Principal stratification with continuous post-treatment variables: nonparametric identification and semiparametric estimation
针对连续事后处理变量导致的主分层问题，提出非参数识别和半参数估计理论，并构建双重稳健估计量，适用于工具变量、中介分析等场景。
Abstract Post-treatment variables often complicate causal inference. They appear in many scientific problems, including non-compliance, truncation by death, mediation, and surrogate endpoint evaluation. Principal stratification is a strategy to address these challenges by adjusting for the potential values of the post-treatment variables, defined as the principal strata. It allows for characterizing treatment effect heterogeneity across principal strata and unveiling the mechanism of the treatment’s impact on the outcome related to post-treatment variables. However, the existing literature has primarily focused on binary post-treatment variables, leaving the case with continuous post-treatment variables largely unexplored. This gap persists due to the complexity of infinitely many principal strata, which present challenges to both the identification and estimation of causal effects. We fill this gap by providing nonparametric identification and semiparametric estimation theory for principal stratification with continuous post-treatment variables. We propose to use working models to approximate the underlying causal effect surfaces and derive the efficient influence functions of the corresponding model parameters. Based on the theory, we construct doubly robust estimators and implement them in the R package continuousPCE.