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Extended Bayesian information criterion in the Cox model with a high-dimensional feature space

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  • Shan Luo
  • Jinfeng Xu
  • Zehua Chen

Abstract

Variable selection in the Cox proportional hazards model (the Cox model) has manifested its importance in many microarray genetic studies. However, theoretical results on the procedures of variable selection in the Cox model with a high-dimensional feature space are rare because of its complicated data structure. In this paper, we consider the extended Bayesian information criterion (EBIC) for variable selection in the Cox model and establish its selection consistency in the situation of high-dimensional feature space. The EBIC is adopted to select the best model from a model sequence generated from the SIS-ALasso procedure. Simulation studies and real data analysis are carried out to demonstrate the merits of the EBIC. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:2:p:287-311
    DOI: 10.1007/s10463-014-0448-y
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    References listed on IDEAS

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    1. 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.
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    4. David Siegmund, 2004. "Model selection in irregular problems: Applications to mapping quantitative trait loci," Biometrika, Biometrika Trust, vol. 91(4), pages 785-800, December.
    5. Karl W. Broman & Terence P. Speed, 2002. "A model selection approach for the identification of quantitative trait loci in experimental crosses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 641-656, October.
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    Cited by:

    1. 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.
    2. 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.
    3. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.

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