Improving Estimation Efficiency of Cox Model via Using Other Related Survival Data

Cox model is the most popular model in modelling the relationship between a survival outcome and predictive covariates, and has been gotten great success about regression modelling survival data. It is well known that the maximum partial likelihood estimates of regression parameters of Cox model are consistent, asymptotically normal and semiparametrically efficient. In this paper, based on marginal proportional hazards model and a partitioning-based method, we develop an approach to improve estimation efficiency of regression parameters in Cox model through introducing some other handy or easily collected survival data. Practically, for each subject, there frequently exist some other possibly-multivariate survival data available in addition to the main endpoint of survival times, which are easily collected or handy, and belong to the same subject or group as the survival data of interest. All the data construct multivariate survival data, and the famous WLW model, one important marginal proportional hazards model of multivariate survival data proposed in 1989 by Wei, Lin and Weissfels (1989), is the model of natural choice to regression modelling the aforementioned multivariate survival data. But, as pointed out in this paper, by making direct use of the WLW method , the estimation efficiency of regression parameters of interest cannot be improved. Based on the partitioning-based method for WLW model, an approach to improve the estimation of regression parameter of Cox model is proposed and discussed. Simulation studies are conducted to investigate behavior of the proposed approach under practical sample size. Our results show that it performs well, only if the constructed multivariate survival data are correlated between the survival data of interest and the introduced survival data, even for small to moderate sample size.