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