L1 penalized estimation in the Cox proportional hazards model

Biometrical Journal

Volumn 52, Issue 1, 2010, Pages 70-84

  Goeman, Jelle J ^a  

^a LEIDEN UNIVERSITY MEDICAL CENTER   (Netherlands)

Author keywords

Gradient ascent; Lasso; Penalty; Survival

Indexed keywords

GENE EXPRESSION; HAZARDS; NEWTON-RAPHSON METHOD;

COX PROPORTIONAL HAZARD MODEL; ESTIMATES OF PARAMETERS; GRADIENT ASCENT; HIGH-DIMENSIONAL MODELS; LASSO; NOVEL ALGORITHM; PENALIZED ESTIMATION; PENALTY; PROPERTY; SURVIVAL;

CLUSTERING ALGORITHMS;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BREAST TUMOR; COMPARATIVE STUDY; COMPUTER SIMULATION; FEMALE; GENE EXPRESSION PROFILING; GENETICS; HUMAN; METHODOLOGY; PROPORTIONAL HAZARDS MODEL; SURVIVAL;

ALGORITHMS; BREAST NEOPLASMS; COMPUTER SIMULATION; FEMALE; GENE EXPRESSION PROFILING; HUMANS; MODELS, GENETIC; PROPORTIONAL HAZARDS MODELS; SURVIVAL ANALYSIS;

EID: 77952568988     PISSN: 03233847     EISSN: 15214036     Source Type: Journal    
DOI: 10.1002/bimj.200900028     Document Type: Article

References (26)

1. Beer, D. G., Kardia, S. L. R., Huang, C. C., Giordano, T. J., Levin, A. M., Misek, D. E., Lin, L., Chen, G. A., Gharib, T. G., Thomas, D. G., Lizyness, M. L., Kuick, R., Hayasaka, S., Taylor, J. M. G., Iannettoni, M. D., Orringer, M. B. and Hanash, S., (2002). Gene-expression profiles predict survival of patients with lung adenocarcinoma. Nature Medicine 8, 816-824.
2. Bøvelstad, H. M., Nygard, S., Størvold, H. L., Aldrin, M., Borgan, Ø., Frigessi, A. and Lingjærde, O. C., (2007). Predicting survival from microarray data - a comparative study. Bioinformatics 23, 2080-2087.
3. De Boer, W. J., Den Besten, P. J. and Ter Braak, C. F., (2002). Statistical analysis of sediment toxicity by additive monotone regression splines. Ecotoxicology 11, 435-450.
4. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R., (2004). Least angle regression. Annals of Statistics 32, 407-451.
5. Genkin, A., Lewis, D. D. and Madigan, D., (2007). Large-scale Bayesian logistic regression for text categorization. Technometrics 49, 291-304.
6. Goeman, J. J., Oosting, J., Cleton-Jansen, A. M., Anninga, J. K. and van Houwelingen, J. C., (2005). Testing association of a pathway with survival using gene expression data. Bioinformatics 21, 1950-1957.
7. Gui, J. and Li, H. Z., (2005). Penalized cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21, 3001-3008.
8. Keerthi, S. S. and Shevade, S., (2007). A fast tracking algorithm for generalized LARS/LASSO. IEEE Transactions on Neural Networks 18, 1826-1830.
9. Kim, Y. and Kim, J., (2004). Gradient lasso for feature selection. In Proceedings of the 21st International Conference on Machine Learning, Volume 69 of ACM International Conference Proceeding Series, pp. 473-480.
10. Meier, L., van de Geer, S. A. and Bühlmann, P., (2008). The group lasso for logistic regression. Journal of The Royal Statistical Society Series B 70, 53-71.
11. Osborne, M. R., Presnell, B. and Turlach, B. A., (2000). On the lasso and its dual. Journal of Computational and Graphical Statistics 9, 319-337.
12. 1 regularization path algorithm for generalized linear models. Journal of the Royal Statistical Society Series B 19, 659-677.
13. Rosenwald, A., Wright, G., Chan, W. C., Connors, J. M., Campo, E., Fisher, R. I., Gascoyne, R. D., Muller-Hermelink, H. K., Smeland, E. B. and Staudt, L. M., (2002). The use of molecular profiling to predict survival after chemotherapy for diffuse large-b-cell lymphoma. New England Journal of Medicine 346, 1937-1947.
14. Segal, M. R., (2006). Microarray gene expression data with linked survival phenotypes: diffuse large-b-cell lymphoma revisited. Biostatistics 7, 268-285.
15. Shevade, S. K. and Keerthi, S. S., (2003). A simple and efficient algorithm for gene selection using sparse logistic regression. Bioinformatics 19, 2246-2253.
16. Tibshirani, R., (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society Series B 58, 267-288.
17. Tibshirani, R., (1997). The LASSO method for variable selection in the Cox model. Statistics in Medicine 16, 385-395.
18. Van de Vijver,M. J., He, Y. D., van 't Veer, L. J., Dai, H., Hart, A. A.M., Voskuil, D. W., Schreiber, G. J., Peterse, J. L., Roberts, C., Marton, M. J., Parrish, M.,Atsma,D., Witteveen, A.,Glas, A., Delahaye, L., van der Velde, T., Bartelink, H., Rodenhuis, S., Rutgers, E. T., Friend, S. H. and Bernards, R., (2002). A gene-expression signature as a predictor of survival in breast cancer. New England Journal of Medicine 347, 1999-2009.
19. Van Houwelingen, J. C., Bruinsma, T., Hart, A. A. M., van 't Veer, L. J. and Wessels, L. F. A., (2006). Crossvalidated Cox regression on microarray gene expression data. Statistics in Medicine 25, 3201-3216.
20. Van 't Veer, L. J., Dai, H. Y., van de Vijver, M. J., He, Y. D. D., Hart, A. A. M., Mao, M., Peterse, H. L., van der Kooy, K., Marton, M. J., Witteveen, A. T., Schreiber, G. J., Kerkhoven, R. M., Roberts, C., Linsley, P. S., Bernards, R. and Friend, S. H., (2002). Gene expression profiling predicts clinical outcome of breast cancer. Nature 415, 530-536.
21. van Wieringen, W. N., Kun, D., Hampel, R. and Boulesteix, A. L., (2009). Survival prediction using gene expression data: A review and comparison. Computational Statistics & Data Analysis 53, 1590-1603.
22. Verweij, P. J. M. and Van Houwelingen, H. C., (1993). Cross-validation in survival analysis. Statistics in Medicine 12, 2305-2314.
23. Wang, Y. X., Klijn, J. G. M., Zhang, Y., Sieuwerts, A., Look, M. P., Yang, F., Talantov, D., Timmermans, M., Meijer-van Gelder,M. E., Yu, J., Jatkoe, T., Berns, E. M. J. J., Atkins, D. and Foekens, J. A., (2005). Geneexpression pro-files to predict distant metastasis of lymph-node-negative primary breast cancer. Lancet 365, 671-679.
24. Yuan, M. and Lin, Y., (2006). Model selection and estimation in regression with grouped variables. Journal of The Royal Statistical Society Series B 68, 49-67.
25. Zou, H. and Hastie, T., (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B 67, 301-320.
26. Zou, H., Hastie, T. and Tibshirani, R., (2007). On the "degrees of freedom" of the lasso. Annals of Statistics 35, 2173-2192.