [.05,.10], β = .38, t = 5.31, p = .02), self-esteem ( B = −.03, 95% CI [−.05, −.01], β = −.18, t = −2.41, p = .02), and positive affect ( B = −.03, 95% CI [−.04, −.02], β = −.27, t = −4.36, p <.001) significantly explained depression. When stress (i.e., the mediator) was controlled for, predictability was reduced somewhat but was still significant for anxiety ( B = .05, 95% CI [.02,.08], β = .05, t = 4.29, p <.001) and for positive affect ( B = −.02, 95% CI [−.04, −.01], β = −.20, t = −3.16, p = .002), whereas self-esteem did not reach significance ( p < = .08). In the second step, the mediator (i.e., stress) predicted depression even when anxiety, self-esteem, and positive affect were controlled for ( B = .02, 95% CI [.08,.04], β = .25, t = 3.07, p = .002). Stress improved the prediction of depression over-and-above the independent variables (i.e., anxiety, self-esteem and positive affect) (Δ R 2 = .02, F (1, 197) = 9.40, p = .002). See Table 3 for the details.

https://doi.org/10.1371/journal.pone.0073265.t003

Furthermore, the Sobel test indicated that the complete pathways from the independent variables (anxiety: z = 2.81, p = .004; self-esteem: z = 2.05, p = .04; positive affect: z = 2.58, p <.01) to the mediator (i.e., stress), to the outcome (i.e., depression) were significant. These specific results might be explained on the basis that stress partially mediated the effects of both anxiety and positive affect on depression while stress completely mediated the effects of self-esteem on depression. In other words, anxiety and positive affect contributed directly to explain the variation in depression and indirectly via the experienced level of stress. Self-esteem contributed only indirectly via the experienced level of stress to explain the variation in depression. In other words, stress effects on depression originate from “its own power” and explained more of the variation in depression than self-esteem (see Figure 2 ).

https://doi.org/10.1371/journal.pone.0073265.g002

Moderation analysis

Multiple linear regression analyses were used in order to examine moderation effects between anxiety, stress, self-esteem and affect on depression. The analysis indicated that about 52% of the variation in the dependent variable (i.e., depression) could be explained by the main effects and the interaction effects ( R 2 = .55, adjusted R 2 = .51, F (55, 186) = 14.87, p <.001). When the variables (dependent and independent) were standardized, both the standardized regression coefficients beta (β) and the unstandardized regression coefficients beta (B) became the same value with regard to the main effects. Three of the main effects were significant and contributed uniquely to high levels of depression: anxiety ( B = .26, t = 3.12, p = .002), stress ( B = .25, t = 2.86, p = .005), and self-esteem ( B = −.17, t = −2.17, p = .03). The main effect of positive affect was also significant and contributed to low levels of depression ( B = −.16, t = −2.027, p = .02) (see Figure 3 ). Furthermore, the results indicated that two moderator effects were significant. These were the interaction between stress and negative affect ( B = −.28, β = −.39, t = −2.36, p = .02) (see Figure 4 ) and the interaction between positive affect and negative affect ( B = −.21, β = −.29, t = −2.30, p = .02) ( Figure 5 ).

https://doi.org/10.1371/journal.pone.0073265.g003

Low stress and low negative affect leads to lower levels of depression compared to high stress and high negative affect.

https://doi.org/10.1371/journal.pone.0073265.g004

High positive affect and low negative affect lead to lower levels of depression compared to low positive affect and high negative affect.

https://doi.org/10.1371/journal.pone.0073265.g005

The results in the present study show that (i) anxiety partially mediated the effects of both stress and self-esteem on depression, (ii) that stress partially mediated the effects of anxiety and positive affect on depression, (iii) that stress completely mediated the effects of self-esteem on depression, and (iv) that there was a significant interaction between stress and negative affect, and positive affect and negative affect on depression.

Mediating effects

The study suggests that anxiety contributes directly to explaining the variance in depression while stress and self-esteem might contribute directly to explaining the variance in depression and indirectly by increasing feelings of anxiety. Indeed, individuals who experience stress over a long period of time are susceptible to increased anxiety and depression [30] , [31] and previous research shows that high self-esteem seems to buffer against anxiety and depression [32] , [33] . The study also showed that stress partially mediated the effects of both anxiety and positive affect on depression and that stress completely mediated the effects of self-esteem on depression. Anxiety and positive affect contributed directly to explain the variation in depression and indirectly to the experienced level of stress. Self-esteem contributed only indirectly via the experienced level of stress to explain the variation in depression, i.e. stress affects depression on the basis of ‘its own power’ and explains much more of the variation in depressive experiences than self-esteem. In general, individuals who experience low anxiety and frequently experience positive affect seem to experience low stress, which might reduce their levels of depression. Academic stress, for instance, may increase the risk for experiencing depression among students [34] . Although self-esteem did not emerged as an important variable here, under circumstances in which difficulties in life become chronic, some researchers suggest that low self-esteem facilitates the experience of stress [35] .

Moderator effects/interaction effects

The present study showed that the interaction between stress and negative affect and between positive and negative affect influenced self-reported depression symptoms. Moderation effects between stress and negative affect imply that the students experiencing low levels of stress and low negative affect reported lower levels of depression than those who experience high levels of stress and high negative affect. This result confirms earlier findings that underline the strong positive association between negative affect and both stress and depression [36] , [37] . Nevertheless, negative affect by itself did not predicted depression. In this regard, it is important to point out that the absence of positive emotions is a better predictor of morbidity than the presence of negative emotions [38] , [39] . A modification to this statement, as illustrated by the results discussed next, could be that the presence of negative emotions in conjunction with the absence of positive emotions increases morbidity.

The moderating effects between positive and negative affect on the experience of depression imply that the students experiencing high levels of positive affect and low levels of negative affect reported lower levels of depression than those who experience low levels of positive affect and high levels of negative affect. This result fits previous observations indicating that different combinations of these affect dimensions are related to different measures of physical and mental health and well-being, such as, blood pressure, depression, quality of sleep, anxiety, life satisfaction, psychological well-being, and self-regulation [40] – [51] .

Limitations

The result indicated a relatively low mean value for depression ( M = 3.69), perhaps because the studied population was university students. These might limit the generalization power of the results and might also explain why negative affect, commonly associated to depression, was not related to depression in the present study. Moreover, there is a potential influence of single source/single method variance on the findings, especially given the high correlation between all the variables under examination.

Conclusions

The present study highlights different results that could be arrived depending on whether researchers decide to use variables as mediators or moderators. For example, when using meditational analyses, anxiety and stress seem to be important factors that explain how the different variables used here influence depression–increases in anxiety and stress by any other factor seem to lead to increases in depression. In contrast, when moderation analyses were used, the interaction of stress and affect predicted depression and the interaction of both affectivity dimensions (i.e., positive and negative affect) also predicted depression–stress might increase depression under the condition that the individual is high in negative affectivity, in turn, negative affectivity might increase depression under the condition that the individual experiences low positive affectivity.

Acknowledgments

The authors would like to thank the reviewers for their openness and suggestions, which significantly improved the article.

Author Contributions

Conceived and designed the experiments: AAN TA. Performed the experiments: AAN. Analyzed the data: AAN DG. Contributed reagents/materials/analysis tools: AAN TA DG. Wrote the paper: AAN PR TA DG.

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Regression assumptions in clinical psychology research practice-a systematic review of common misconceptions

Affiliation.

1 Heymans Institute for Psychological Research, University of Groningen, Groningen, The Netherlands.
PMID: 28533971
PMCID: PMC5436580
DOI: 10.7717/peerj.3323

Misconceptions about the assumptions behind the standard linear regression model are widespread and dangerous. These lead to using linear regression when inappropriate, and to employing alternative procedures with less statistical power when unnecessary. Our systematic literature review investigated employment and reporting of assumption checks in twelve clinical psychology journals. Findings indicate that normality of the variables themselves, rather than of the errors, was wrongfully held for a necessary assumption in 4% of papers that use regression. Furthermore, 92% of all papers using linear regression were unclear about their assumption checks, violating APA-recommendations. This paper appeals for a heightened awareness for and increased transparency in the reporting of statistical assumption checking.

Keywords: Linear regression; Literature review; Misconceptions about normality; Statistical assumptions.

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The authors declare there are no competing interests.

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Published: 06 September 2024

Examining the influence of anxiety and depression on medication adherence among patients diagnosed with acute myocardial infarction

Audai M. Ashour 1 ,
Rami Masa’deh 1 ,
Shaher H. Hamaideh 2 ,
Rami A. Elshatarat 3 ,
Mohammed Ibrahim Yacoub 4 ,
Wesam T. Almagharbeh 5 ,
Asim Abdullah Alhejaili 3 ,
Bassam Dhafer Alshahrani 3 , 7 ,
Dena Eltabey Sobeh 6 &
Mudathir M. Eltayeb 6

BMC Psychology volume 12 , Article number: 473 ( 2024 ) Cite this article

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Effective medication adherence is vital for managing acute myocardial infarction (AMI) and enhancing patient well-being. This study aimed to evaluate medication adherence levels and associated factors among AMI patients using standardized assessment tools.

