  In this paper, we discuss causal inference on the efficacy of a treatment or
medication on a time-to-event outcome with competing risks. Although the
treatment group can be randomized, there can be confoundings between the
compliance and the outcome. Unmeasured confoundings may exist even after
adjustment for measured co- variates. Instrumental variable (IV) methods are
commonly used to yield consistent estimations of causal parameters in the
presence of unmeasured confoundings. Based on a semi-parametric additive hazard
model for the subdistribution hazard, we pro- pose an instrumental variable
estimator to yield consistent estimation of efficacy in the presence of
unmeasured confoundings for competing risk settings. We derived the asymptotic
properties for the proposed estimator. The estimator is shown to be well per-
formed under finite sample size according to simulation results. We applied our
method to a real transplant data example and showed that the unmeasured
confoundings lead to significant bias in the estimation of the effect (about
50% attenuated).
