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A note on path-based variable selection in the penalized proportional hazards model

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  • Hui Zou

Abstract

We propose an efficient and adaptive shrinkage method for variable selection in the Cox model. The method constructs a piecewise-linear regularization path connecting the maximum partial likelihood estimator and the origin. Then a model is selected along the path. We show that the constructed path is adaptive in the sense that, with a proper choice of regularization parameter, the fitted model works as well as if the true underlying submodel were given in advance. A modified algorithm of the least-angle-regression type efficiently computes the entire regularization path of the new estimator. Furthermore, we show that, with a proper choice of shrinkage parameter, the method is consistent in variable selection and efficient in estimation. Simulation shows that the new method tends to outperform the lasso and the smoothly-clipped-absolute-deviation estimators with moderate samples. We apply the methodology to data concerning nursing homes. Copyright 2008, Oxford University Press.

Suggested Citation

  • Hui Zou, 2008. "A note on path-based variable selection in the penalized proportional hazards model," Biometrika, Biometrika Trust, vol. 95(1), pages 241-247.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:1:p:241-247
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    File URL: http://hdl.handle.net/10.1093/biomet/asm083
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    Cited by:

    1. Haixiang Zhang & Jian Huang & Liuquan Sun, 2022. "Projection‐based and cross‐validated estimation in high‐dimensional Cox model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 353-372, March.
    2. Yichao Wu, 2011. "An ordinary differential equation-based solution path algorithm," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 185-199.
    3. Zhang, Hao Helen & Lu, Wenbin & Wang, Hansheng, 2010. "On sparse estimation for semiparametric linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1594-1606, August.
    4. Hong, Hyokyoung G. & Zheng, Qi & Li, Yi, 2019. "Forward regression for Cox models with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 268-290.
    5. Yan, Xiaodong & Wang, Hongni & Wang, Wei & Xie, Jinhan & Ren, Yanyan & Wang, Xinjun, 2021. "Optimal model averaging forecasting in high-dimensional survival analysis," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1147-1155.
    6. Shan Luo & Jinfeng Xu & Zehua Chen, 2015. "Extended Bayesian information criterion in the Cox model with a high-dimensional feature space," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 287-311, April.
    7. Ke Yu & Shan Luo, 2022. "A sequential feature selection procedure for high-dimensional Cox proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1109-1142, December.
    8. Huang, Zhensheng & Pang, Zhen & Lin, Bingqing & Shao, Quanxi, 2014. "Model structure selection in single-index-coefficient regression models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 159-175.
    9. Antoniadis, Anestis & Fryzlewicz, Piotr & Letué, Frédérique, 2010. "The Dantzig selector in Cox's proportional hazards model," LSE Research Online Documents on Economics 30992, London School of Economics and Political Science, LSE Library.
    10. Anestis Antoniadis & Piotr Fryzlewicz & Frédérique Letué, 2010. "The Dantzig Selector in Cox's Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 531-552, December.
    11. Xifen Huang & Chaosong Xiong & Tao Jiang & Junfeng Lu & Jinfeng Xu, 2022. "Efficient Estimation and Inference in the Proportional Odds Model for Survival Data," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    12. Yingli Pan & Wen Cai & Zhan Liu, 2022. "Inference for non-probability samples under high-dimensional covariate-adjusted superpopulation model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 955-979, October.
    13. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.

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