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, i.e., the average treatment effect among a subpopulation in the principal strata of 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, its expansion to multi-arm clinical trials remains unknown. 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. As a further improvement, we then derive the efficient influence function to motivate doubly robust estimators for the survivor average causal effects in multi-arm clinical trials. We also articulate sensitivity methods under violations of key causal assumptions. Extensive simulations are conducted to investigate the finite-sample performance of the proposed methods, and a real data example is used to illustrate how to operationalize the proposed estimators and the sensitivity methods in practice.