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Variable selection in semiparametric hazard regression for multivariate survival data

Author

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  • Liu, Jicai
  • Zhang, Riquan
  • Zhao, Weihua
  • Lv, Yazhao

Abstract

This paper is concerned with how to select significant variables in the partially linear varying-coefficient hazard model for multivariate survival data. A new variable selection procedure is proposed to simultaneously estimate the parameters and select variables for the parametric parts. Compared to the profile pseudo-partial likelihood proposed by Cai et al. (2008), the advantage of our method is to be practically feasible and easily implemented. We show that the estimators of both the parametric and nonparametric parts achieve the best convergence rates and establish their asymptotic normality. Moreover, we demonstrate that proposed procedures perform as well as an oracle procedure. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed procedures and a real dataset from the Colon Cancer Study is analyzed for illustration.

Suggested Citation

  • Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2015. "Variable selection in semiparametric hazard regression for multivariate survival data," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 26-40.
    • Handle: RePEc:eee:jmvana:v:142:y:2015:i:c:p:26-40
    DOI: 10.1016/j.jmva.2015.07.015
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    References listed on IDEAS

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    1. Chen, Kani & Guo, Shaojun & Sun, Liuquan & Wang, Jane-Ling, 2010. "Global Partial Likelihood for Nonparametric Proportional Hazards Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 750-760.
    2. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    3. Yin, Guosheng & Li, Hui & Zeng, Donglin, 2008. "Partially Linear Additive Hazards Regression With Varying Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1200-1213.
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    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Jianwen Cai & Jianqing Fan & Runze Li & Haibo Zhou, 2005. "Variable selection for multivariate failure time data," Biometrika, Biometrika Trust, vol. 92(2), pages 303-316, June.
    7. Carroll, R.J. & Fan, Jianqing. & Gijbels, Irene. & Wand, M.P., "undated". "Generalized Partially Linear Single-Index Models," Statistics Working Paper 95010, Australian Graduate School of Management.
    8. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, June.
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    Cited by:

    1. Kaida Cai & Hua Shen & Xuewen Lu, 2022. "Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 968-993, December.

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