Statistical Mediation Analysis for Models with a Binary Mediator and a Binary Outcome: the Differences Between Causal and Traditional Mediation Analysis

SAS Macro for Causal Mediation Analysis with Survival Data

An important recent development in mediation analysis is the use of causal mediation analysis. Causal mediation analysis decomposes the total exposure effect into causal direct and indirect effects in the presence of exposure-mediator interaction. However, in practice, traditional mediation analysis is still most widely used. The aim of this paper is to demonstrate the similarities and differences between the causal and traditional estimators for mediation models with a continuous mediator, a binary outcome, and exposure-mediator interaction. A real-life data example, analytical comparisons, and a simulation study were used to demonstrate the similarities and differences between the traditional and causal estimators. The causal and traditional estimators provide similar indirect effect estimates, but different direct and total effect estimates. Traditional mediation analysis may only be used when conditional direct effect estimates are of interest. Causal mediation analysis is the generally preferred method as its casual effect estimates help unravel causal mechanisms.

Commentary: Mediation Analyses in the Real World.

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 has been widely applied to explain why and assess the extent to which an exposure or treatment has an impact on the outcome in health psychology studies. Identifying a mediator or assessing the impact of a mediator has been the focus of many scientific investigations. This tutorial aims to introduce causal mediation analysis with binary exposure, mediator, and outcome variables, with a focus on the resampling and weighting methods, under the potential outcomes framework for estimating natural direct and indirect effects. We emphasize the importance of the temporal order of the study variables and the elimination of confounding. We define the causal effects in a hypothesized causal mediation chain in the context of one exposure, one mediator, and one outcome variable, all of which are binary variables. Two commonly used and actively maintained R packages, mediation and medflex, were used to analyze a motivating example. R code examples for implementing these methods are provided. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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).

Mediation analysis is a methodology used to understand how and why behavioral phenomena occur. New mediation methods based on the potential outcomes framework are a seminal advancement for mediation analysis because they focus on the causal basis of mediation. Despite the importance of the potential outcomes framework in other fields, the methods are not well known in prevention and other disciplines. The interaction of a treatment (X) and a mediator (M) on an outcome variable (Y) is central to the potential outcomes framework for causal mediation analysis and provides a way to link traditional and modern causal mediation methods. As described in the paper, for a continuous mediator and outcome, if the XM interaction is zero, then potential outcomes estimators of the mediated effect are equal to the traditional model estimators. If the XM interaction is nonzero, the potential outcomes estimators correspond to simple direct and simple mediated contrasts for the treatment and the control groups in traditional mediation analysis. Links between traditional and causal mediation estimators clarify the meaning of potential outcomes framework mediation quantities. A simulation study demonstrates that testing for a XM interaction that is zero in the population can reduce power to detect mediated effects, and ignoring a nonzero XM interaction in the population can also reduce power to detect mediated effects in some situations. We recommend that prevention scientists incorporate evaluation of the XM interaction in their research.

In a recent manuscript, VanderWeele and Vansteelandt (American Journal of Epidemiology, 2010,172:1339-1348) (hereafter VWV) build on results due to Judea Pearl on causal mediation analysis and derive simple closed-form expressions for so-called natural direct and indirect effects in an odds ratio context for a binary outcome and a continuous mediator. The expressions obtained by VWV make two key simplifying assumptions: The mediator is normally distributed with constant variance,The binary outcome is rare. Assumption A may not be appropriate in settings where, as can happen in routine epidemiologic applications, the distribution of the mediator variable is highly skew. However, in this note, the author establishes that under a key assumption of "no mediator-exposure interaction" in the logistic regression model for the outcome, the simple formulae of VWV continue to hold even when the normality assumption of the mediator is dropped. The author further shows that when the "no interaction" assumption is relaxed, the formula of VWV for the natural indirect effect in this setting continues to apply when assumption A is also dropped. However, an alternative formula to that of VWV for the natural direct effect is required in this context and is provided in an appendix. When the disease is not rare, the author replaces assumptions A and B with an assumption C that the mediator follows a so-called Bridge distribution in which case simple closed-form formulae are again obtained for the natural direct and indirect effects.

