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Clinical studies sometimes encounter truncation by death, rendering outcomesundefined. Statistical analysis based solely on observed survivors may givebiased results because the characteristics of survivors differ betweentreatment groups. By principal stratification, the survivor average causaleffect was proposed as a causal estimand defined in always-survivors. However,this estimand is not identifiable when there is unmeasured confounding betweenthe treatment assignment and survival or outcome process. In this paper, weconsider the comparison between an aggressive treatment and a conservativetreatment with monotonicity on survival. First, we show that the survivoraverage causal effect on the conservative treatment is identifiable based on asubstitutional variable under appropriate assumptions, even when the treatmentassignment is not ignorable. Next, we propose an augmented inverse probabilityweighting (AIPW) type estimator for this estimand with double robustness.Finally, large sample properties of this estimator are established. Theproposed method is applied to investigate the effect of allogeneic stem celltransplantation types on leukemia relapse.

Causal Inference with Truncation-by-Death and Unmeasured Confounding