  Instrumental variable is an essential tool for addressing unmeasured
confounding in observational studies. Two stage predictor substitution (2SPS)
estimator and two stage residual inclusion(2SRI) are two commonly used
approaches in applying instrumental variables. Recently 2SPS was studied under
the additive hazards model in the presence of competing risks of time-to-events
data, where linearity was assumed for the relationship between the treatment
and the instrument variable. This assumption may not be the most appropriate
when we have binary treatments. In this paper, we consider the 2SRI estimator
under the additive hazards model for general survival data and in the presence
of competing risks, which allows generalized linear models for the relation
between the treatment and the instrumental variable. We derive the asymptotic
properties including a closed-form asymptotic variance estimate for the 2SRI
estimator. We carry out numerical studies in finite samples, and apply our
methodology to the linked Surveillance, Epidemiology and End Results (SEER) -
Medicare database comparing radical prostatectomy versus conservative treatment
in early-stage prostate cancer patients.