Causal mediation analysis is used to decompose the total effect of an exposure on an outcome into an indirect effect, taking the path through an intermediate variable, and a direct effect. To estimate these effects, strong assumptions are made about unconfoundedness of the relationships between the exposure, mediator and outcome. These assumptions are difficult to verify in a given situation and therefore a mediation analysis should be complemented with a sensitivity analysis to assess the possible impact of violations. In this paper we present a method for sensitivity analysis to not only unobserved mediator-outcome confounding, which has largely been the focus of previous literature, but also unobserved confounding involving the exposure. The setting is estimation of natural direct and indirect effects based on parametric regression models. We present results for combinations of binary and continuous mediators and outcomes and extend the sensitivity analysis for mediator-outcome confounding to cases where the continuous outcome variable is censored or truncated. The proposed methods perform well also in the presence of interactions between the exposure, mediator and observed confounders, allowing for modeling flexibility as well as exploration of effect modification. The performance of the method is illustrated through simulations and an empirical example.

In this article, we review the formulas for the natural direct and indirect effects' risk ratios introduced by Ananth and VanderWeele (Am J Epidemiol. 2011;174(1):99-108) for causal mediation analysis of a binary mediator and a binary outcome. In particular, we show that the closed-form equations Ananth and VanderWeele provided do not correspond to the log-binomial model specified by these authors for the mediator variable, but rather to a logistic model. We then provide risk ratio equations for natural direct and indirect effects that truly pertain to a log-binomial model. We conclude with a discussion on the practical implications of the binary mediator model's specification by analysts. The related impact can be negligible or not, depending on the rareness of the mediator.

BackgroundIn the causal mediation analysis framework, several parametric regression-based approaches have been introduced in past years for decomposing the total effect of an exposure on a binary outcome into a direct effect and an indirect effect through a target mediator. In this context, a well-known strategy involves specifying a logistic model for the outcome and invoking the rare outcome assumption (ROA) to simplify estimation. Recently, exact estimators for natural direct and indirect effects have been introduced to circumvent the challenges prompted by the ROA. As for the approximate approaches relying on the ROA, these exact approaches cannot be used as is on case-control data where the sampling mechanism depends on the outcome.MethodsConsidering a continuous or a binary mediator, we empirically compare the approximate and exact approaches using simulated data under various case-control scenarios. An illustration of these approaches on case-control data is provided, where the natural mediation effects of long-term use of oral contraceptives on ovarian cancer, with lifetime number of ovulatory cycles as the mediator, are estimated.ResultsIn the simulations, we found few differences between the performances of the approximate and exact approaches when the outcome was rare, both marginally and conditionally on variables. However, the performance of the approximate approaches degraded as the prevalence of the outcome increased in at least one stratum of variables. Differences in behavior were also observed among the approximate approaches. In the data analysis, all studied approaches were in agreement with respect to the natural direct and indirect effects estimates.ConclusionsIn the case where a violation of the ROA applies or is expected, approximate mediation approaches should be avoided or used with caution, and exact estimators favored.

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 aims to estimate natural direct and natural indirect effects under clearly specified assumptions. Traditional mediation analysis based on Ordinary Least Squares assumes an absence of unmeasured causes to the putative mediator and outcome. When these assumptions cannot be justified, instrumental variable estimators can be used in order to produce an asymptotically unbiased estimator of the mediator-outcome link, commonly referred to as a Two-Stage Least Squares estimator. Such bias removal, however, comes at the cost of variance inflation. A Semi-Parametric Stein-Like estimator has been proposed in the literature that strikes a natural trade-off between the unbiasedness of the Two-Stage Least Squares procedure and the relatively small variance of the Ordinary Least Squares estimator. The Semi-Parametric Stein-Like estimator has the advantage of allowing for a direct estimation of its shrinkage parameter. In this paper, we demonstrate how this Stein-like estimator can be implemented in the context of the estimation of natural direct and natural indirect effects of treatments in randomized controlled trials. The performance of the competing methods is studied in a simulation study, in which both the strength of hidden confounding and the strength of the instruments are independently varied. These considerations are motivated by a trial in mental health, evaluating the impact of a primary care-based intervention to reduce depression in the elderly.

