On two-step residual inclusion estimator for instrument variable additive hazards model

Instrumental variable (IV) methods are popular in non-experimental settings to estimate the causal effects of scientific interventions. These approaches allow for the consistent estimation of treatment effects even if major confounders are unavailable. There have been some extensions of IV methods to survival analysis recently. We specifically consider the two-step residual inclusion (2SRI) estimator proposed recently in the literature for the additive hazards regression model in this paper. Assuming linear structural equation models for the hazard function, we may attain a closed-form, two-stage estimator for the causal effect in the additive hazards model. The main contribution of this paper is to provide theoretical works for the 2SRI approach. The asymptotic properties of the estimators are rigorously established and the resulting inferences are shown to perform well in numerical studies.