Additive Hazards Regression With Auxiliary Information

In survival analysis, we could only obtain the information of primary covariate in the validation set due to the financial limitation or technical difficulty. Sometimes, one could measure the primary covariate only on a subset of the study subjects, which is called as validation set. Meanwhile, an auxiliary covariate, that is an error-prone version of the primary covariate, is measured for all subjects. As we know, if we only use the validation set for statistical inference, which may result in a loss of efficiency. Under the missing completely random assumption, our concern is on how to take use of auxiliary information to improve the statistical inference. We propose a new method to overcome the problem, and to improve the efficiency of statistical inference. Our study concerns with the following two situations:First, we propose a nonparametric empirical method to imputate the information of primary covariate in non validation set using the information of primary covariate in validation set by utilizing discrete auxiliary covariate information. Under the framework of additive hazards regression model, we construct a martingale-based estimated esti-mating equation for the regression parameter. We establish the asymptotic consistency and normality of the estimator of regression parameter. We conduct the simulation s-tudies to evaluate the finite sample performances of proposed estimator. We apply the proposed method to the data from the Mayo Clinic trial in the primary biliary cirrhosis of the liver.Second, we employ nonparametric kernel estimation to calibrate the information of primary covariate in non validation set using the information of primary covariate in val-idation set by utilizing continuous auxiliary covariate information. Under the framework of additive hazards regression model, we constructed a martingale-based estimated esti-mating equation for the regression parameter. We establish the asymptotic consistency and normality of the proposed estimator. We conduct the simulation to evaluate the finite sample approximations and the efficiency gains of the proposed method. A data set from the Mayo Clinic trial in the primary biliary cirrhosis of the liver is analyzed to illustrate the proposed method.