Research on Improved Estimation Method of the Cox Model with Contaminated Covariable and Auxiliary Survival Information

Cox model is one of the most popular semi-parametric regression models in epidemiology, biomedical science and clinical trials. In the modeling process, the observed covariates are usually contaminated, and the pollution factor can be measured, but the pollution function is unknown. Therefore, the direct use of the contaminated covariate for parameter estimation may lead to incorrect statistical inference. Researchers often find the best time for disease treatment, and omission of such survival information may lead to a decrease in the estimated effectiveness. In this paper, an improved estimation of the Cox model with contaminated covariates and auxiliary survival information is studied. Kernel smoothing method is used to calibrate the contaminated covariates, and auxiliary survival information is extracted by grouping for parameter estimation. Then, generalized moment estimation method is used to solve the problem of hyperdimensional equations. The results of simulation analysis and empirical study show that the generalized moment estimation method based on the Cox model with covariate calibration is better than the partial likelihood estimation method and the generalized moment estimation method based on the Cox model with the unadjusted covariates.