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:: Volume 25, Issue 1 (1-2021) ::
Andishe 2021, 25(1): 53-67 Back to browse issues page
Penalized Estimators in Cox Regression Model
Zahra Eslami * , Mina Norouzirad , Mohammad Arashi
Abstract:   (2144 Views)
The proportional hazard Cox regression models play a key role in analyzing censored survival data. We use penalized methods in high dimensional scenarios to achieve more efficient models. This article reviews the penalized Cox regression for some frequently used penalty functions. Analysis of medical data namely ”mgus2” confirms the penalized Cox regression performs better than the cox regression model. Among all penalty functions, LASSO provides the best fit.
Keywords: Cox regression, Hazard function, Penalized regression, Lasso, Survival function.
Full-Text [PDF 380 kb]   (1150 Downloads)    
Type of Study: Applicable | Subject: Special
Received: 2020/03/5 | Accepted: 2021/01/20 | Published: 2021/01/29
References
1. Abramsky, S., and Jung, A. (1994). Domain Theory, in: S. Abramsky, D.M. Gabbay, T.S.E. Maibaum (Eds). Handbook of Logic in Computer Science, 3, Clarendon Press, Oxford, 1-68.
2. Askarishahi, M., Moazen, H., Akhavan, A., Bibesh, F., and Falahzadeh, H. (2017). Applying Cox proportional hazard model to identifying the factors affecting the survival of patients with brain metastases. The Journal of Toloo-e-behdasht, 16(1), 33-46.
3. Bondell, H. D., and Reich, B. J. (2008). Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR. Biometrics, 64(1), 115-123.
4. Casella, G. and Berger, R. (2001). Statistical Inference. Wadsworth, Belmont, CA.
5. Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B, 34(2), 187-202.
6. Cox, D. R, and Oakes, D. (1984). Analysis of survival data, Second ed, London., Champan and Hall Press.
7. Dicker, L., Huang, B., and Lin, X. (2013). Vriable selection and estimaton with the seamless L0 penalty. Statistica Sinica, 23(2), 929-962.
8. Fan, J., and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association , 96(456), 1348-1360.
9. Feigl, P., and Zelen, M. (1965). Estimation of exponential survival probabilities with concomitant information .Biometrics 21(4), 826-838.
10. Gohari, M., Vahabi, N., and Moghadamifard, Z. (2012). Semi-parametric Cox regression for factor affecting hospitallzation length. Daneshvar Medicine, 19(99), 23-30.
11. Grambsh, P. M., and Therneau, T. M. (1994). Proportional hazards tests and diagnostics based on weighted residuals. Biometrika, 81(3), 515–526
12. Haselimashhadi, H., and Vinciotti, V. (2016). A Differentiable alternative to the Lasso penalty. arXiv preprint arXiv:1609.04985.
13. Hoerl, A. E., and Kennard, R. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.
14. Hosseini Teshnizi, S., Tazhibi, M., and Tavasoli Farahi, M. (2013). Comparsion of Cox regression and Artificial Neural Network models in prediction of survival in acute leukemia patients. The Scientific Journal of Iranian Blood Transfusion Organization, 10(2), 154-162.
15. Jang, W., Lim, J,. Lazar, N. A., Loh, J. M., and Yu, D. (2013). Regression shrinkage and grouping of highly correlated predictors with HORSES. arXiv:1302.0256.
16. Kyle,R., Therneau, T., Rajkumar, V., Offord,J., Larson, D., Plevak, M., and Joseph, L. (2002). Melton III, A longterms study of prognosis in monoclonal gammopathy of undertermined significance. New England Journal of Medicine, 346, 564-569.
17. Li, C., Wei, X., and Dai, H. (2015). Adaptive Elastic net method for cox model. arXiv:1507.06371v1.
18. Machin, D., Cheung, Y. B., and Parmar, M. K. B.(2006).Survival analysis: A Practical approch, 2nd Ed., John Wiey.
19. Mentel,T. J.(1966) . Study and development of simple matrix methods for inelastic structures. Journal of Spacecraft and Rockets, 3(4), 449-457.
20. Pourhoseingholi, M., Hajizadeh, E., Abadi, A., Safaee, A., Moghimi Dehkordi, B., and Zali, M. (2007). Comparing Cox regression and parametric models for Survival analysis of patients with Gastric cancer. Iranian Journal of Epidemiology, 3(1 and 2), 25-29.
21. Roudbari, M., Abbasi Asl, M., Barfei, F., Gohari, M. R., and Khodabakhshi, R. (2015). Survival analysis of Colorectal cancer patients and its Prognostic factors using Cox regression. Razi Jornal of Medical Science, 22(130), 21-28.
22. Su, X. (2015). Variable selection via subtle uprooting, Journal of Computational and Graphical Statistics, 24(4), 1092–1113.
23. Su, X., Wijayasinghe, C. s., Fan, J., and Zhang, Y. (2016). Sparse estimation of Cox proportional hazards models via approximated information criteria. Biometrics, 72(3), 751-759.
24. Tibshirani, R. (1996). Regression Shrinkage and selection via the Lasso. Royal Statistical Society, 58(1), 267-288.
25. Tibshirani, R. (1997). The Lasso method for variable selection in the Cox model, Statistics in medicine, 16(4), 385-395.
26. Tibshirani, R.,Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005). Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1), 91-108.
27. Verweij, P. J. M., and Van Houwelingen, H. C. (1994). Penalized likelihood in Cox regression, in: Department of Medical Statistics. Statistics in Medicine, 13, 2427-2436.
28. Wang, D. Q., Chukova, S. and Lai, C. D. (2004). On the relationship between regression analysis and mathematical programming. Journal of Applied Mathematical and Decision Sciences, 8, 131-140.
29. Wang, Y., and Zhu, L. (2016). Variable selection and parameter estimation with the Atan regularization method. Journal of Probability and Statistics, 2016, 1-12.
30. Yao, Y. (2008). Statistical Applications of linear programming for feature selection via regularization methods. Ph.D. disseration, The Ohio Stat University.
31. Zhang, C. H. (2010). Nearly unbiased variable selection under Minimax Concave Penalty. The Annals of Statistics, 38(2), 894-942.
32. Zou, H. (2006). The Adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101(476), 1418-1429.
33. Zou, H., and Hastie, T.(2005). Regularization and variable selection via the elastic net. Royal Statistical Society: Series B, 67(2), 301–320.
34. Zou, H., and Zhang, H. H. (2009). On The adaptive Elastic-net with a diverging number of parameters. The Annals of Statistics, 37(4), 1733–1751.
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Eslami Z, Norouzirad M, Arashi M. Penalized Estimators in Cox Regression Model. Andishe 2021; 25 (1) :53-67
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Volume 25, Issue 1 (1-2021) Back to browse issues page
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