Additive hazard causal model with a binary instrumental variable.

The causal effect of a treatment on a censored outcome is often of fundamental interest and instrumental variable (IV) is a useful tool to tame bias caused by unmeasured confounding. The two-stage least squares commonly used for IV analysis in linear regression have been developed for regression analysis in a survival context under an additive hazards model. In this work, we study a distinctive binary IV framework with censored data where the causal treatment effect is quantified through an additive hazard model for compliers. Employing the special characteristics of the binary IV and adapting the principle of conditional score, we establish a weighted estimator with explicit form. We establish the asymptotic properties of the proposed estimators and provide plug-in and perturbed variance estimators. The finite sample performance of the proposed estimator is examined by extensive simulations. The proposed method is applied to a data set from the U.S. renal data system to compare dialytic modality-specific survival for end-stage renal disease patients.