Instrumental variable estimation in semi‐parametric additive hazards models

Instrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two‐stage least‐squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi‐parametric additive hazard model which can include time‐independent and time‐dependent covariate effects is particularly suited for the two‐stage residual inclusion method, since it allows direct estimation of time‐independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two‐stage residual inclusion estimators of regression coefficients in a semi‐parametric additive hazard model with time‐independent and time‐dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure‐dependent censoring.