B0916
Title: Mediation in case control studies when both the outcome and mediator are binary
Authors: Minna Genback - Umea University (Sweden) [presenting]
Marco Doretti - University of Perugia (Italy)
Elena Stanghellini - University of Perugia (Italy)
Abstract: Given a treatment $X$, a mediator $M$ and an outcome $Y$, the aim of mediation analysis is to decompose the total (marginal) effect of $X$ on $Y$ into a direct one and an indirect one, i.e. mediated by $M$. This decomposition is usually made in a nonparametric way, though parametric contributions also exist. Parametric contributions are of particular interest when considering continuous treatments. We focus on a situation with both $M$ and $Y$ are binary, and we assume that they can be modelled via a series of univariate logistic regressions, possibly with covariates and the interaction term between $M$ and $X$ in the outcome equation. When the outcome is rare, in order to increase precision, it is customary to perform outcome dependent sampling designs, such as case-control studies. In this context, although features of the conditional distribution of $Y$ given $X$ and $M$ can be identified, also nonparametrically, the conditional distribution of $M$ given $X$, which is necessary to perform mediation analysis, is distorted. We here present a procedure to identify and estimate the parameters (by $M$ estimation and maximum likelihood) of the logistic models of interest and therefore to perform mediation analysis.
