Improve efficiency and reduce bias of Cox regression models for two-stage randomization designs using auxiliary covariates

Two-stage randomization designs are broadly accepted and becoming increasingly popular in clinical trials for cancer and other chronic diseases to assess and compare the effects of different treatment policies. In this paper, we propose an inferential method to estimate the treatment effects in two-stage randomization designs, which can improve the efficiency and reduce bias in the presence of chance imbalance of a robust covariate-adjustment without additional assumptions required by Lokhnygina and Helterbrand (Biometrics, 63:422-428)'s inverse probability weighting (IPW) method. The proposed method is evaluated and compared with the IPW method using simulations and an application to data from an oncology clinical trial. Given the predictive power of baseline covariates collected in this real data, our proposed method obtains 17–38% gains in efficiency compared with the IPW method in terms of overall survival outcome.