  In this paper, we develop a semiparametric sensitivity analysis approach
designed to address unmeasured confounding in observational studies with
time-to-event outcomes. We target estimation of the marginal distributions of
potential outcomes under competing exposures using influence function-based
techniques. We derived the non-parametric influence function for uncensored
data and mapped the uncensored data influence function to the observed data
influence function. Our methodology is motivated by and applied to an
observational study evaluating the effectiveness of radical prostatectomy (RP)
versus external beam radiotherapy with androgen deprivation (EBRT+AD) for the
treatment of prostate cancer. We also present a simulation study to evaluate
the statistical properties of our methodology.
