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Adaptive Lasso for Cox's proportional hazards model

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  • Hao Helen Zhang
  • Wenbin Lu
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    Abstract

    We investigate the variable selection problem for Cox's proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively weighted L 1 penalty on regression coefficients, providing what we call the adaptive Lasso estimator. The method incorporates different penalties for different coefficients: unimportant variables receive larger penalties than important ones, so that important variables tend to be retained in the selection process, whereas unimportant variables are more likely to be dropped. Theoretical properties, such as consistency and rate of convergence of the estimator, are studied. We also show that, with proper choice of regularization parameters, the proposed estimator has the oracle properties. The convex optimization nature of the method leads to an efficient algorithm. Both simulated and real examples show that the method performs competitively. Copyright 2007, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 94 (2007)
    Issue (Month): 3 ()
    Pages: 691-703

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    Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:691-703

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    Cited by:
    1. Anestis Antoniadis & Piotr Fryzlewicz & Frédérique Letué, 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.
    2. Lian, Heng & Li, Jianbo & Hu, Yuao, 2013. "Shrinkage variable selection and estimation in proportional hazards models with additive structure and high dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 99-112.
    3. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    4. 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.
    5. Hess, Wolfgang & Persson, Maria & Rubenbauer, Stephanie & Gertheiss, Jan, 2013. "Using Lasso-Type Penalties to Model Time-Varying Covariate Effects in Panel Data Regressions - A Novel Approach Illustrated by the 'Death of Distance' in International Trade," Working Papers 2013:5, Lund University, Department of Economics.
    6. Lian, Heng & Li, Jianbo & Tang, Xingyu, 2014. "SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 50-64.
    7. Chen, Xiaolin & Wang, Qihua, 2013. "Variable selection in the additive rate model for recurrent event data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 491-503.
    8. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    9. Pötscher, Benedikt M. & Schneider, Ulrike, 2007. "On the distribution of the adaptive LASSO estimator," MPRA Paper 6913, University Library of Munich, Germany.
    10. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    11. Hu, Yuao & Lian, Heng, 2013. "Variable selection in a partially linear proportional hazards model with a diverging dimensionality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 61-69.
    12. Pötscher, Benedikt M., 2007. "Confidence Sets Based on Sparse Estimators Are Necessarily Large," MPRA Paper 5677, University Library of Munich, Germany.

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