Weighted Competing Risks Quantile Regression Models and Variable Selection
Erqian Li,
Jianxin Pan,
Manlai Tang,
Keming Yu,
Wolfgang Karl Härdle,
Xiaowen Dai,
Maozai Tian
Affiliations
Erqian Li
College of Science, North China University of Technology, Beijing 100144, China
Jianxin Pan
School of Mathematics, University of Manchester, Manchester M13 9PL, UK
Manlai Tang
Department of Physics, Astronomy and Mathematics, School of Physics, Engineering & Computer Science, University of Hertfordshire, Hatfield AL10 9EU, UK
Keming Yu
Department of Mathematics, College of Engineering, Design and Physical Sciences Brunel University, Uxbridge UB8 3PH, UK
Wolfgang Karl Härdle
School of Business and Economics, Humboldt-Universität zu Berlin, 10117 Berlin, Germany
Xiaowen Dai
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China
Maozai Tian
Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China
The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure.
