The Correspondence Between Causal and Traditional Mediation Analysis: the Link Is the Mediator by Treatment Interaction

Abstract

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.

The Use of Traditional and Causal Estimators for Mediation Models with a Binary Outcome and Exposure-Mediator Interaction

“…It seems rare to observe a statistically significant XM interaction in practice (Anthopolos et al, 2014;Bauer & Scheim, 2019). An explanation might be that researchers choose mediators that are unlikely to have differential effects across the exposure groups (MacKinnon et al, 2020). Furthermore, significance tests of the h coefficient and the mediated interaction, i.e., ha, are underpowered in small samples and for small effect sizes (MacKinnon et al, 2020).…”

“…To assess whether the methodology described by MacKinnon et al (2020) is also successful for the estimation of causal effects for mediation models with a continuous mediator and binary outcome, we analytically compared the causal estimators for models with a continuous mediator and a continuous outcome with the causal estimators for models with a continuous mediator and a binary outcome. Table 2 shows the results of these analytical comparisons.…”

“…A recent study demonstrated how, in the presence of XM interaction, traditional mediation analysis can be used to estimate causal effects for models with a continuous mediator and a continuous outcome variable (MacKinnon et al, 2020). However, the traditional mediation analysis methodology is less suited for the estimation of causal mediation effects when the outcome is binary.…”

The Centrality of Law for Prevention

“…Second, rarely have mechanisms of how policies affect outcomes been studied, especially through formal mediation analyses. The field of prevention science has articulated theoretical and methodological standards for the study of causal mechanisms through mediation analyses (Gottfredson et al 2015 ; MacKinnon et al 2020 ); Wiedermann et al 2019 ). Theory, measurement of hypothesized mediators, and mediation analysis would contribute to the existing scientific basis of laws’ effects on MEB development, health, and well-being.…”

Causal Mediation Analysis in the Presence of Post-treatment Confounding Variables: A Monte Carlo Simulation Study

“…When the X and M interaction is non-zero, Pearl (2001) demonstrated that the sum of the natural direct and indirect effects equal to the total effect (TE) (i.e., TE − NDE = NIE) at selected levels of X and, importantly, this result also holds in models with non-linear effects such as logistic regression. MacKinnon et al (2020) illustrates the correspondence between potential outcomes and traditional estimators of the indirect effect when the X and M interaction is non-zero, in the form of simple direct and indirect effects.…”