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.