Estimation of direct and indirect effects under the counterfactual models

Abstract

When a causal effect between treatment and outcome variables is observed, effects on the outcome are of interest to investigate the mechanisms among the outcome and treatment. Indirect effect is defined as the causal effect of the treatment on the outcome via the mediator. Direct effect is defined as the causal effect of the treatment on the outcome that is not through the mediator. In this paper, we discuss the estimation of direct and indirect effects based on the framework of potential response models focusing on the 4-way decomposition. Direct and indirect effect estimations are illustrated with two examples where the outcome, mediator, covariate variables are continuous and categorical data. Moreover, we discuss the estimation of clausal effects and the effect decomposition in the settings that include confounder of mediator and outcome affected by treatment, multiple mediators, or time-varying treatment in the presence of time-dependent confounder.