Sharp Bounds on Survivor Average Causal Effects When the Outcome Is Binary and Truncated by Death

In randomized trials with follow-up, outcomes may be undefined for individuals who die before the follow-up is complete. In such settings, Frangakis and Rubin [2002] proposed the “principal stratum effect” or “Survivor Average Causal Effect” (SACE), which is a fair treatment comparison in the subpopulation that would have survived under either treatment arm. Many of the existing results for estimating the SACE are difficult to carry out in practice. In this article, when the outcome is binary, we apply the symbolic Balke-Pearl linear programming method to derive simple formulas for the sharp bounds on the SACE under the monotonicity assumption commonly used by many researchers.