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Weighted Competing Risks Quantile Regression Models and Variable Selection

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Erqian Li & Jianxin Pan & Manlai Tang & Keming Yu & Wolfgang Karl Härdle & Xiaowen Dai & Maozai Tian, 2023. "Weighted Competing Risks Quantile Regression Models and Variable Selection," Mathematics, MDPI, vol. 11(6), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1295-:d:1090860
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    References listed on IDEAS

    as
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    2. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    3. Kwang Woo Ahn & Anjishnu Banerjee & Natasha Sahr & Soyoung Kim, 2018. "Group and within-group variable selection for competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 407-424, July.
    4. Zhixuan Fu & Chirag R. Parikh & Bingqing Zhou, 2017. "Penalized variable selection in competing risks regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 353-376, July.
    5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    6. Peng, Limin & Fine, Jason P., 2009. "Competing Risks Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1440-1453.
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