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Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates

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  • Hu, Jianwei
  • Chai, Hao

Abstract

Based on Stute’s weighted least squares method, we consider the estimate procedures for the accelerated failure time (AFT) model with high dimensional covariates. We use Kaplan–Meier weights and Stute’s estimator to account for censoring in least squares estimation. We consider two regularization approaches, the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty (MCP) for estimation and variable selection in the AFT model. Our work includes the following contributions: (1) we adjust the penalty term in the objective function and show that this adjustment is crucial for the AFT model when the scales of covariates are heterogeneous; (2) with this adjustment, we also get a desired property for LASSO estimator in the AFT model, just like the uncensored case; (3) we replace a key assumption required in the high dimensional AFT model with a set of conditions which essentially require the fraction of censored data to be small; (4) we get selection consistency of MCP in the AFT model.

Suggested Citation

  • Hu, Jianwei & Chai, Hao, 2013. "Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 96-114.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:96-114
    DOI: 10.1016/j.jmva.2013.07.011
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    1. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    2. Heejung Bang & Anastasios A. Tsiatis, 2002. "Median Regression with Censored Cost Data," Biometrics, The International Biometric Society, vol. 58(3), pages 643-649, September.
    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. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    5. Brent A. Johnson, 2008. "Variable selection in semiparametric linear regression with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 351-370, April.
    6. Andrea H. Bild & Guang Yao & Jeffrey T. Chang & Quanli Wang & Anil Potti & Dawn Chasse & Mary-Beth Joshi & David Harpole & Johnathan M. Lancaster & Andrew Berchuck & John A. Olson & Jeffrey R. Marks &, 2006. "Oncogenic pathway signatures in human cancers as a guide to targeted therapies," Nature, Nature, vol. 439(7074), pages 353-357, January.
    7. Weaver, Mark A. & Zhou, Haibo, 2005. "An Estimated Likelihood Method for Continuous Outcome Regression Models With Outcome-Dependent Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 459-469, June.
    8. Jian Huang & Shuangge Ma & Huiliang Xie, 2006. "Regularized Estimation in the Accelerated Failure Time Model with High-Dimensional Covariates," Biometrics, The International Biometric Society, vol. 62(3), pages 813-820, September.
    9. Haibo Zhou & M. A. Weaver & J. Qin & M. P. Longnecker & M. C. Wang, 2002. "A Semiparametric Empirical Likelihood Method for Data from an Outcome-Dependent Sampling Scheme with a Continuous Outcome," Biometrics, The International Biometric Society, vol. 58(2), pages 413-421, June.
    10. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    11. Brent A. Johnson & Qi Long & Matthias Chung, 2011. "On Path Restoration for Censored Outcomes," Biometrics, The International Biometric Society, vol. 67(4), pages 1379-1388, December.
    12. 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.
    13. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
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    Cited by:

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