Employing a cross-sectional descriptive design, the study involved 210 patients diagnosed with acute myocardial infarction. Participants completed the General Medication Adherence Scale (GMAS), Hospital Anxiety and Depression Scale (HADS), and provided socio-demographic details.

The study revealed partial adherence to medications among AMI patients, with mean scores of 24.89 (± 3.64) out of 33. Notably, good adherence was observed in non-adherence due to patient behavior (mean ± SD = 11.8 ± 2.3 out of 15) and additional disease burden (mean ± SD = 8.65 ± 2.21 out of 12), while partial adherence was noted in non-adherence due to financial constraints (mean ± SD = 4.44 ± 1.34 out of 6). Patients reported mild anxiety (mean ± SD = 8.38 ± 2.81) and no depressive symptoms (mean ± SD = 7.43 ± 2.42). Multiple linear regression analysis indicated that employed status, younger age, shorter duration of MI, lower anxiety, and depression levels were associated with higher medication adherence. However, factors such as monthly income, gender, educational level, and marital status did not predict medication adherence.

The study highlights the significance of addressing anxiety and depression levels and considering socio-demographic factors when designing interventions to enhance medication adherence among AMI patients. Further research is needed to explore additional determinants of medication adherence and develop tailored interventions to improve patient outcomes post-AMI.

Peer Review reports

Introduction

Cardiovascular diseases (CVDs) represent a significant health concern globally, encompassing a range of conditions affecting the heart and blood vessels, including coronary heart disease and acute myocardial infarction (AMI). According to the World Health Organization (WHO), CVDs are responsible for a substantial portion of global mortality, with nearly 18 million deaths annually, accounting for approximately 32% of all deaths worldwide [ 1 ]. In Jordan, CVD-related fatalities constitute a staggering 40% of total deaths, with an adjusted death rate of 136 per 100,000 population, positioning Jordan at 46th globally in terms of CVD mortality [ 2 ]. This high prevalence can be attributed to various factors, including a significant percentage of the population engaging in smoking, being overweight, neglecting cholesterol assessments, and having a family history of CVDs.

AMI, commonly known as a heart attack, is a critical medical condition characterized by restricted blood flow to myocardial tissue, resulting in tissue necrosis or death. The leading cause is typically a blockage in the coronary artery, often due to coronary artery disease, though coronary spasms induced by medication usage or uncontrolled hypertension can also contribute [ 3 ]. The treatment protocol for AMI patients is multifaceted and intricate, with pharmacological therapy serving as a cornerstone. Adherence to prescribed medications plays a pivotal role in symptom management, reducing hospital readmission rates, and enhancing survival prospects [ 4 , 5 ].

Despite the acknowledged importance of medication adherence, previous research indicates suboptimal adherence rates among AMI patients, ranging from 40 to 60% 6 . Various factors influence medication adherence, categorized by the WHO into five dimensions: patient-related, therapy-related, healthcare system-related, socioeconomic, and condition-related psychological factors [ 7 ]. Patient-related factors encompass physical and cognitive impairments, alongside low social support, which can hinder adherence [ 8 , 9 ]. Therapy-related factors such as complex medication regimens and adverse effects can also pose challenges [ 10 ]. Effective patient-provider relationships within the healthcare system are crucial for fostering adherence, with supportive interactions positively influencing medication compliance [ 11 ].

Moreover, socioeconomic factors, including social support networks and economic status, significantly impact adherence to self-care management [ 12 ]. Psychological factors such as anxiety and depression, categorized under condition-related factors, further complicate adherence efforts. Studies have linked anxiety and depression to decreased medication adherence among CVD patients, including those with AMI, emphasizing the need for tailored interventions [ 13 , 14 ]. Notably, non-adherence to medications has been documented in a substantial proportion of cardiovascular patients, with rates as high as 60%, underscoring the urgency of addressing this issue, particularly in the context of AMI [ 15 ].

The emotional dimensions of CVDs play a crucial role in patient outcomes, particularly in the context of self-care and medication adherence. Emotional regulation processes, anxiety, and depression significantly impact the quality of life and adherence behaviors in patients with AMI [ 16 , 17 , 18 ]. Studies have shown that emotional dysregulation can exacerbate cardiovascular risks, influencing both physical and psychological health outcomes [ 19 , 20 , 21 , 22 ]. For instance, the interplay between anxiety, emotional regulation, and cardiovascular risk factors underscores the need for tailored interventions to address these emotional dimensions in AMI patients [ 19 , 23 ]. Additionally, the level of adherence to prescribed medication regimens, such as dual antiplatelet therapy, has been linked to the emotional well-being of patients, highlighting the importance of integrating psychological care into cardiovascular treatment plans [ 24 ]. By reinforcing the connection between emotional health and cardiovascular disease management, this study aims to provide a comprehensive understanding of the factors influencing medication adherence among AMI patients.

The role of self-care in the management of CVDs is increasingly recognized as a critical component in improving patient outcomes, particularly for those with AMI [ 20 , 23 ]. Effective self-care practices, including adherence to medication and lifestyle modifications, are essential for managing symptoms and preventing disease progression. Psychological characteristics such as anxiety and emotional dysregulation significantly impact a patient’s ability to engage in self-care and adapt to their disease, affecting overall health outcomes. For instance, the interplay between cardiovascular risk factors and psychological states like anxiety underscores the need for holistic management approaches that address both physical and emotional health [ 23 ]. Furthermore, tailored interventions that focus on enhancing self-care behaviors have been shown to improve quality of life and reduce the burden of CVDs [ 19 , 25 , 26 ]. By incorporating insights from the literature on self-care and the psychological dimensions of CVDs, this study aims to deepen the understanding of factors influencing medication adherence among AMI patients, offering valuable implications for both clinical practice and future research [ 27 , 28 ].

In Jordan, despite several studies addressing medication adherence in various populations, including psychiatric and hypertensive patients, research specific to CVDs, particularly AMI, remains scarce. Given the rising burden of CVDs and the prevalence of comorbidities, there is a pressing need to investigate medication adherence among AMI patients comprehensively. By identifying and addressing the multifaceted factors influencing adherence, tailored interventions can be developed to optimize treatment outcomes and mitigate the adverse impact of AMI.

In Jordan, there’s a significant gap in our understanding of how psychosocial factors, such as anxiety and depression, relate to medication adherence among AMI patients. This study aims to address this gap by investigating adherence levels and the factors that influence medication adherence among AMI patients in Jordan. Furthermore, the study endeavors to contribute to existing literature by conducting a comprehensive evaluation of medication adherence and its association with psychosocial factors, particularly anxiety and depression, among AMI patients in Jordan. The findings from this research will not only deepen our understanding of adherence behaviors within this population but also provide crucial insights for healthcare providers. This information can be utilized to develop targeted interventions and strategies aimed at promoting medication adherence among AMI patients. Additionally, the study aims to lay the groundwork for the development of programs tailored to meet the specific psychosocial needs of AMI patients. By addressing these needs, the study seeks to enhance overall treatment outcomes and improve the quality of life for AMI patients in Jordan.

Research objectives

The research objectives are as follows: (1) Determine the levels of medication adherence, anxiety, and depression among patients diagnosed with AMI in Jordan, and (2) Investigate whether anxiety, depression, and socio-demographic variables serve as predictors for medication adherence among patients diagnosed with AMI in Jordan.

A cross-sectional descriptive design was employed to investigate the correlation between psychosocial factors (anxiety and depression) and medication adherence among AMI patients in Jordan.

The study is set within the multifaceted healthcare sector of Jordan, encompassing a spectrum of institutions managed by the Ministry of Health, university hospitals, private facilities, and military establishments [ 29 ]. Five hospitals were strategically selected to ensure a broad representation across geographical regions and healthcare sectors. Among these were two public hospitals overseen by the Ministry of Health, a university hospital renowned for its specialized services and research, a private hospital catering to diverse socio-economic backgrounds, and a military hospital addressing the healthcare needs of service personnel and their families. Each hospital, equipped with outpatient clinics specializing in CVDs, serves as a pivotal site for the study’s investigation into the correlation between psychosocial factors, such as anxiety and depression, and medication adherence among AMI patients.

This diverse selection of hospitals and specialized outpatient clinics not only ensures access to a wide range of AMI patients but also facilitates the recruitment of a sufficient number of participants for the study. By incorporating these varied healthcare settings, the study aims to provide a comprehensive understanding of the factors influencing medication adherence among AMI patients in Jordan. Through this approach, the research endeavors to shed light on the intricate interplay between psychosocial factors and adherence behaviors, ultimately contributing valuable insights to the enhancement of patient care and treatment outcomes within the Jordanian healthcare landscape.

