  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).
