The Dantzig Selector in Cox's Proportional Hazards Model

Scandinavian Journal of Statistics

Volumn 37, Issue 4, 2010, Pages 531-552

  Antoniadis, Anestis ^a   Fryzlewicz, Piotr ^b   Letué, Frédérique ^a  

^a UNIV GRENOBLE ALPES   (France)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Dantzig selector; Generalized linear models; LASSO; Penalized partial likelihood; Proportional hazards model; Variable selection

Indexed keywords

EID: 78349291870     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2009.00685.x     Document Type: Article

References (40)

1. Andersen, P. K. & Gill, R. D. (1982). Cox's regression model for counting processes: a large sample study. Ann. Statist. 10, 1100-1120.
2. Andersen, P. K., Borgan, Ø., Gill, R. D. & Keiding, N. (1993). Statistical models based on counting processes. Springer-Verlag, New York.
3. Bair, E., Hastie, T., Paul, D. & Tibshirani, R. (2006). Prediction by supervised principal components. J. Amer. Statist. Assoc. 101, 119-137.
4. Barlow, W. E. & Prentice, R. L. (1988). Residuals for relative risk regression. Biometrika 75, 65-74.
5. Bickel, P., Ritov, Y. & Tsybakov, A. (2009). Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist. 37, 1705-1732.
6. Boulesteix, A. & Strimmer, K. (2007). Partial least squares: a versatile tool for the analysis of high-dimensional genomic data. Brief. Bioinform. 8, 24-32.
7. Bøvelstad, H., Nygård, S., Størvold, H., Aldrin, M., Borgan, Ø., Frigessi, A. & Lingjærde, O. C. (2007). Predicting survival from microarray data - a comparative study. Bioinformatics 23, 2080-2087.
8. Candès, E. & Tao, T. (2007). The Dantzig selector: statistical estimation when p is much larger than n. Ann. Statist. 35, 2313-2351.
9. Craven, P. & Wahba, G. (1979). Smoothing noisy data with spline functions. Numer. Math. 31, 377-403.
10. Delong, D., Guirguis, G. & So, Y. (1994). Efficient computation of subset selection probabilities with application to Cox regression. Biometrika 81, 607-611.
11. Fan, J. & Li, R. (2002). Variable selection for Cox's proportional hazards model and frailty model. Ann. Statist. 30, 74-99.
12. Fan, J. & Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space (with discussion). J. Roy. Statist. Soc. Ser. B Stat. Methodol. 70, 849-911.
13. Faraggi, D. & Simon, R. (1998). Bayesian variable selection method for censored survival data. Biometrics 54, 1475-1485.
14. Van De Geer, S. (1995). Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes. Ann. Statist. 23, 1779-1801.
15. Graf, E., Schmoor, C., Sauerbrei, W. & Schumacher, M. (1999). Assessment and comparison of prognostic classification schemes for survival data. Stat. Med. 18, 2529-2545.
16. Gui, J. & Li, H. (2005). Threshold gradient descent method for censored data regression with applications in pharmacogenomics. Pac. Symp. Biocomput. 10, 272-283.
17. Harrell, F. E. (2001). Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis. Springer-Verlag, New York.
18. Horn, R. A. & Johnson, C. R. (1985). Matrix analysis. Cambridge University Press, Cambridge.
19. Van Houwelingen, H., Bruinsma, T. A. H., Van't Veer, L. J. & Wessels, L. (2006). Cross-validated Cox regression on microarray gene expression data. Stat. Med. 25, 3201-3216.
20. Huang, J. (1996). Efficient estimation for the Cox model with interval censoring. Ann. Statist. 24, 540-568.
21. Ibrahim, J., Chen, M.-H. & Kim, S. (2008). Bayesian variable selection for the Cox regression model with missing covariates. Lifetime Data Anal. 14, 496-520.
22. James, G. & Radchenko, P. (2009). A generalized Dantzig selector with shrinkage tuning. Biometrika 96, 323-337.
23. Jenssen, T., Kuo, W., Stokke, T. & Hovig, E. (2002). Associations between gene expressions in beast cancer and patient survival. Hum. Genet. 111, 411-420.
24. Jovanovic, B. D., Hosmer, D. & Buonaccorsi, J. P. (1995). Equivalence of several methods for efficient best subsets selection in generalized linear models. Comput. Statist. Data Anal. 20, 59-64.
25. Lounici, K. (2008). Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators. Electron. J. Stat. 2, 90-102.
26. Martinussen, T. & Scheike, T. H. (2009a). The Aalen additive hazards model with high dimensional regressors. Lifetime Data Anal. 15, 330-342.
27. Martinussen, T. & Scheike, T. H. (2009b). Covariate selection for the semiparametric additive risk model. Scand. J. Statist. 36, 602-619.
28. Marx, B. D. (1996). Iteratively reweighted partial least squares estimation for generalized linear regression. Technometrics 38, 374-381.
29. McCullagh, P. & Nelder, J. (1989). Generalized linear models, 2nd edn. Chapman and Hall, London.
30. Nguyen, D. V. & Rocke, D. M. (2002). Partial least squares proportional hazard regression for application to DNA microarray survival data. Bioinformatics 18, 1625-1632.
31. Nygård, S., Borgan, Ø., Lingjærde, O. & Størvold, H.-L. (2008). Partial least squares Cox regression for genome-wide data. Lifetime Data Anal. 14, 179-195.
32. Park, P., Tian, L. & Kohane, I. (2002). Linking expression data with patient survival times using partial least squares. Bioinformatics 18, 120-127.
33. Rosset, S. & Zhu, J. (2007). Piecewise linear regularized solution paths. Ann. Statist. 35, 1012-1030.
34. Shorack, G. R. & Wellner, J. A. (1986). Empirical processes with applications to statistics. Wiley, New York.
35. Tibshirani, R. (1997). The lasso method for variable selection in the Cox model. Stat. Med. 16, 385-395.
36. Van't Veer, L. J., Dai, H., Van de Vijver, M. J., He, Y., Hart, A., Mao, M., Peterse, H., Van der Kooy, K., Marton, M., Witteveen, A., Schreiber, G., Kerkhoven, R., Roberts, C., Linsley, P., Bernards, R. & Friend, S. (2002). Gene expression profiling predicts clinical outcome of breast cancer. Nature 415, 530-536.
37. Wang, H. & Leng, C. (2007). Unified LASSO estimation by least squares approximation. J. Amer. Statist. Assoc. 102, 1039-1048.
38. Van Wieringen, D., Kun, D., Hampel, R. & Boulesteix, A.-L. (2009). Survival prediction using gene expression data: a review and comparison. Comput. Statist. Data Anal. 53, 1590-1603.
39. Zhang, H. H. & Lu, W. (2007). Adaptive Lasso for Cox's proportional hazards model. Biometrika 94, 691-703.
40. Zou, H. (2008). A note on path-based variable selection in the penalized proportional hazards model. Biometrika 95, 241-247.