Institute of Mathematical Statistics Collections

High-dimensional variable selection for Cox’s proportional hazards model

Jianqing Fan, Yang Feng, and Yichao Wu

Full-text: Open access


Variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines. Recent technological advances have made it possible to collect a huge amount of covariate information such as microarray, proteomic and SNP data via bioimaging technology while observing survival information on patients in clinical studies. Thus, the same challenge applies in survival analysis in order to understand the association between genomics information and clinical information about the survival time. In this work, we extend the sure screening procedure [6] to Cox’s proportional hazards model with an iterative version available. Numerical simulation studies have shown encouraging performance of the proposed method in comparison with other techniques such as LASSO. This demonstrates the utility and versatility of the iterative sure independence screening scheme.

Chapter information

James O. Berger, T. Tony Cai and Iain M. Johnstone, eds., Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 70-86

First available in Project Euclid: 26 October 2010

Permanent link to this document

Digital Object Identifier

Primary: 62N02: Estimation
Secondary: 62J99: None of the above, but in this section

Cox’s proportional hazards model variable selection

Copyright © 2010, Institute of Mathematical Statistics


Fan, Jianqing; Feng, Yang; Wu, Yichao. High-dimensional variable selection for Cox’s proportional hazards model. Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown, 70--86, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL606.

Export citation


  • [1] Cox, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187–220.
  • [2] Cox, D. R. (1975). Partial likelihood. Biometrika 62 269–76.
  • [3] Fan, J., Feng, Y. and Song, R. (2010). Nonparametric independence screening in sparse ultra-high dimensional additive models. Submitted.
  • [4] Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348–1360.
  • [5] Fan, J. and Li, R. (2002). Variable selection for cox’s proportional hazards model and frailty model. Ann. Statist. 30 74–99.
  • [6] Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space (with discussion). J. Roy. Statist. Soc. Ser. B 70 849–911.
  • [7] Fan, J., Samworth, R. and Wu, Y. (2009). Ultrahigh dimensional variable selection: beyond the lienar model. J. Mach. Learn. Res. To appear.
  • [8] Fan, J. and Song, R. (2010). Sure independence screening in generalized linear models with np-dimensionality. Ann. Statist. To appear.
  • [9] Faraggi, D. and Simon, R. (1998). Bayesian variable selection method for censored survival data. Biometrics 54 1475–5.
  • [10] Ibrahim, J. G., Chen, M.-H. and Maceachern, S. N. (1999). Bayesian variable selection for proportional hazards models. Canand. J. Statist. 27 70117.
  • [11] Klein, J. P. and Moeschberger, M. L. (2005). Survival Analysis, 2nd ed. Springer.
  • [12] Li, Y. and Dicker, L. (2009). Dantzig selector for censored linear regression. Technical report, Harvard Univ. Biostatistics.
  • [13] Oberthuer, A., Berthold, F., Warnat, P., Hero, B., Kahlert, Y., Spitz, R., Ernestus, K., König, R., Haas, S., Eils, R., Schwab, M., Brors, B., Westermann, F. and Fischer, M. (2006). Customized oligonucleotide microarray gene expressionbased classification of neuroblastoma patients outperforms current clinical risk stratification. Journal of Clinical Oncology 24 5070–5078.
  • [14] Sauerbrei, W. and Schumacher, M. (1992). A bootstrap resampling procedure for model building: Application to the cox regression model. Statist. Med. 11 2093–2109.
  • [15] Tibshirani, R. (1997). The lasso method for variable selection in the cox model. Statist. Med. 16 385–95.
  • [16] Tibshirani, R. J. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
  • [17] Wu, Y. and Liu, Y. (2009). Variable selection in quantile regression. Statist. Sinica 19 801–817.
  • [18] Zhang, C.-H. (2009). Penalized linear unbiased selection. Ann. Statist. To appear.
  • [19] Zhang, H. H. and Lu, W. (2007). Adaptive lasso for cox’s proportional hazards model. Biometrika 94 691–703.
  • [20] Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418–1429.
  • [21] Zou, H. and Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models (with discussion). Ann. Statist. 36 1509–1566.
  • [22] Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J. Roy. Statist. Soc. Ser. B 67 301–320.