Doubly Robust Estimation and Sensitivity Analysis With Outcomes Truncated by Death in Multi‐Arm Clinical Trials

In clinical trials, the observation of participant outcomes may frequently be hindered by death, leading to ambiguity in defining a scientifically meaningful final outcome for those who die. Principal stratification methods are valuable tools for addressing the average causal effect among always-survivors, that is, the average treatment effect among a subpopulation defined as those who would survive regardless of treatment assignment. Although robust methods for the truncation-by-death problem in two-arm clinical trials have been previously studied, their expansion to multi-arm clinical trials remains elusive. In this article, we study the identification of a class of survivor average causal effect estimands with multiple treatments under monotonicity and principal ignorability, and first propose simple weighting and regression approaches for point estimation. As a further improvement, we derive the efficient influence function to motivate doubly robust estimators for the survivor average causal effects in multi-arm clinical trials. We also propose sensitivity methods under violations of key causal assumptions. Extensive simulations are conducted to investigate the finite-sample performance of the proposed methods against the existing methods, and a real data example is used to illustrate how to operationalize the proposed estimators and the sensitivity methods in practice.