Identifiability and Estimation of Causal Effects by Principal Stratification With Outcomes Truncated by Death

In medical studies, there are many situations where the final outcomes are truncated by death, in which patients die before outcomes of interest are measured. In this article we consider identifiability and estimation of causal effects by principal stratification when some outcomes are truncated by death. Previous studies mostly focused on large sample bounds, Bayesian analysis, sensitivity analysis. In this article, we propose a new method for identifying the causal parameter of interest under a nonparametric and semiparametric model. We show that the causal parameter of interest is identifiable under some regularity assumptions and the assumption that there exists a pretreatment covariate whose conditional distributions among two principal strata are not the same, but our approach does not need the assumption of a mixture normal distribution for outcomes as required by Zhang, Rubin, and Mealli (2009). Hence, the proposed method is applicable not only to a continuous outcome but also to a binary outcome. When some of the assumptions are violated, we discuss biases of estimators and propose methods to reduce these biases. We conduct several simulation studies to evaluate the finite-sample performance of the proposed approach. Finally, we apply the proposed approach to a real dataset from a Southwest Oncology Group (SWOG) clinical trial.