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.

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