Employing a convenient sampling method, participants were recruited from the accessible population due to its practicality and alignment with the study’s logistical constraints. To ensure the inclusion of representative and reliable participants, specific inclusion criteria were established. These criteria encompassed a diagnosis of AMI for more than six months to ensure consistent medication adherence, an age of 18 years or older, a minimum attendance of three months at the outpatient clinic to signify commitment to prescribed medications and clinic appointments, absence of chronic mental health disorders to mitigate potential confounding factors, and proficiency in Arabic reading, writing, and comprehension to accurately complete study instruments and questionnaires. By adhering to these stringent inclusion criteria, the study aimed to minimize biases and enhance the validity of its findings, thereby ensuring robust and meaningful conclusions.

Two co-authors, who hold PhDs in nursing and specialize in clinical research with a focus on psychosocial well-being and quality of life among CVD patients, were tasked with data collection. These researchers were actively involved in recruiting patients and gathering both demographic and clinical information. To ensure accuracy, they conducted health assessments during patient interviews, meticulously adhering to the study’s inclusion and exclusion criteria. The integrity of the data was further validated by cross-referencing with patients’ medical records. These same researchers also administered the psychological assessment tools, ensuring a consistent and professional approach throughout the data collection process.

In determining the sample size for this study, a meticulous calculation based on a power of 0.80, an α-level of 0.05, and an anticipated medium-size effect indicated that a total of 210 participants would be necessary to detect statistically significant differences for the nine predictors under investigation. The researchers interviewed 247 participants and collected data from them. However, 21 participants did not complete the interviews or questionnaires and chose to withdraw. Additionally, 16 participants did not answer all questionnaire items; these incomplete questionnaires were excluded from the final analysis due to potential impact on results. Thus, the final data analysis included 210 participants, meeting the calculated effective sample size.

The target population encompassed all individuals diagnosed with AMI within the Jordanian healthcare system. From this broader target pool, the accessible population consisted specifically of those AMI patients who sought treatment at outpatient clinics between July and September 2022 within the selected hospital settings.

Data collection procedure

Two PhD co-authors in nursing gathered data through structured self-reports during direct interviews, using valid and reliable questionnaires. They validated this information against medical records and administered health and psychological assessments to ensure accuracy. The data collection procedure commenced with the researcher seeking approval and access from the medical department at the selected study settings, ensuring compliance with institutional protocols. Subsequently, data collection was conducted within the waiting rooms of outpatient clinics at designated hospitals, targeting patients seeking treatment for AMI. An informed consent process was meticulously followed, wherein potential participants received information sheets detailing the study’s purpose and procedures, accompanied by consent forms to indicate voluntary participation. Upon obtaining consent, participants were administered a paper-based questionnaire covering various aspects such as medication adherence, anxiety, depression, socio-demographic factors, and more.

Throughout the questionnaire administration, participants were offered assistance and clarification by the researcher as needed, fostering a supportive environment conducive to accurate data collection. Following completion, filled-out questionnaires were collected, and participant identifiers were removed to maintain confidentiality. Data handling procedures adhered to ethical guidelines, ensuring secure storage and protection of participant information. Overall, this structured approach aimed to gather comprehensive and reliable data from AMI patients, prioritizing ethical standards to uphold the integrity and validity of the study.

Instruments

The data collection instrument for this study comprises three main parts, meticulously designed to capture relevant information essential for the research objectives.

Socio-demographic characteristics

The first part of the instrument focuses on gathering socio-demographic data pertinent to the participants. This includes variables such as age, gender, marital status, educational level, employment status, monthly income, and the duration of Myocardial Infarction (MI) in months. These details provide valuable context and insights into the characteristics of the study population.

General medication adherence scale (GMAS)

The second part of the instrument utilizes the GMAS, developed by Naqvi et al. (2018) [ 30 ]. This scale comprises 11 items aimed at assessing the level of medication adherence among patients. GMAS consists of three subscales: non-adherence due to patient behavior (5 items), non-adherence due to additional diseases and pill burden (4 items), and non-adherence due to financial constraints (2 items). Each item is scored on a scale from 0 to 3, with higher scores indicating better adherence [ 30 , 31 ].

The scores on the GMAS were categorized as follows: For the first subscale, a score of 13–15 indicated high adherence, 11–12 denoted good adherence, 8–10 signified partial adherence, 5–7 represented low adherence, and 0–4 indicated poor adherence. Similarly, on the second subscale, scores of 11–12 reflected high adherence, 9–10 indicated good adherence, 6–8 represented partial adherence, 4–5 signified low adherence, and 0–3 indicated poor adherence. For the third subscale, a score of 6 indicated high adherence, 5 denoted good adherence, 3–4 represented partial adherence, 2 signified low adherence, and 0–1 indicated poor adherence. Overall scoring categorized participants into high adherence (30–33), good adherence (27–29), partial adherence (17–26), low adherence (11–16), and poor adherence (0–10). Additionally, a participant scoring 27 or above was considered adherent, while a score of 26 or lower was considered non-adherent [ 31 ].

The scale has been validated for reliability and validity in its Arabic version by Naqvi et al. (2020), with Cronbach’s alpha for GMAS in the current study reaching 0.84, with subscales ranging between 0.68 and 0.78 [ 32 ]. Scoring criteria are provided for each subscale, enabling categorization of adherence levels ranging from high to poor adherence.

Hospital anxiety and depression scale (HADS)

The third component of the instrument employs the HADS to evaluate participants’ experiences of anxiety and depressive symptoms within the previous week. Originally developed by Zigmond and Snaith in 1986 [ 33 , 34 ], the HADS comprises two distinct subscales: one focusing on anxiety and the other on depression. Each subscale consists of seven items, which participants rate using a Likert-Type scale ranging from 0 to 3. Higher scores on the scale indicate heightened levels of anxiety and depression. The HADS generates scores ranging from 0 to 21 for each subscale, with established guidelines categorizing scores as normal (0–7), mild (8–10), moderate (11–14), and severe (15–21) based on the severity of symptoms [ 34 , 35 ].

The scale has demonstrated strong psychometric properties, including good internal consistency and convergent validity. In this study, the Arabic version of HADS was utilized, ensuring reliability and validity with Cronbach’s alpha for anxiety subscale at 0.85 and for depression subscale at 0.82 [ 36 ]. Participants’ scores are categorized to delineate levels of anxiety and depression severity, facilitating a comprehensive assessment of psychosocial factors influencing medication adherence among AMI patients.

Ethical considerations and consent to participate

The study upheld rigorous ethical standards, receiving approval from both the Institutional Review Board (IRB) affiliated with the principal investigator’s (Applied Science Private University [IRB approval No.: 2022-NC-254]) in Amman, Jordan and all relevant data collection settings. The research adhered strictly to relevant guidelines and regulations, including the ethical principles of the Declaration of Helsinki [ 37 ]. Prior to participation, all participants provided formal written informed consent. We ensured they fully understood the study’s purpose, procedures, potential risks and benefits. We emphasized confidentiality and took steps to anonymize all participant information used in the manuscript and supplementary materials. Moreover, participant confidentiality was paramount. To protect their anonymity, we did not collect any identifying information and anonymized all data throughout the research process. Furthermore, the study did not involve violence, any physically or psychologically harmful procedures, or the collection of sensitive personal or clinical details that could compromise anonymity.

Throughout the research process, ethical principles rooted in respect for human dignity guided every aspect, ensuring the protection of participants’ rights and well-being. Prior to participation, individuals received detailed information about the study’s objectives, procedures, and potential risks and benefits through an informative sheet, empowering them to make informed decisions. Participation was entirely voluntary, with participants having the autonomy to withdraw at any stage without repercussions. Written consent was obtained from each participant before completing the questionnaire, affirming their informed agreement to partake in the study.

To safeguard participants’ privacy and confidentiality, stringent measures were implemented. All data collection activities were conducted in private settings, and participants’ identities were anonymized using assigned codes. Data were securely stored and accessible only to authorized researchers, ensuring confidentiality. Additionally, participants’ rights were prioritized throughout the study, with measures in place to minimize any potential risks or discomfort. Participants were assured that their decision to participate or withdraw would not affect their ongoing medical care or relationship with healthcare providers. By adhering to these ethical considerations, the study upheld the highest standards of integrity and transparency, fostering trust and ensuring the well-being of all participants involved.

