Direct and indirect effects under sample selection and outcome attrition

This paper extends the evaluation of direct and indirect treatment effects, i.e., mediation analysis, to the case that outcomes are only partially observed due to sample selection or outcome attrition. We assume sequential conditional independence of the treatment and the mediator, i.e., the variable through which the indirect effect operates. We also impose missing at random or instrumental variable assumptions on the outcome attrition process. Under these conditions, we derive identification results for the effects of interest that are based on inverse probability weighting by specific treatment, mediator, and/or selection propensity scores. We also provide a simulation study and an empirical application to the U.S. Project STAR data in which we assess the direct impact and indirect effect (via absenteeism) of smaller kindergarten classes on math test scores. The estimators considered are available in the "causalweight" package for the statistical software "R".