![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
We propose an additive hazards model with latent variables to investigate the observed and latent risk factors of the failure time of interest. Each latent risk factor is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a hybrid procedure that combines the expectation–maximization (EM) algorithm and the borrow-strength estimation approach to estimate the model parameters. We establish the consistency and asymptotic normality of the parameter estimators. Various nice features, including finite sample performance of the proposed methodology, are demonstrated by simulation studies. Our model is applied to a study concerning the risk factors of chronic kidney disease for Type 2 diabetic patients. Supplementary materials for this article are available online.
Additional information
Notes on contributors
Deng Pan
Deng Pan is Lecturer, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (E-mail: [email protected]). Haijin He (E-mail: [email protected]) is Post-doctoral Fellow, and Xinyuan Song (E-mail: [email protected]) is Associate Professor, Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China. Liuquan Sun is Professor, Institute of Applied Mathematics, Chinese Academy of Science (CAS), Beijing 100190, China (E-mail: [email protected]). This research was supported by GRF 404711 from the Research Grant Council of the Hong Kong Special Administration Region, the National Natural Science Foundation of China Grants (no. 11471277, 11231010, 11171330, and 11021161), Key Laboratory of RCSDS, CAS (no. 2008DP173182), and BCMIIS. The authors are thankful to the editor, the associate editor, two anonymous reviewers, and Professor Sik-Yum Lee for their valuable comments and suggestions that improved the article substantially, to Dr. Feng C. for pointing out an error in the proof and providing methods to correct it, and to Professor Juliana Chan from the Department of Medicine and Therapeutics, and Prince of Wales Hospital of the Chinese University of Hong Kong, for providing the data in the real example.
Haijin He
Deng Pan is Lecturer, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (E-mail: [email protected]). Haijin He (E-mail: [email protected]) is Post-doctoral Fellow, and Xinyuan Song (E-mail: [email protected]) is Associate Professor, Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China. Liuquan Sun is Professor, Institute of Applied Mathematics, Chinese Academy of Science (CAS), Beijing 100190, China (E-mail: [email protected]). This research was supported by GRF 404711 from the Research Grant Council of the Hong Kong Special Administration Region, the National Natural Science Foundation of China Grants (no. 11471277, 11231010, 11171330, and 11021161), Key Laboratory of RCSDS, CAS (no. 2008DP173182), and BCMIIS. The authors are thankful to the editor, the associate editor, two anonymous reviewers, and Professor Sik-Yum Lee for their valuable comments and suggestions that improved the article substantially, to Dr. Feng C. for pointing out an error in the proof and providing methods to correct it, and to Professor Juliana Chan from the Department of Medicine and Therapeutics, and Prince of Wales Hospital of the Chinese University of Hong Kong, for providing the data in the real example.
Xinyuan Song
Deng Pan is Lecturer, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (E-mail: [email protected]). Haijin He (E-mail: [email protected]) is Post-doctoral Fellow, and Xinyuan Song (E-mail: [email protected]) is Associate Professor, Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China. Liuquan Sun is Professor, Institute of Applied Mathematics, Chinese Academy of Science (CAS), Beijing 100190, China (E-mail: [email protected]). This research was supported by GRF 404711 from the Research Grant Council of the Hong Kong Special Administration Region, the National Natural Science Foundation of China Grants (no. 11471277, 11231010, 11171330, and 11021161), Key Laboratory of RCSDS, CAS (no. 2008DP173182), and BCMIIS. The authors are thankful to the editor, the associate editor, two anonymous reviewers, and Professor Sik-Yum Lee for their valuable comments and suggestions that improved the article substantially, to Dr. Feng C. for pointing out an error in the proof and providing methods to correct it, and to Professor Juliana Chan from the Department of Medicine and Therapeutics, and Prince of Wales Hospital of the Chinese University of Hong Kong, for providing the data in the real example.
Liuquan Sun
Deng Pan is Lecturer, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (E-mail: [email protected]). Haijin He (E-mail: [email protected]) is Post-doctoral Fellow, and Xinyuan Song (E-mail: [email protected]) is Associate Professor, Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China. Liuquan Sun is Professor, Institute of Applied Mathematics, Chinese Academy of Science (CAS), Beijing 100190, China (E-mail: [email protected]). This research was supported by GRF 404711 from the Research Grant Council of the Hong Kong Special Administration Region, the National Natural Science Foundation of China Grants (no. 11471277, 11231010, 11171330, and 11021161), Key Laboratory of RCSDS, CAS (no. 2008DP173182), and BCMIIS. The authors are thankful to the editor, the associate editor, two anonymous reviewers, and Professor Sik-Yum Lee for their valuable comments and suggestions that improved the article substantially, to Dr. Feng C. for pointing out an error in the proof and providing methods to correct it, and to Professor Juliana Chan from the Department of Medicine and Therapeutics, and Prince of Wales Hospital of the Chinese University of Hong Kong, for providing the data in the real example.