No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the databases, collected confounders are not exhaustive, 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 confounders 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 treatment assignment, 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 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 (IBD).
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