Data analysis

The data analysis for this study was conducted using IBM-SPSS version 26, beginning with thorough screening to address any missing data or outliers that could potentially bias the results. Descriptive statistics, including means, standard deviations, frequencies, and percentages, were computed to elucidate the levels of medication adherence, anxiety, and depression among the participants. Multiple linear regression analysis was then employed to investigate the predictors of medication adherence, exploring the relationships between adherence and various factors such as socio-demographic variables, anxiety levels, and depression levels. Factors entered into the model included employment status, age, duration of MI, gender, educational level, monthly income, marital status, anxiety, and depression. Dummy variables were created for categorical variables with more than two categories (employment, monthly income, educational level, and marital status), with specific coding for each: Employment status (employed vs. retired), Gender (male vs. female), Educational level (≤ school vs. ≥ high diploma), Marital status (single vs. has been married), Monthly income (< 600 JD [$ 845] vs. ≥ 600 JD [$ 845]).

Before conducting the regression analysis, critical assumptions were assessed, including checks for multicollinearity and evaluation of the normal distribution of the adherence variable using the Kolmogorov-Smirnov Test. This rigorous methodology ensured the reliability and integrity of the study’s findings, providing valuable insights into the factors influencing medication adherence among AMI patients, including the complex interplay between socio-demographic factors and psychosocial variables such as anxiety and depression.

Description of socio-demographic characteristics

The demographic profile of the study participants, as outlined in Table 1 , encompasses various aspects of their background. Among the 210 individuals involved, the mean age was 53.59 years, with a standard deviation of 9.81. Gender distribution showed a slight majority of males, constituting 53.3% ( n = 112), while females accounted for 46.7% ( n = 98) of the sample. Regarding marital status, the majority were married (76.7%, n = 161), with smaller proportions reporting being single (2.4%, n = 5), divorced (8.1%, n = 17), or widowed (12.9%, n = 27). Educational attainment varied among participants, with 6.2% ( n = 13) categorized as illiterate, 21.0% ( n = 44) having an education level of ≤ high school, 26.7% ( n = 56) holding a high diploma, 34.8% ( n = 73) possessing a bachelor’s degree, and 11.4% ( n = 24) holding a post-graduate degree. Employment status indicated that 41.9% ( n = 88) worked in the public sector, 43.3% ( n = 91) in the private sector, and 14.8% ( n = 31) were retired. Concerning monthly income, the majority (80.5%, n = 169) reported earnings below 600 JD ($ 845), with the remaining 19.5% ( n = 41) having an income of 600 JD ($ 845) or above. The average duration of AMI among participants was 5.20 months, with a standard deviation of 2.48. These demographic insights provide a foundational understanding of the study population, facilitating further exploration and interpretation of the research outcomes.

Participants’ adherence to medication

The analysis of participants’ adherence to their prescribed medication regimen revealed insightful patterns across various factors, as detailed in Table 2 . Participants exhibited diverse responses regarding the difficulty in remembering to take medications and forgetting doses due to a busy schedule or other commitments. Notably, 16.7% ( n = 35) reported “Always” experiencing difficulty remembering, while 21.4% ( n = 45) stated they “Never” had this issue. Similarly, responses concerning forgetting doses due to a hectic schedule showed variation, with 19.5% ( n = 41) reporting “Always” forgetting, and 44 (21%) never experiencing this. Moreover, a considerable proportion of participants acknowledged discontinuing medication when feeling well (21.9%, n = 46) or experiencing adverse effects (22.4%, n = 47). Additionally, 24.8% ( n = 52) admitted to stopping medication without informing their healthcare provider. The total of non-adherence due to patient behavior, measured on a scale of 0 to 15, ranged from poor to good-high adherence. Specifically, 21% ( n = 44) demonstrated poor adherence, while 17.6% ( n = 37) showed good to high adherence.

The analysis investigated the extent of non-adherence among participants, focusing on factors such as additional diseases and pill burden, using a scoring system ranging from 0 to 12 to gauge adherence levels. Results revealed that 28.1% of participants fell into the category of poor adherence, indicating minimal compliance with their medication regimen due to challenges associated with additional diseases or pill complexity. Furthermore, 39.5% exhibited low adherence levels, suggesting some compliance but still falling short of optimal adherence. Approximately 20% demonstrated partial adherence, indicating moderate compliance despite facing challenges. A minority of participants, comprising 12.4%, achieved good to high adherence scores, showcasing commendable compliance despite the presence of additional diseases and pill burden. The mean score for non-adherence due to additional disease and pill burden was 8.65, with a standard deviation of 2.21, providing an overall assessment of participants’ adherence levels in this regard. These findings underscore the diverse spectrum of adherence behaviors observed among participants and highlight the impact of additional diseases and pill burden on medication adherence. Addressing these challenges through tailored interventions and support mechanisms is crucial to enhancing medication adherence and ultimately improving patient outcomes.

The analysis delved into participants’ adherence to medication, particularly examining the influence of financial constraints on adherence levels. Utilizing a scoring system ranging from 0 to 6, participants’ adherence levels due to financial limitations were categorized into four groups. Results indicated that a notable proportion of participants experienced challenges in adhering to their medication regimen due to financial constraints. Specifically, nearly a quarter of the participants (24.8%) demonstrated poor adherence, while a significant portion (41.9%) exhibited low adherence levels. However, some participants showed moderate adherence despite financial limitations, with approximately 19.5% demonstrating partial adherence. Moreover, a minority of participants (13.8%) showcased commendable adherence levels despite facing financial challenges. The mean score for non-adherence due to financial constraints was 4.44, indicating an overall assessment of participants’ adherence concerning financial obstacles.

Additionally, an overall medication adherence score was computed on a scale of 0 to 33, encompassing various factors influencing adherence beyond financial constraints. The findings revealed a diverse spectrum of adherence behaviors among participants. While a quarter of participants fell into the category of poor adherence, similar proportions exhibited low adherence levels. A moderate level of adherence was observed in approximately 19.5% of participants, with a minority achieving good to high adherence scores. The study determined that patients with AMI demonstrated partial adherence to medications, as indicated by a mean overall medication adherence score of 24.89 (± 3.64).

The findings reveal the complex nature of medication adherence influenced by forgetfulness, discontinuation patterns, regimen complexity, and financial constraints. Addressing these nuances is crucial for effective interventions, with financial constraints notably impacting adherence, requiring targeted support to enhance patient outcomes.

Participants’ anxiety symptoms

The anxiety subscale of the HADS (Table 3 ) was administered to gauge participants’ emotional states over the preceding week, categorizing responses based on symptom severity. The majority of respondents experienced feelings of being tense or ‘wound up’ occasionally (31%, n = 65) or not at all (38.5%, n = 81), with smaller cohorts reporting these sensations more frequently. Similarly, responses varied regarding feelings of impending doom, with a substantial proportion reporting no such feelings, while others experienced them to varying degrees, ranging from mild to intense.

Participants also disclosed the frequency of worrying thoughts, with the highest percentage reporting occasional occurrences, followed by varying degrees of frequency. The participants’ ability to feel relaxed showed diversity, with a notable portion indicating regular relaxation, while others reported infrequent or nonexistent feelings of relaxation. Moreover, participants reported different frequencies of sensations such as butterflies in the stomach, restlessness, and sudden panic feelings.

The severity of anxiety symptoms was categorized based on the total score of the anxiety subscale of HADS. Results indicate that 39.5% ( n = 83) had normal anxiety levels, 28.6% ( n = 60) experienced mild anxiety, 19.5% ( n = 41) had moderate anxiety, and 12.4% ( n = 26) had severe anxiety. The mean total score for the anxiety subscale was 8.38, with a standard deviation of 2.81. These findings provide valuable insights into the prevalence and severity of anxiety symptoms among the participants, contributing to a comprehensive understanding of their mental health status.

Participants’ depressive symptoms

The depression sub-scale of the HADS (Table 4 ) was employed to evaluate participants’ emotional states over the preceding week, assigning scores to responses to gauge the severity of depressive symptoms. Many participants (40.5%, n = 85) reported continued enjoyment of activities previously found pleasurable, while others noted a reduction in enjoyment levels to varying degrees.

Responses regarding the ability to find humor varied, with a notable portion (38.1%, n = 80) reporting no change in their capacity to perceive the lighter side of life, while others experienced varying levels of reduced enjoyment. Feelings of cheerfulness also exhibited diversity, with a significant proportion (42.9%, n = 90) expressing a sense of cheerfulness most of the time, contrasting with others who reported feeling cheerful less frequently or hardly at all. Participants reported feeling slowed down with varying frequency, reflecting differing levels of symptom severity, while responses regarding interest in appearance ranged from significant loss of interest to maintaining usual levels of care.

Additionally, participants expressed varying levels of anticipation for enjoyable activities, indicating diverse levels of depressive symptom severity, and reported different frequencies of being able to derive pleasure from activities, underscoring the complexity of their emotional experiences.

