Parametric causal mediation analysis with asymmetric binary regression model

Mediation analysis is an important statistical method in prevention research, as it can be used to determine effective intervention components. Traditional mediation analysis defines direct and indirect effects in terms of linear regression coefficients. It is unclear how these traditional effects are estimated in settings with binary variables. An important recent methodological advancement in the mediation analysis literature is the development of the causal mediation analysis framework. Causal mediation analysis defines causal effects as the difference between two potential outcomes. These definitions can be applied to any mediation model to estimate natural direct and indirect effects, including models with binary variables and an exposure–mediator interaction. This paper aims to clarify the similarities and differences between the causal and traditional effect estimates for mediation models with a binary mediator and a binary outcome. Causal and traditional mediation analyses were applied to an empirical example to demonstrate these similarities and differences. Causal and traditional mediation analysis provided similar controlled direct effect estimates, but different estimates of the natural direct effects, natural indirect effects, and total effect. Traditional mediation analysis methods do not generalize well to mediation models with binary variables, while the natural effect definitions can be applied to any mediation model. Causal mediation analysis is therefore the preferred method for the analysis of mediation models with binary variables.

Causal mediation analysis has gained increasing attention in recent years. This article guides empirical researchers through the concepts and challenges of causal mediation analysis. I first clarify the difference between traditional and causal mediation analysis and highlight the importance of adjusting for the treatment-by-mediator interaction and confounders of the treatment–mediator, treatment–outcome, and mediator–outcome relationships. I then introduce the definition of causal mediation effects under the potential outcomes framework and different methods for the identification and estimation of the effects. After that, I highlight the importance of conducting a sensitivity analysis to assess the sensitivity of analysis results to potential unmeasured confounding. I also list various statistical software that can conduct causal mediation analysis and sensitivity analysis and provide suggestions for writing a causal mediation analysis paper. Finally, I briefly introduce some extensions that I made with my colleagues, including power analysis, multisite causal mediation analysis, causal moderated mediation analysis, and relaxing the assumption of no post-treatment confounding.

Mediation analysis is widely used in psychology to assess how an independent variable transmits its causal effect on an outcome both directly and indirectly through intermediary variables known as mediators. Causal mediation analysis addresses numerous criticisms of product-of-coefficients approach, often regarded as the primary method for estimating indirect effects in psychological research. However, navigating causal mediation analysis, especially in settings with multiple mediators, can be challenging for those unfamiliar with its concepts, assumptions, and estimation strategies. In this tutorial, we therefore offer a comprehensive guide to conducting causal mediation analysis with two mediators across three data-generating mechanisms: setups with causally dependent mediators, independent mediators, and noncausally dependent mediators. For each of these mechanisms, we provide formal mathematical definitions and assumptions for the natural direct and indirect effects, along with less technical explanations of these concepts. We also provide R and Stata codes for estimating the natural direct effect, the joint natural indirect effect, and the path-specific natural indirect effects using four different estimators: the imputation approach, the extended imputation approach, the inverse probability weighted approach, and the extended quasi-Bayesian Monte Carlo approach. Additionally, we illustrate each of these methods with examples from the International Dating Violence Study. This tutorial aims to equip applied researchers in psychology with all the necessary tools to conduct causal mediation analysis involving two mediators across various multiple mediators setups. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Disentangling contextual effects from musculoskeletal treatments

Causal mediation analysis is a useful tool for epidemiologic research, but it has been criticized for relying on a "cross-world" independence assumption that counterfactual outcome and mediator values are independent even in causal worlds where the exposure assignments for the outcome and mediator differ. This assumption is empirically difficult to verify and problematic to justify based on background knowledge. In the present article, we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and nonparametric identification of natural direct and indirect effects. In particular, we give a practical example of an applied setting where the cross-world independence assumption is violated even without any post-treatment confounding. Further, we review possible alternatives to the cross-world independence assumption, including the use of bounds that avoid the assumption altogether. Finally, we carry out a numeric study in which the cross-world independence assumption is violated to assess the ensuing bias in estimating natural direct and indirect effects. We conclude with recommendations for carrying out causal mediation analyses.

Causal mediation analysis seeks to decompose the effect of a treatment or exposure among multiple possible paths and provide casually interpretable path-specific effect estimates. Recent advances have extended causal mediation analysis to situations with a sequence of mediators or multiple contemporaneous mediators. However, available methods still have limitations, and computational and other challenges remain. The present paper provides an extended causal mediation and path analysis methodology. The new method, implemented in the new R package, gmediation (described in a companion paper), accommodates both a sequence (two stages) of mediators and multiple mediators at each stage, and allows for multiple types of outcomes following generalized linear models. The methodology can also handle unsaturated models and clustered data. Addressing other practical issues, we provide new guidelines for the choice of a decomposition, and for the choice of a reference group multiplier for the reduction of Monte Carlo error in mediation formula computations. The new method is applied to data from a cohort study to illuminate the contribution of alternative biological and behavioral paths in the effect of socioeconomic status on dental caries in adolescence.

