Efficient estimation of a Cox model when integrating the subgroup incidence rate information.
Pei-Fang Su, Junjiang Zhong, Yi-Chia Liu, Tzu-Hsuan Lin, Huang-Tz Ou
Author Information
Pei-Fang Su: Department of Statistics, National Cheng Kung University, Tainan, Taiwan. ORCID
Junjiang Zhong: School of Mathematics and Statistics, Xiamen University of Technology, Xiamen, People's Republic of China.
Yi-Chia Liu: The Center for Quantitative Sciences, Clinical Medicine Research Center, National Cheng Kung University Hospital, Tainan, Taiwan.
Tzu-Hsuan Lin: Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI, USA.
Huang-Tz Ou: Institute of Clinical Pharmacy and Pharmaceutical Sciences, Department of Pharmacy, College of Medicine, National Cheng Kung University, Tainan, Taiwan.
Incidence rates for diseases are widely used in the field of medical research because they lead to clear and simple physical and clinical interpretations. In this study, we propose an efficient estimation method that incorporates auxiliary subgroup information related to the incidence rate into the estimation of the Cox proportional hazard model. The results show that utilizing the incidence rate information improves the efficiency of the estimation of regression parameters based on the double empirical likelihood method compared to that for conventional models that do not incorporation such information. We show that estimators of regression parameters asymptotically follow a multivariate normal distribution with a variance-covariance matrix that can be consistently estimated. Simulation results indicate that the proposed estimators significantly increase efficiency. Finally, an example of the effects of type 2 diabetes on stroke is applied to demonstrate the proposed method.
