Clarifying causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects

This paper aims to contribute to helping practitioners of causal mediation analysis gain a better understanding of estimation options. We take as inputs two familiar strategies (weighting and model-based prediction) and a simple way of combining them (weighted models), and show how we can generate a range of estimators with different modeling requirements and robustness properties. The primary goal is to help build intuitive appreciation for robust estimation that is conducive to sound practice that does not require advanced statistical knowledge. A second goal is to provide a "menu" of estimators that practitioners can choose from for the estimation of marginal natural (in)direct effects. The estimators generated from this exercise include some that coincide or are similar to existing estimators and others that have not appeared in the literature. We use a random continuous weights bootstrap to obtain confidence intervals, and also derive general asymptotic (sandwich) variance formulas for the estimators. The estimators are illustrated using data from an adolescent alcohol use prevention study.