With reference to causal mediation analysis, a parametric expression for natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator, both modelled via a logistic regression. The proposed effect decomposition operates on the odds ratio scale and does not require the outcome to be rare. It generalizes the existing ones, allowing for interactions between both the exposure and the mediator and the confounding covariates. The derived parametric formulae are flexible, in that they readily adapt to the two different natural effect decompositions defined in the mediation literature. In parallel with results derived under the rare outcome assumption, they also outline the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, isolating the controlled direct effect in the natural direct effect expressions. Formulae for standard errors, obtained via the delta method, are also given. An empirical application to data coming from a microfinance experiment performed in Bosnia and Herzegovina is illustrated.

Traditional mediation analysis, which relies on linear regression models, has faced criticism due to its limited suitability for cases involving different types of variables and complex covariates, such as interactions. This can result in unclear definitions of direct and indirect effects. As an alternative, causal mediation analysis using the counterfactual framework has been introduced to provide clearer definitions of direct and indirect effects while allowing for more flexible modeling methods. However, the conceptual understanding of this approach based on the counterfactual framework remains challenging for applied researchers. To address this issue, the present article was written to highlight and illustrate the definitions of causal estimands, including controlled direct effect, natural direct effect, and natural indirect effect, based on the key concept of nested counterfactuals. Furthermore, we recommend using 2 R packages, ‘medflex’ and ‘mediation’, to perform causal mediation analysis and provide public health examples. The article also offers caveats and guidelines for accurate interpretation of the results.

The objective of the study was to investigate the contribution of work factors and health-related lifestyle to educational inequalities in physical health among older workers in Germany by applying causal mediation analysis with longitudinal data. Data from the German lidA study was used. 2653 persons (53% female, 47% male) aged 46 (born 1965) and 52 (born 1959) at baseline were followed up for seven years with exposure and outcome assessments in 2011 (t0), 2014 (t1) and 2018 (t2). The total effect of education on physical health was decomposed into a natural direct effect (NDE) and a natural indirect effect (NIE) by using a sex-stratified causal mediation analysis with an inverse odds weighting approach. Baseline health, partner status and working hours were entered as a first set of mediators preceding the putative mediators of interest. All analyses were adjusted for age and migrant status. Independent of the first set of mediators, work factors explained 21% of educational inequalities in physical health between low and high educated women and 0% comparing moderate versus high educated women. The addition of health behaviors explained further 26% (low vs. high education) and 20% (moderate vs. high education), respectively. Among men, net of the first set of mediators, work factors explained 5% of educational inequalities in physical health between low and high educated and 6% comparing moderate versus high educated persons. Additional 24% (low vs. high education) and 27% (moderate vs. high education) were explained by adding health behaviors to the models. To reduce educational inequalities in physical health among older workers in Germany, interventions to promote healthy behaviors are promising. Improving working conditions is likely an important prerequisite.

Background:Surgical interventions allow for tailoring of treatment to individual patients and implementation may vary with surgeon and healthcare provider. In addition, in clinical trials assessing two competing surgical interventions, the treatments may be accompanied by co-interventions.Aims:This study explores the use of causal mediation analysis to (1) delineate the treatment effect that results directly from the surgical intervention under study and the indirect effect acting through a co-intervention and (2) to evaluate the benefit of the surgical intervention if either everybody in the trial population received the co-intervention or nobody received it.Methods:Within a counterfactual framework, relevant direct and indirect effects of a surgical intervention are estimated and adjusted for confounding via parametric regression models, for the situation where both mediator and outcome are binary, with baseline stratification factors included as fixed effects and surgeons as random intercepts. The causal difference in probability of a successful outcome (estimand of interest) is calculated using Monte Carlo simulation with bootstrapping for confidence intervals. Packages for estimation within standard statistical software are reviewed briefly. A step by step application of methods is illustrated using the Amaze randomised trial of ablation as an adjunct to cardiac surgery in patients with irregular heart rhythm, with a co-intervention (removal of the left atrial appendage) administered to a subset of participants at the surgeon’s discretion. The primary outcome was return to normal heart rhythm at one year post surgery.Results:In Amaze, 17% (95% confidence interval: 6%, 28%) more patients in the active arm had a successful outcome, but there was a large difference between active and control arms in the proportion of patients who received the co-intervention (55% and 30%, respectively). Causal mediation analysis suggested that around 1% of the treatment effect was attributable to the co-intervention (16% natural direct effect). The controlled direct effect ranged from 18% (6%, 30%) if the co-intervention were mandated, to 14% (2%, 25%) if it were prohibited. Including age as a moderator of the mediation effects showed that the natural direct effect of ablation appeared to decrease with age.Conclusions:Causal mediation analysis is a useful quantitative tool to explore mediating effects of co-interventions in surgical trials. In Amaze, investigators could be reassured that the effect of the active treatment, not explainable by differential use of the co-intervention, was significant across analyses.