The severity of depressive symptoms, as assessed by the depression subscale of HADS, revealed varying degrees of impact among participants. Results indicated that 40.5% ( n = 85) exhibited normal levels of depressive symptoms, while 27.6% ( n = 58) experienced mild depression, 17.6% ( n = 37) reported moderate depression, and 14.3% ( n = 30) demonstrated severe depression. The mean total score for the depression subscale was 7.43, with a standard deviation of 2.42, indicating a predominance of normal (no depression) depressive symptoms. These findings offer valuable insights into the prevalence and severity of depressive symptoms within the studied population, contributing significantly to a comprehensive understanding of their mental health status.

Predictors of adherence to medications

The analysis utilized multiple linear regression to explore predictors of medication adherence among patients diagnosed with AMI (Table 5 ). The final regression model demonstrated statistical significance (p-value = 0.005), elucidating 21.9% of the total variance in medication adherence (adjusted R² = 0.219). Significant predictors of adherence encompassed employment status, age, duration of MI, anxiety, and depression, all with p-values less than 0.05. Specifically, the analysis unveiled a positive association between employment status and adherence, with employed participants demonstrating heightened adherence levels (β = 0.235, p = 0.002). Conversely, older age was correlated with diminished adherence (β = -0.177, p = 0.025), alongside a longer duration of MI (β = -0.172, p = 0.015). Additionally, higher levels of anxiety (β = -0.150, p = 0.030) and depression (β = -0.146, p = 0.034) were linked to poorer adherence. However, variables such as gender, educational level, and marital status did not significantly associate with adherence ( p > 0.05), nor did monthly income ( p = 0.238).

The findings of this study shed light on the complex interplay of factors influencing medication adherence among patients diagnosed with AMI in Jordan. By employing a comprehensive approach that assesses medication adherence across different subscales and explores the prevalence of anxiety and depression, as well as demographic predictors such as employment status and age, this study contributes significantly to the existing literature on medication adherence in cardiac patients. The identification of partial adherence patterns, particularly in relation to financial constraints, underscores the multifaceted nature of medication adherence challenges post-AMI. Moreover, the observed associations between adherence levels and psychological factors like anxiety and depression highlight the importance of addressing mental health in interventions aimed at improving medication adherence and overall patient outcomes. Furthermore, the study’s findings regarding demographic predictors such as employment status and age provide valuable insights into potential targets for tailored interventions to enhance medication adherence among AMI patients in Jordan. Overall, this study’s comprehensive examination of medication adherence and its determinants offers valuable implications for clinical practice and underscores the need for holistic approaches to improve patient care and outcomes in this population.

The study findings indicated good adherence in the first two subscales, related to patient behavior and additional disease/pill burden, while partial adherence was observed in the third subscale, attributed to financial constraints. These results align with previous studies [ 6 , 38 , 39 ], which similarly highlighted challenges in medication adherence post-AMI. For instance, Pietrzykowski et al. (2020) reported a decrease in medication adherence among two-thirds of patients over time [ 38 ], while Hussain et al. (2018) found declining adherence rates over a one-month follow-up period in Karachi [ 39 ]. Additionally, Shang et al. (2019) reported a significant decline in medication adherence among post-AMI patients in China after one year of follow-up, consistent with the current study’s findings on partial adherence [ 15 ].

Moreover, the study investigated the prevalence of anxiety and depression among AMI patients in Jordan. While nearly one-third of participants exhibited normal anxiety levels, the majority reported mild to severe anxiety. This contrasts with previous studies reporting higher anxiety levels among AMI patients [ 40 , 41 ]. Notably, the current study attributed the lower anxiety levels to good medication adherence, suggesting a potential relationship between adherence and reduced anxiety [ 42 , 43 , 44 , 45 ]. Similarly, depression levels varied among participants, with a significant portion experiencing mild to severe depression [ 41 , 46 , 47 ]. These findings corroborate previous research highlighting the prevalence of depressive symptoms among cardiac patients and their impact on medication adherence [ 13 , 14 , 28 , 48 ].

Furthermore, the study identified demographic factors influencing medication adherence among AMI patients in Jordan. Employed individuals demonstrated significantly higher adherence, likely due to factors such as financial stability and access to healthcare. Similarly, younger age was associated with better adherence, attributed to factors like forgetfulness among elderly patients. These findings are consistent with previous studies highlighting the influence of employment status and age on medication adherence among chronic disease patients [ 10 , 49 , 50 ].

Additionally, the study found that a lower duration of MI predicted significantly higher medication adherence. This aligns with previous research indicating a decline in adherence over time post-AMI [ 15 , 50 ]. Furthermore, lower levels of anxiety and depression were associated with higher adherence levels, highlighting the impact of psychological factors on medication adherence. These findings are supported by previous studies exploring the relationship between anxiety, depression, and medication adherence among cardiac patients [ 43 , 44 ].

In conclusion, the study provides valuable insights into medication adherence patterns and associated factors among AMI patients in Jordan, contributing to the existing literature on this topic. These findings underscore the pivotal role of employment status, age, duration of MI, anxiety, and depression as predictors of medication adherence among AMI patients. Thus, targeted interventions are warranted to bolster adherence, particularly among demographic groups susceptible to lower adherence rates and individuals confronting psychological distress.

Research implementations and recommendations

The findings of this study have several implications for research and clinical practice in the context of medication adherence among patients diagnosed with AMI in Jordan. Firstly, future research endeavors could focus on exploring the underlying mechanisms contributing to partial adherence, particularly concerning financial constraints, which emerged as a significant barrier in this study. Investigating the specific financial challenges faced by patients, such as medication costs and access to healthcare services, can provide valuable insights for developing targeted interventions aimed at alleviating these barriers. Additionally, longitudinal studies could be conducted to further elucidate the temporal dynamics of medication adherence post-AMI, allowing for a more nuanced understanding of adherence patterns over time and the identification of critical intervention points.

Furthermore, given the observed associations between medication adherence and psychological factors such as anxiety and depression, integrating mental health screening and support services into cardiac care settings is recommended. Collaborative care models that involve interdisciplinary teams comprising cardiologists, psychiatrists, and clinical psychologists can facilitate the early detection and management of mental health issues, thereby improving medication adherence and overall patient outcomes. Moreover, tailored interventions incorporating behavioral strategies, psychoeducation, and cognitive-behavioral therapy techniques could be developed to address the specific needs of patients with AMI who experience anxiety and depression.

In terms of clinical practice, healthcare providers should prioritize routine assessment of medication adherence and its determinants during patient consultations following AMI diagnosis. Utilizing validated screening tools to identify patients at risk of non-adherence and providing targeted education and counseling can help mitigate adherence barriers and promote treatment adherence. Additionally, interventions aimed at enhancing patient empowerment, such as medication reminder systems, adherence monitoring tools, and patient education materials, should be integrated into routine care practices to support patients in adhering to their prescribed medication regimens.

Overall, by addressing the multifaceted nature of medication adherence challenges and adopting a patient-centered approach that considers individual needs and preferences, healthcare providers can optimize treatment outcomes and improve the quality of care for patients with AMI in Jordan.

Study limitations

While this study offers valuable insights into medication adherence among patients with AMI in Jordan, it faces several limitations. Firstly, its cross-sectional design hinders the establishment of causal relationships between variables. Future longitudinal studies are needed to uncover the temporal dynamics of medication adherence post-AMI. Secondly, reliance on self-reported measures may introduce response bias and measurement error, suggesting the need for objective measures like medication refill rates. Additionally, the study’s single-center recruitment approach may limit generalizability, urging the need for multicenter studies with larger and more diverse samples. Moreover, the study overlooks cultural and contextual factors influencing medication adherence in Jordan, suggesting the need for qualitative exploration and culturally tailored interventions. Despite these limitations, the study provides valuable insights, laying a foundation for future research and clinical interventions in this field.

This study sheds light on the complex dynamics of medication adherence among patients diagnosed with AMI in Jordan. Despite facing limitations, such as its cross-sectional design and reliance on self-reported measures, the findings underscore the importance of addressing medication adherence post-AMI. The study highlights the need for longitudinal research to establish causal relationships and objective measures to validate adherence levels. Moreover, multicenter studies with diverse samples are crucial for enhancing generalizability. Culturally tailored interventions addressing sociocultural determinants of adherence are also imperative. Despite these challenges, this study contributes valuable insights, laying the groundwork for future research and clinical interventions aimed at improving medication adherence and ultimately enhancing patient outcomes post-AMI in Jordan.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors express their gratitude to the patients who contributed to the study. They acknowledge the Applied Science Private University in Amman, Jordan, for providing formal ethical approval and supporting the research project. This study is supported via funding from Prince Sattam Bin Abdulaziz University project number (PSAU/2023/R/1445).

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O.A., R.M., S.H., and R.E. had the major input into the design, analysis and interpretation of the data. O.A., R.M., S.H., R.E., M.Y., W.M. A.A., B.A., D.S., and M. E. were drafting the article or revising it critically for important intellectual content. All authors have seen and approved the final version of the manuscript.

