Identification of the Heterogeneous Survivor Average Causal Effect in Observational Studies

Clinical studies are often encountered with truncation-by-death issues, which render the outcomes undefined. Statistical analysis based only on observed survivors may lead to biased results because the characters of survivors may differ greatly between treatment groups. Under the principal stratification framework, a meaningful causal parameter, the survivor average causal effect, in the always-survivor group can be defined. This causal parameter may not be identifiable in observational studies where the treatment assignment and the survival or outcome process are confounded by unmeasured features. In this paper, we propose a new method to deal with unmeasured confounding when the outcome is truncated by death. First, a new method is proposed to identify the heterogeneous conditional survival average causal effect based on a substitutional variable under monotonicity. Second, under additional assumptions, the survivor average causal effect on the whole population is identified. Furthermore, we consider estimation and inference for the conditional survivor average causal effect based on parametric and nonparametric methods. The proposed method can be used for post marketing drug safety or efficiency by utilizing real world data.