Multiply robust estimation of principal causal effects with noncompliance and survival outcomes.

Treatment noncompliance and censoring are two common complications in clinical trials. Motivated by the ADAPTABLE pragmatic clinical trial, we develop methods for assessing treatment effects in the presence of treatment noncompliance with a right-censored survival outcome. We classify the participants into principal strata, defined by their joint potential compliance status under treatment and control. We propose a multiply robust estimator for the causal effects on the survival probability scale within each principal stratum. This estimator is consistent even if one, sometimes two, of the four working models-on the treatment assignment, the principal strata, censoring, and the outcome-is misspecified. A sensitivity analysis strategy is developed to address violations of key identification assumptions, the principal ignorability and monotonicity. We apply the proposed approach to the ADAPTABLE trial to study the causal effect of taking low- versus high-dosage aspirin on all-cause mortality and hospitalization from cardiovascular diseases.