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Published: 31 January 2022

The clinician’s guide to interpreting a regression analysis

Sofia Bzovsky 1 ,
Mark R. Phillips ORCID: orcid.org/0000-0003-0923-261X 2 ,
Robyn H. Guymer ORCID: orcid.org/0000-0002-9441-4356 3 , 4 ,
Charles C. Wykoff 5 , 6 ,
Lehana Thabane ORCID: orcid.org/0000-0003-0355-9734 2 , 7 ,
Mohit Bhandari ORCID: orcid.org/0000-0001-9608-4808 1 , 2 &
Varun Chaudhary ORCID: orcid.org/0000-0002-9988-4146 1 , 2

on behalf of the R.E.T.I.N.A. study group

Eye volume 36 , pages 1715–1717 ( 2022 ) Cite this article

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Outcomes research

Introduction

When researchers are conducting clinical studies to investigate factors associated with, or treatments for disease and conditions to improve patient care and clinical practice, statistical evaluation of the data is often necessary. Regression analysis is an important statistical method that is commonly used to determine the relationship between several factors and disease outcomes or to identify relevant prognostic factors for diseases [ 1 ].

This editorial will acquaint readers with the basic principles of and an approach to interpreting results from two types of regression analyses widely used in ophthalmology: linear, and logistic regression.

Linear regression analysis

Linear regression is used to quantify a linear relationship or association between a continuous response/outcome variable or dependent variable with at least one independent or explanatory variable by fitting a linear equation to observed data [ 1 ]. The variable that the equation solves for, which is the outcome or response of interest, is called the dependent variable [ 1 ]. The variable that is used to explain the value of the dependent variable is called the predictor, explanatory, or independent variable [ 1 ].

In a linear regression model, the dependent variable must be continuous (e.g. intraocular pressure or visual acuity), whereas, the independent variable may be either continuous (e.g. age), binary (e.g. sex), categorical (e.g. age-related macular degeneration stage or diabetic retinopathy severity scale score), or a combination of these [ 1 ].

When investigating the effect or association of a single independent variable on a continuous dependent variable, this type of analysis is called a simple linear regression [ 2 ]. In many circumstances though, a single independent variable may not be enough to adequately explain the dependent variable. Often it is necessary to control for confounders and in these situations, one can perform a multivariable linear regression to study the effect or association with multiple independent variables on the dependent variable [ 1 , 2 ]. When incorporating numerous independent variables, the regression model estimates the effect or contribution of each independent variable while holding the values of all other independent variables constant [ 3 ].

When interpreting the results of a linear regression, there are a few key outputs for each independent variable included in the model:

Estimated regression coefficient—The estimated regression coefficient indicates the direction and strength of the relationship or association between the independent and dependent variables [ 4 ]. Specifically, the regression coefficient describes the change in the dependent variable for each one-unit change in the independent variable, if continuous [ 4 ]. For instance, if examining the relationship between a continuous predictor variable and intra-ocular pressure (dependent variable), a regression coefficient of 2 means that for every one-unit increase in the predictor, there is a two-unit increase in intra-ocular pressure. If the independent variable is binary or categorical, then the one-unit change represents switching from one category to the reference category [ 4 ]. For instance, if examining the relationship between a binary predictor variable, such as sex, where ‘female’ is set as the reference category, and intra-ocular pressure (dependent variable), a regression coefficient of 2 means that, on average, males have an intra-ocular pressure that is 2 mm Hg higher than females.

Confidence Interval (CI)—The CI, typically set at 95%, is a measure of the precision of the coefficient estimate of the independent variable [ 4 ]. A large CI indicates a low level of precision, whereas a small CI indicates a higher precision [ 5 ].

P value—The p value for the regression coefficient indicates whether the relationship between the independent and dependent variables is statistically significant [ 6 ].

Logistic regression analysis

As with linear regression, logistic regression is used to estimate the association between one or more independent variables with a dependent variable [ 7 ]. However, the distinguishing feature in logistic regression is that the dependent variable (outcome) must be binary (or dichotomous), meaning that the variable can only take two different values or levels, such as ‘1 versus 0’ or ‘yes versus no’ [ 2 , 7 ]. The effect size of predictor variables on the dependent variable is best explained using an odds ratio (OR) [ 2 ]. ORs are used to compare the relative odds of the occurrence of the outcome of interest, given exposure to the variable of interest [ 5 ]. An OR equal to 1 means that the odds of the event in one group are the same as the odds of the event in another group; there is no difference [ 8 ]. An OR > 1 implies that one group has a higher odds of having the event compared with the reference group, whereas an OR < 1 means that one group has a lower odds of having an event compared with the reference group [ 8 ]. When interpreting the results of a logistic regression, the key outputs include the OR, CI, and p-value for each independent variable included in the model.

Clinical example

Sen et al. investigated the association between several factors (independent variables) and visual acuity outcomes (dependent variable) in patients receiving anti-vascular endothelial growth factor therapy for macular oedema (DMO) by means of both linear and logistic regression [ 9 ]. Multivariable linear regression demonstrated that age (Estimate −0.33, 95% CI − 0.48 to −0.19, p < 0.001) was significantly associated with best-corrected visual acuity (BCVA) at 100 weeks at alpha = 0.05 significance level [ 9 ]. The regression coefficient of −0.33 means that the BCVA at 100 weeks decreases by 0.33 with each additional year of older age.

Multivariable logistic regression also demonstrated that age and ellipsoid zone status were statistically significant associated with achieving a BCVA letter score >70 letters at 100 weeks at the alpha = 0.05 significance level. Patients ≥75 years of age were at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those <50 years of age, since the OR is less than 1 (OR 0.96, 95% CI 0.94 to 0.98, p = 0.001) [ 9 ]. Similarly, patients between the ages of 50–74 years were also at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those <50 years of age, since the OR is less than 1 (OR 0.15, 95% CI 0.04 to 0.48, p = 0.001) [ 9 ]. As well, those with a not intact ellipsoid zone were at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those with an intact ellipsoid zone (OR 0.20, 95% CI 0.07 to 0.56; p = 0.002). On the other hand, patients with an ungradable/questionable ellipsoid zone were at an increased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those with an intact ellipsoid zone, since the OR is greater than 1 (OR 2.26, 95% CI 1.14 to 4.48; p = 0.02) [ 9 ].

The narrower the CI, the more precise the estimate is; and the smaller the p value (relative to alpha = 0.05), the greater the evidence against the null hypothesis of no effect or association.

Simply put, linear and logistic regression are useful tools for appreciating the relationship between predictor/explanatory and outcome variables for continuous and dichotomous outcomes, respectively, that can be applied in clinical practice, such as to gain an understanding of risk factors associated with a disease of interest.

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R.E.T.I.N.A. study group

Varun Chaudhary 1,2 , Mohit Bhandari 1,2 , Charles C. Wykoff 5,6 , Sobha Sivaprasad 8 , Lehana Thabane 2,7 , Peter Kaiser 9 , David Sarraf 10 , Sophie J. Bakri 11 , Sunir J. Garg 12 , Rishi P. Singh 13,14 , Frank G. Holz 15 , Tien Y. Wong 16,17 , and Robyn H. Guymer 3,4

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Department of Surgery, McMaster University, Hamilton, ON, Canada

Sofia Bzovsky, Mohit Bhandari & Varun Chaudhary

Department of Health Research Methods, Evidence & Impact, McMaster University, Hamilton, ON, Canada

Mark R. Phillips, Lehana Thabane, Mohit Bhandari & Varun Chaudhary

Centre for Eye Research Australia, Royal Victorian Eye and Ear Hospital, East Melbourne, VIC, Australia

Robyn H. Guymer

Department of Surgery, (Ophthalmology), The University of Melbourne, Melbourne, VIC, Australia

Retina Consultants of Texas (Retina Consultants of America), Houston, TX, USA

Charles C. Wykoff

Blanton Eye Institute, Houston Methodist Hospital, Houston, TX, USA

Biostatistics Unit, St. Joseph’s Healthcare Hamilton, Hamilton, ON, Canada

Lehana Thabane

NIHR Moorfields Biomedical Research Centre, Moorfields Eye Hospital, London, UK

Sobha Sivaprasad

Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA

Peter Kaiser

Retinal Disorders and Ophthalmic Genetics, Stein Eye Institute, University of California, Los Angeles, CA, USA

David Sarraf

Department of Ophthalmology, Mayo Clinic, Rochester, MN, USA

Sophie J. Bakri

The Retina Service at Wills Eye Hospital, Philadelphia, PA, USA

Sunir J. Garg

Center for Ophthalmic Bioinformatics, Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA

Rishi P. Singh

Cleveland Clinic Lerner College of Medicine, Cleveland, OH, USA

Department of Ophthalmology, University of Bonn, Bonn, Germany

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Singapore Eye Research Institute, Singapore, Singapore

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Singapore National Eye Centre, Duke-NUD Medical School, Singapore, Singapore

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Varun Chaudhary
, Mohit Bhandari
, Charles C. Wykoff
, Sobha Sivaprasad
, Lehana Thabane
, Peter Kaiser
, David Sarraf
, Sophie J. Bakri
, Sunir J. Garg
, Rishi P. Singh
, Frank G. Holz
, Tien Y. Wong
& Robyn H. Guymer

Contributions

SB was responsible for writing, critical review and feedback on manuscript. MRP was responsible for conception of idea, critical review and feedback on manuscript. RHG was responsible for critical review and feedback on manuscript. CCW was responsible for critical review and feedback on manuscript. LT was responsible for critical review and feedback on manuscript. MB was responsible for conception of idea, critical review and feedback on manuscript. VC was responsible for conception of idea, critical review and feedback on manuscript.