SAS Macro for Causal Mediation Analysis with Survival Data

Recent work has considerably advanced the definition, identification and estimation of controlled direct, and natural direct and indirect effects in causal mediation analysis. Despite the various estimation methods and statistical routines being developed, a unified approach for effect estimation under different effect decomposition scenarios is still needed for epidemiologic research. G-computation offers such unification and has been used for total effect and joint controlled direct effect estimation settings, involving different types of exposure and outcome variables. In this study, we demonstrate the utility of parametric g-computation in estimating various components of the total effect, including (1) natural direct and indirect effects, (2) standard and stochastic controlled direct effects, and (3) reference and mediated interaction effects, using Monte Carlo simulations in standard statistical software. For each study subject, we estimated their nested potential outcomes corresponding to the (mediated) effects of an intervention on the exposure wherein the mediator was allowed to attain the value it would have under a possible counterfactual exposure intervention, under a pre-specified distribution of the mediator independent of any causes, or under a fixed controlled value. A final regression of the potential outcome on the exposure intervention variable was used to compute point estimates and bootstrap was used to obtain confidence intervals. Through contrasting different potential outcomes, this analytical framework provides an intuitive way of estimating effects under the recently introduced 3- and 4-way effect decomposition. This framework can be extended to complex multivariable and longitudinal mediation settings.

Exploring the mediators of the BOOST intervention on walking disability at 12 months: a causal mediation analysis.

BackgroundEpidemiological studies examining the direct and indirect effects of gestational diabetes mellitus (GDM) on offspring early childhood developmental vulnerability are lacking. Therefore, the aims of this study were to estimate the direct and indirect effects of GDM (through preterm birth) on early childhood developmental vulnerability.MethodsWe conducted a retrospective population-based cohort study on the association between gestational diabetes mellitus and early childhood developmental vulnerability in children born in Western Australia (WA) using maternal, infant and birth records from the Midwives Notification, Hospitalizations, Developmental Anomalies, and the Australian Early Development Census (AEDC) databases. We used two aggregated outcome measures: developmentally vulnerable on at least one AEDC domain (DV1) and developmentally vulnerable on at least two AEDC domains (DV2). Causal mediation analysis was applied to estimate the natural direct (NDE), indirect (NIE), and total (TE) effects as relative risks (RR).ResultsIn the whole cohort (n = 64,356), approximately 22% were classified as DV1 and 11% as DV2 on AEDC domains. Estimates of the natural direct effect suggested that children exposed to GDM were more likely to be classified as DV1 (RR = 1.20, 95% CI: 1.10–1.31) and DV2 (RR = 1.34, 95% CI: 1.19–1.50) after adjusting for potential confounders. About 6% and 4% of the effect of GDM on early childhood developmental vulnerability was mediated by preterm birth for DV1 and DV2, respectively.ConclusionChildren exposed to gestational diabetes mellitus were more likely to be developmentally vulnerable in one or more AEDC domains. The biological mechanism for these associations is not well explained by mediation through preterm birth.

The ε4 allele of the APOE gene (APOE4) is known for its negative association with human longevity; however, the mechanism is unclear. APOE4 is also linked to changes in body weight, and the latter changes were associated with survival in some studies. Here, we explore the role of aging changes in weight in the connection between APOE4 and longevity using the causal mediation analysis (CMA) approach to uncover the mechanisms of genetic associations. Using the Health and Retirement Study (HRS) data, we tested a hypothesis of whether the association of APOE4 with reduced survival to age 85+ is mediated by key characteristics of age trajectories of weight, such as the age at reaching peak values and the slope of the decline in weight afterward. Mediation effects were evaluated by the total effect (TE), natural indirect effect, and percentage mediated. The controlled direct effect and natural direct effect are also reported. The CMA results suggest that APOE4 carriers have 19%–22% (TE p = 0.020–0.039) lower chances of surviving to age 85 and beyond, in part, because they reach peak values of weight at younger ages, and their weight declines faster afterward compared to non-carriers. This finding is in line with the idea that the detrimental effect of APOE4 on longevity is, in part, related to the accelerated physical aging of ε4 carriers.