Flexible Mediation Analysis for Complex Data

Mediation analysis seeks to quantify the portion of the effect of an exposure on an outcome that occurs through a postulated causal pathway. Changes in an observable mediator variable reflect activity on the pathway. To measure effects within mediation analysis, one needs estimates of both the outcome and mediator that might have occurred had a subject's exposure been different; such unobservable values are called potential outcomes. Using the assumptions of sequential ignorability and non-parametric identification, Imai et al. (2010a) proposed a flexible approach to measuring effects in mediation analysis within a frequentist framework. We address mediation analysis within complex data settings, where the complexity lies within the distribution of the data or the study design. For the scenario with complex data distribution, we develop a simple, but flexible, parametric modeling framework to accommodate the common situation where the responses are mixed continuous and binary. We apply this method to a zero-one inflated beta model for the outcome and mediator, show how to estimate both average and quantile mediation effects for boundary-censored data, and show how to conduct a meaningful sensitivity analysis. For the scenario with a complex study design, we develop a framework to estimate mediation effects for a two-stage SMART within the context of a single mediator, measured at one point in time.