Sensitivity analysis of treatment effect to unmeasured confounding in observational studies with survival and competing risks outcomes.

No unmeasured confounding is often assumed in estimating treatment effects in observational data, whether using classical regression models or approaches such as propensity scores and inverse probability weighting. However, in many such studies collection of confounders cannot possibly be exhaustive in practice, and it is crucial to examine the extent to which the resulting estimate is sensitive to the unmeasured confounders. We consider this problem for survival and competing risks data. Due to the complexity of models for such data, we adapt the simulated potential confounder approach of Carnegie et al (2016), which provides a general tool for sensitivity analysis due to unmeasured confounding. More specifically, we specify one sensitivity parameter to quantify the association between an unmeasured confounder and the exposure or treatment received, and another set of parameters to quantify the association between the confounder and the time-to-event outcomes. By varying the magnitudes of the sensitivity parameters, we estimate the treatment effect of interest using the stochastic expectation-maximization (EM) and the EM algorithms. We demonstrate the performance of our methods on simulated data, and apply them to a comparative effectiveness study in inflammatory bowel disease. An R package "survSens" is available on CRAN that implements the proposed methodology.