  Comparative effectiveness research 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. The proposed estimator is consistent
even if one, and sometimes two, of the working models are misspecified. We
apply 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. 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. We further perform a formal sensitivity analysis for
investigating the robustness of our causal conclusions under violation of two
identification assumptions specific to noncompliance.

Methodology;Applications