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Hierarchically penalized Cox regression with grouped variables

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  • S. Wang
  • B. Nan
  • N. Zhu
  • J. Zhu

Abstract

In many biological and other scientific applications, predictors are often naturally grouped. For example, in biological applications, assayed genes or proteins are grouped by biological roles or biological pathways. When studying the dependence of survival outcome on these grouped predictors, it is desirable to select variables at both the group level and the within-group level. In this article, we develop a new method to address the group variable selection problem in the Cox proportional hazards model. Our method not only effectively removes unimportant groups, but also maintains the flexibility of selecting variables within the identified groups. We also show that the new method offers the potential for achieving the asymptotic oracle property. Copyright 2009, Oxford University Press.

Suggested Citation

  • S. Wang & B. Nan & N. Zhu & J. Zhu, 2009. "Hierarchically penalized Cox regression with grouped variables," Biometrika, Biometrika Trust, vol. 96(2), pages 307-322.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:307-322
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    File URL: http://hdl.handle.net/10.1093/biomet/asp016
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    Citations

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    Cited by:

    1. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    2. Toshio Honda & Wolfgang Karl Härdle, 2012. "Variable selection in Cox regression models with varying coefficients," SFB 649 Discussion Papers SFB649DP2012-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Wenyan Zhong & Xuewen Lu & Jingjing Wu, 2021. "Bi-level variable selection in semiparametric transformation models with right-censored data," Computational Statistics, Springer, vol. 36(3), pages 1661-1692, September.
    4. Ling Zhou & Lu Tang & Angela T. Song & Diane M. Cibrik & Peter X.-K. Song, 2017. "A LASSO Method to Identify Protein Signature Predicting Post-transplant Renal Graft Survival," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 431-452, December.
    5. Ethan X. Fang & Yang Ning & Han Liu, 2017. "Testing and confidence intervals for high dimensional proportional hazards models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1415-1437, November.
    6. Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.
    7. J. Choi & S. Ye & K. H. Eng & K. Korthauer & W. H. Bradley & J. S. Rader & C. Kendziorski, 2017. "IPI59: An Actionable Biomarker to Improve Treatment Response in Serous Ovarian Carcinoma Patients," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 1-12, June.
    8. Ahn, Kwang Woo & Sahr, Natasha & Kim, Soyoung, 2018. "Screening group variables in the proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 20-25.
    9. G. Yi & J. Q. Shi & T. Choi, 2011. "Penalized Gaussian Process Regression and Classification for High-Dimensional Nonlinear Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1285-1294, December.
    10. He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
    11. Huang, Longlong & Kopciuk, Karen & Lu, Xuewen, 2020. "Adaptive group bridge selection in the semiparametric accelerated failure time model," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    12. Yuanjia Wang & Huaihou Chen & Runze Li & Naihua Duan & Roberto Lewis-Fernández, 2011. "Prediction-Based Structured Variable Selection through the Receiver Operating Characteristic Curves," Biometrics, The International Biometric Society, vol. 67(3), pages 896-905, September.
    13. 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.
    14. 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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