2026/06/09 by Chao Cheng, Rui Wang, Yichi Zhang
#stat.ME
Post-treatment variables (PVs), such as intercurrent events, treatment noncompliance, and behavioral responses to treatment, provide information about individuals' post-treatment responses and may help characterize heterogeneity in treatment effects on the primary outcome. This paper develops an empirical stratification framework to study the treatment effect heterogeneity across baseline-predicted PV response profiles. Specifically, we construct empirical scores from baseline-covariate predictions of potential PV responses and use these scores to define empirically accessible subgroups for treatment effect evaluation. The resulting empirical-stratum treatment effects (ETEs) quantify treatment effects across these baseline-predicted PV response profiles, and are identifiable under a standard set of assumptions in causal inference. We further introduce projected ETE curves and develop efficient-influence-function-based estimators that allow flexible nuisance estimation. We clarify the distinction and connection of our framework to principal stratification analysis, which address two inferential questions. We evaluate the proposed framework through simulation studies and illustrate its use in two real-world applications.