Background:Gender inequity, a deeply-rooted driver of poor health globally, is expressed in society through gender norms, the unspoken rules that govern gender-related roles and behavior. The development of public health interventions focused on promoting equitable gender norms are gaining momentum internationally, but there remain critical gaps in the evidence about how these interventions are working to change behavioral outcomes.Methods:A four-arm cluster randomized control trial (cRCT) was conducted to evaluate the effects of the Reaching Married Adolescents in Niger (RMA) intervention on modern contraceptive use and intimate partner violence (IPV) among married adolescent girls and their husbands in Dosso, Niger (T1: 1042 dyads; 24 mos. follow-up: 737 dyads, 2016–2019). This study seeks to understand if changes in perceived inequitable gender norms among husbands are the mechanism behind effects on modern contraceptive use and IPV. We estimated natural direct and indirect effects via these gender norms using inverse odds ratio weighting. An intention-to-treat approach and a difference-in-differences estimator in a hierarchical linear probability model was used to estimate prevalence differences, along with bootstrapping to estimate confidence intervals.Results:The total effects of the RMA small group intervention (Arm 2) is estimated to be an 8% reduction in prevalence of IPV [95% CI: −0.18, 0.01]. For this arm, the natural indirect effect through gender inequitable social norms is associated with a 2% decrease (95% CI: −0.07, 0.12), accounting for 22.3% of this total effect, and the natural direct effect with a 6% decrease (95% CI: −0.20, −0.02) in IPV. Of the total effect of the RMA household visit intervention (Arm 1) on contraceptive use (20% increase), indirect effects via inequitable gender norms were associated with an 11% decrease (95% CI: −0.18, −0.01) and direct effects with a 32% increase (95% CI: 0.13, 0.44) in contraceptive use. For the combination arm, of the total effects on contraceptive use (19% increase), indirect effects were associated with a 9% decrease (95% CI: −0.20, 0.02) and direct effects with a 28% increase (95% CI: 0.12, 0.46).Conclusion:The present study contributes experimental evidence that the small group RMA intervention reduced IPV partially via reductions in perceived inequitable gender norms among husbands. Evidence also suggests that increases in perceived inequitable gender norms resulted in decreased contraceptive use among those receiving the household visit intervention component. Not only do these results open the “black box” around how the RMA small group intervention may create behavior change to help inform its future use, they provide evidence supporting behavior change theories and frameworks that postulate the importance of changing underlying social norms in order to reduce IPV and increase modern contraceptive use.

Mediation analysis provides an attractive causal inference framework to decompose the total effect of an exposure on an outcome into natural direct effects and natural indirect effects acting through a mediator. For binary outcomes, mediation analysis methods have been developed using logistic regression when the binary outcome is rare. These methods will not hold in practice when a disease is common. In this paper, we develop mediation analysis methods that relax the rare disease assumption when using logistic regression. We calculate the natural direct and indirect effects for common diseases by exploiting the relationship between logit and probit models. Specifically, we derive closed-form expressions for the natural direct and indirect effects on the odds ratio scale. Mediation models for both continuous and binary mediators are considered. We demonstrate through simulation that the proposed method performs well for common binary outcomes. We apply the proposed methods to analyze the Normative Aging Study to identify DNA methylation sites that are mediators of smoking behavior on the outcome of obstructed airway function.