Corresponding author

Correspondence to Varun Chaudhary .

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Competing interests.

SB: Nothing to disclose. MRP: Nothing to disclose. RHG: Advisory boards: Bayer, Novartis, Apellis, Roche, Genentech Inc.—unrelated to this study. CCW: Consultant: Acuela, Adverum Biotechnologies, Inc, Aerpio, Alimera Sciences, Allegro Ophthalmics, LLC, Allergan, Apellis Pharmaceuticals, Bayer AG, Chengdu Kanghong Pharmaceuticals Group Co, Ltd, Clearside Biomedical, DORC (Dutch Ophthalmic Research Center), EyePoint Pharmaceuticals, Gentech/Roche, GyroscopeTx, IVERIC bio, Kodiak Sciences Inc, Novartis AG, ONL Therapeutics, Oxurion NV, PolyPhotonix, Recens Medical, Regeron Pharmaceuticals, Inc, REGENXBIO Inc, Santen Pharmaceutical Co, Ltd, and Takeda Pharmaceutical Company Limited; Research funds: Adverum Biotechnologies, Inc, Aerie Pharmaceuticals, Inc, Aerpio, Alimera Sciences, Allergan, Apellis Pharmaceuticals, Chengdu Kanghong Pharmaceutical Group Co, Ltd, Clearside Biomedical, Gemini Therapeutics, Genentech/Roche, Graybug Vision, Inc, GyroscopeTx, Ionis Pharmaceuticals, IVERIC bio, Kodiak Sciences Inc, Neurotech LLC, Novartis AG, Opthea, Outlook Therapeutics, Inc, Recens Medical, Regeneron Pharmaceuticals, Inc, REGENXBIO Inc, Samsung Pharm Co, Ltd, Santen Pharmaceutical Co, Ltd, and Xbrane Biopharma AB—unrelated to this study. LT: Nothing to disclose. MB: Research funds: Pendopharm, Bioventus, Acumed—unrelated to this study. VC: Advisory Board Member: Alcon, Roche, Bayer, Novartis; Grants: Bayer, Novartis—unrelated to this study.

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Bzovsky, S., Phillips, M.R., Guymer, R.H. et al. The clinician’s guide to interpreting a regression analysis. Eye 36 , 1715–1717 (2022). https://doi.org/10.1038/s41433-022-01949-z

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Received : 08 January 2022

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Accepted : 18 January 2022

Published : 31 January 2022

Issue Date : September 2022

DOI : https://doi.org/10.1038/s41433-022-01949-z

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Dennis G O'Connell

2 Hardin-Simmons University, Department of Physical Therapy, Abilene, TX

Research related to cardiorespiratory fitness often uses regression analysis in order to predict cardiorespiratory status or future outcomes. Reading these studies can be tedious and difficult unless the reader has a thorough understanding of the processes used in the analysis. This feature seeks to “simplify” the process of regression analysis for prediction in order to help readers understand this type of study more easily. Examples of the use of this statistical technique are provided in order to facilitate better understanding.

INTRODUCTION

Graded, maximal exercise tests that directly measure maximum oxygen consumption (VO 2 max) are impractical in most physical therapy clinics because they require expensive equipment and personnel trained to administer the tests. Performing these tests in the clinic may also require medical supervision; as a result researchers have sought to develop exercise and non-exercise models that would allow clinicians to predict VO 2 max without having to perform direct measurement of oxygen uptake. In most cases, the investigators utilize regression analysis to develop their prediction models.

Regression analysis is a statistical technique for determining the relationship between a single dependent (criterion) variable and one or more independent (predictor) variables. The analysis yields a predicted value for the criterion resulting from a linear combination of the predictors. According to Pedhazur, 15 regression analysis has 2 uses in scientific literature: prediction, including classification, and explanation. The following provides a brief review of the use of regression analysis for prediction. Specific emphasis is given to the selection of the predictor variables (assessing model efficiency and accuracy) and cross-validation (assessing model stability). The discussion is not intended to be exhaustive. For a more thorough explanation of regression analysis, the reader is encouraged to consult one of many books written about this statistical technique (eg, Fox; 5 Kleinbaum, Kupper, & Muller; 12 Pedhazur; 15 and Weisberg 16 ). Examples of the use of regression analysis for prediction are drawn from a study by Bradshaw et al. 3 In this study, the researchers' stated purpose was to develop an equation for prediction of cardiorespiratory fitness (CRF) based on non-exercise (N-EX) data.

SELECTING THE CRITERION (OUTCOME MEASURE)

The first step in regression analysis is to determine the criterion variable. Pedhazur 15 suggests that the criterion have acceptable measurement qualities (ie, reliability and validity). Bradshaw et al 3 used VO 2 max as the criterion of choice for their model and measured it using a maximum graded exercise test (GXT) developed by George. 6 George 6 indicated that his protocol for testing compared favorably with the Bruce protocol in terms of predictive ability and had good test-retest reliability ( ICC = .98 –.99). The American College of Sports Medicine indicates that measurement of VO 2 max is the “gold standard” for measuring cardiorespiratory fitness. 1 These facts support that the criterion selected by Bradshaw et al 3 was appropriate and meets the requirements for acceptable reliability and validity.

SELECTING THE PREDICTORS: MODEL EFFICIENCY

Once the criterion has been selected, predictor variables should be identified (model selection). The aim of model selection is to minimize the number of predictors which account for the maximum variance in the criterion. 15 In other words, the most efficient model maximizes the value of the coefficient of determination ( R 2 ). This coefficient estimates the amount of variance in the criterion score accounted for by a linear combination of the predictor variables. The higher the value is for R 2 , the less error or unexplained variance and, therefore, the better prediction. R 2 is dependent on the multiple correlation coefficient ( R ), which describes the relationship between the observed and predicted criterion scores. If there is no difference between the predicted and observed scores, R equals 1.00. This represents a perfect prediction with no error and no unexplained variance ( R 2 = 1.00). When R equals 0.00, there is no relationship between the predictor(s) and the criterion and no variance in scores has been explained ( R 2 = 0.00). The chosen variables cannot predict the criterion. The goal of model selection is, as stated previously, to develop a model that results in the highest estimated value for R 2 .

According to Pedhazur, 15 the value of R is often overestimated. The reasons for this are beyond the scope of this discussion; however, the degree of overestimation is affected by sample size. The larger the ratio is between the number of predictors and subjects, the larger the overestimation. To account for this, sample sizes should be large and there should be 15 to 30 subjects per predictor. 11 , 15 Of course, the most effective way to determine optimal sample size is through statistical power analysis. 11 , 15

Another method of determining the best model for prediction is to test the significance of adding one or more variables to the model using the partial F-test . This process, which is further discussed by Kleinbaum, Kupper, and Muller, 12 allows for exclusion of predictors that do not contribute significantly to the prediction, allowing determination of the most efficient model of prediction. In general, the partial F-test is similar to the F-test used in analysis of variance. It assesses the statistical significance of the difference between values for R 2 derived from 2 or more prediction models using a subset of the variables from the original equation. For example, Bradshaw et al 3 indicated that all variables contributed significantly to their prediction. Though the researchers do not detail the procedure used, it is highly likely that different models were tested, excluding one or more variables, and the resulting values for R 2 assessed for statistical difference.

Although the techniques discussed above are useful in determining the most efficient model for prediction, theory must be considered in choosing the appropriate variables. Previous research should be examined and predictors selected for which a relationship between the criterion and predictors has been established. 12 , 15

It is clear that Bradshaw et al 3 relied on theory and previous research to determine the variables to use in their prediction equation. The 5 variables they chose for inclusion–gender, age, body mass index (BMI), perceived functional ability (PFA), and physical activity rating (PAR)–had been shown in previous studies to contribute to the prediction of VO 2 max (eg, Heil et al; 8 George, Stone, & Burkett 7 ). These 5 predictors accounted for 87% ( R = .93, R 2 = .87 ) of the variance in the predicted values for VO 2 max. Based on a ratio of 1:20 (predictor:sample size), this estimate of R , and thus R 2 , is not likely to be overestimated. The researchers used changes in the value of R 2 to determine whether to include or exclude these or other variables. They reported that removal of perceived functional ability (PFA) as a variable resulted in a decrease in R from .93 to .89. Without this variable, the remaining 4 predictors would account for only 79% of the variance in VO 2 max. The investigators did note that each predictor variable contributed significantly ( p < .05 ) to the prediction of VO 2 max (see above discussion related to the partial F-test).

