Auxiliary covariate in additive hazards regression for survival data

We consider the additive hazards regression analysis by utilising auxiliary covariate information to improve the efficiency of the statistical inference when the primary covariate is ascertained only for a randomly selected subsample. We construct a martingale-based estimating equation for the regression parameter and establish the asymptotic consistency and normality of the resultant estimator. Simulation study shows that our proposed method can improve the efficiency compared with the estimator which discards the auxiliary covariate information. A real example is also analysed as an illustration.