In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of post-treatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due…

In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the…