Additive hazard regression with auxiliary covariates

We consider the additive hazard model when some of the true covariates are measured only on a randomly selected validation set whereas auxiliary covariates are observed for all study subjects. An updated pseudoscore estimation approach is proposed for the parameters of the additive hazard model. It allows one to fit the model with auxiliary covariates, while leaving the baseline hazard unspecified. Asymptotic properties of the proposed estimators are established, and consistent standard error estimators are developed. Simulations demonstrate that the asymptotic approximations of the proposed estimates are adequate for practical use. A real example is used to illustrate the performance of the proposed method.