Comparative effectiveness research with randomized trials or observational studies frequently addresses a time-to-event outcome and can require unique considerations in the presence of treatment noncompliance. Motivated by the challenges in addressing noncompliance in the ADAPTABLE pragmatic trial, we develop a multiply robust estimator to estimate the principal survival causal effects under the principal ignorability and monotonicity assumption. The multiply robust estimator involves several working models including that for the treatment assignment, the compliance strata, censoring, and time to event of interest. We demonstrate that the proposed estimator is consistent even if one, and sometimes two, of the working models are incorrectly specified. We further contribute sensitivity analysis strategies for investigating the robustness of the multiply robust estimator under violation of two identification assumptions specific to noncompliance. We implement the multiply robust method in the ADAPTABLE trial to evaluate the effect of low- versus high-dose aspirin assignment on patients' death and hospitalization from cardiovascular diseases, and further obtain the causal effect estimates when the identification assumptions fail to hold. We find that, comparing to low-dose assignment, assignment to the high-dose leads to differential effects among always high-dose takers, compliers, and always low-dose takers. Such treatment effect heterogeneity contributes to the null intention-to-treatment effect, and suggests that policy makers should design personalized strategies based on potential compliance patterns to maximize treatment benefits to the entire study population.

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