Title: Causal Mediation Analysis for Effect Heterogeneity
Description: It is possible to quantify and understand how an exposure affects an outcome through an intermediate variable via causal mediation analysis. In many cases in practice, however, the effect of the exposure may vary for different subgroups of the population. Combining these two ideas results in the related concepts of moderated mediation and mediated moderation. Addressing questions of why and how an exposure gives rise to an outcome differently for different subsets of the population provides deeper understandings of the effect heterogeneity phenomenon and permits insights that may be both clinically and practically meaningful about what works for whom and through which intermediate(s).This dissertation explores how to understand and explain these causal mechanisms by focusing on explaining effect heterogeneity via causal mediation analysis. Formal definitions and analytical formulas for direct and indirect effect heterogeneity measures are described from a counterfactual perspective. Various types of direct and indirect effect heterogeneity from two-way and three-way decompositions, such as natural direct and indirect effect heterogeneity and pure direct and indirect effect heterogeneity, are introduced and defined.

However, just simply decomposing the total effect heterogeneity into direct and indirect effect heterogeneity does not fully account for the complex mechanism of the two-way and three-way interactions happening in the effect heterogeneity phenomenon. Arising from this, in the context of a regression-based approach, this dissertation shows how direct and indirect effect heterogeneity can be further decomposed to account for possible multi-way interactions between exposure, mediator, and modifier. This is an essential way to account for different portions of interactions along causal pathways of effect heterogeneity. It provides more causal implications about the question for whom and in what context that the effect happens. Identification assumptions that are sufficient for the estimations of effect heterogeneity decompositions are also considered. Analytical expressions for effect heterogeneity decompositions on additive and ratio scales are provided. National Longitudinal Study of Adolescent to Adult Health (Add Health) data is used to illustrate the proposed methodologies in application.