ASSESSING ACCURACY OF THE PREDICTION

Assessing accuracy of the model is best accomplished by analyzing the standard error of estimate ( SEE ) and the percentage that the SEE represents of the predicted mean ( SEE % ). The SEE represents the degree to which the predicted scores vary from the observed scores on the criterion measure, similar to the standard deviation used in other statistical procedures. According to Jackson, 10 lower values of the SEE indicate greater accuracy in prediction. Comparison of the SEE for different models using the same sample allows for determination of the most accurate model to use for prediction. SEE % is calculated by dividing the SEE by the mean of the criterion ( SEE /mean criterion) and can be used to compare different models derived from different samples.

Bradshaw et al 3 report a SEE of 3.44 mL·kg −1 ·min −1 (approximately 1 MET) using all 5 variables in the equation (gender, age, BMI, PFA, PA-R). When the PFA variable is removed from the model, leaving only 4 variables for the prediction (gender, age, BMI, PA-R), the SEE increases to 4.20 mL·kg −1 ·min −1 . The increase in the error term indicates that the model excluding PFA is less accurate in predicting VO 2 max. This is confirmed by the decrease in the value for R (see discussion above). The researchers compare their model of prediction with that of George, Stone, and Burkett, 7 indicating that their model is as accurate. It is not advisable to compare models based on the SEE if the data were collected from different samples as they were in these 2 studies. That type of comparison should be made using SEE %. Bradshaw and colleagues 3 report SEE % for their model (8.62%), but do not report values from other models in making comparisons.

Some advocate the use of statistics derived from the predicted residual sum of squares ( PRESS ) as a means of selecting predictors. 2 , 4 , 16 These statistics are used more often in cross-validation of models and will be discussed in greater detail later.

ASSESSING STABILITY OF THE MODEL FOR PREDICTION

Once the most efficient and accurate model for prediction has been determined, it is prudent that the model be assessed for stability. A model, or equation, is said to be “stable” if it can be applied to different samples from the same population without losing the accuracy of the prediction. This is accomplished through cross-validation of the model. Cross-validation determines how well the prediction model developed using one sample performs in another sample from the same population. Several methods can be employed for cross-validation, including the use of 2 independent samples, split samples, and PRESS -related statistics developed from the same sample.

Using 2 independent samples involves random selection of 2 groups from the same population. One group becomes the “training” or “exploratory” group used for establishing the model of prediction. 5 The second group, the “confirmatory” or “validatory” group is used to assess the model for stability. The researcher compares R 2 values from the 2 groups and assessment of “shrinkage,” the difference between the two values for R 2 , is used as an indicator of model stability. There is no rule of thumb for interpreting the differences, but Kleinbaum, Kupper, and Muller 12 suggest that “shrinkage” values of less than 0.10 indicate a stable model. While preferable, the use of independent samples is rarely used due to cost considerations.

A similar technique of cross-validation uses split samples. Once the sample has been selected from the population, it is randomly divided into 2 subgroups. One subgroup becomes the “exploratory” group and the other is used as the “validatory” group. Again, values for R 2 are compared and model stability is assessed by calculating “shrinkage.”

Holiday, Ballard, and McKeown 9 advocate the use of PRESS-related statistics for cross-validation of regression models as a means of dealing with the problems of data-splitting. The PRESS method is a jackknife analysis that is used to address the issue of estimate bias associated with the use of small sample sizes. 13 In general, a jackknife analysis calculates the desired test statistic multiple times with individual cases omitted from the calculations. In the case of the PRESS method, residuals, or the differences between the actual values of the criterion for each individual and the predicted value using the formula derived with the individual's data removed from the prediction, are calculated. The PRESS statistic is the sum of the squares of the residuals derived from these calculations and is similar to the sum of squares for the error (SS error ) used in analysis of variance (ANOVA). Myers 14 discusses the use of the PRESS statistic and describes in detail how it is calculated. The reader is referred to this text and the article by Holiday, Ballard, and McKeown 9 for additional information.

Once determined, the PRESS statistic can be used to calculate a modified form of R 2 and the SEE . R 2 PRESS is calculated using the following formula: R 2 PRESS = 1 – [ PRESS / SS total ], where SS total equals the sum of squares for the original regression equation. 14 Standard error of the estimate for PRESS ( SEE PRESS ) is calculated as follows: SEE PRESS =, where n equals the number of individual cases. 14 The smaller the difference between the 2 values for R 2 and SEE , the more stable the model for prediction. Bradshaw et al 3 used this technique in their investigation. They reported a value for R 2 PRESS of .83, a decrease of .04 from R 2 for their prediction model. Using the standard set by Kleinbaum, Kupper, and Muller, 12 the model developed by these researchers would appear to have stability, meaning it could be used for prediction in samples from the same population. This is further supported by the small difference between the SEE and the SEE PRESS , 3.44 and 3.63 mL·kg −1 ·min −1 , respectively.

COMPARING TWO DIFFERENT PREDICTION MODELS

A comparison of 2 different models for prediction may help to clarify the use of regression analysis in prediction. Table Table1 1 presents data from 2 studies and will be used in the following discussion.

Comparison of Two Non-exercise Models for Predicting CRF

Variables	Heil et al = 374	Bradshaw et al = 100

Intercept	36.580	48.073
Gender (male = 1, female = 0)	3.706	6.178
Age (years)	0.558	−0.246
Age	−7.81 E-3
Percent body fat	−0.541
Body mass index (kg-m )		−0.619
Activity code (0-7)	1.347
Physical activity rating (0–10)		0.671
Perceived functional abilty		0.712

	)
	.88 (.77)	.93 (.87)


	4.90·mL–kg ·min	3.44 mL·kg min


	12.7%	8.6%

As noted above, the first step is to select an appropriate criterion, or outcome measure. Bradshaw et al 3 selected VO 2 max as their criterion for measuring cardiorespiratory fitness. Heil et al 8 used VO 2 peak. These 2 measures are often considered to be the same, however, VO 2 peak assumes that conditions for measuring maximum oxygen consumption were not met. 17 It would be optimal to compare models based on the same criterion, but that is not essential, especially since both criteria measure cardiorespiratory fitness in much the same way.

The second step involves selection of variables for prediction. As can be seen in Table Table1, 1 , both groups of investigators selected 5 variables to use in their model. The 5 variables selected by Bradshaw et al 3 provide a better prediction based on the values for R 2 (.87 and .77), indicating that their model accounts for more variance (87% versus 77%) in the prediction than the model of Heil et al. 8 It should also be noted that the SEE calculated in the Bradshaw 3 model (3.44 mL·kg −1 ·min −1 ) is less than that reported by Heil et al 8 (4.90 mL·kg −1 ·min −1 ). Remember, however, that comparison of the SEE should only be made when both models are developed using samples from the same population. Comparing predictions developed from different populations can be accomplished using the SEE% . Review of values for the SEE% in Table Table1 1 would seem to indicate that the model developed by Bradshaw et al 3 is more accurate because the percentage of the mean value for VO 2 max represented by error is less than that reported by Heil et al. 8 In summary, the Bradshaw 3 model would appear to be more efficient, accounting for more variance in the prediction using the same number of variables. It would also appear to be more accurate based on comparison of the SEE% .

The 2 models cannot be compared based on stability of the models. Each set of researchers used different methods for cross-validation. Both models, however, appear to be relatively stable based on the data presented. A clinician can assume that either model would perform fairly well when applied to samples from the same populations as those used by the investigators.

The purpose of this brief review has been to demystify regression analysis for prediction by explaining it in simple terms and to demonstrate its use. When reviewing research articles in which regression analysis has been used for prediction, physical therapists should ensure that the: (1) criterion chosen for the study is appropriate and meets the standards for reliability and validity, (2) processes used by the investigators to assess both model efficiency and accuracy are appropriate, 3) predictors selected for use in the model are reasonable based on theory or previous research, and 4) investigators assessed model stability through a process of cross-validation, providing the opportunity for others to utilize the prediction model in different samples drawn from the same population.

A Study on Multiple Linear Regression Analysis

December 2013
Procedia - Social and Behavioral Sciences 106:234–240
106:234–240
CC BY-NC-ND 3.0

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Regression Analysis for Prediction: Understanding the Process

Dennis G O'Connell

INTRODUCTION

SELECTING THE CRITERION (OUTCOME MEASURE)