Variable Selection for Partially Linear Varying Coefficient Transformation Models with Censored Data

Abstract

In this paper, we study the problem of variable selection for varying coefficient transformation models with censored data. We fit the varying coefficient transformation models by maximizing the marginal likelihood subject to a shrink- age-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. We further provide an efficient computation algorithm to implement the proposed methods. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed as an illustration.

Share and Cite:

J. Du, Z. Zhang and Y. Lu, "Variable Selection for Partially Linear Varying Coefficient Transformation Models with Censored Data," Open Journal of Statistics, Vol. 2 No. 5, 2012, pp. 565-570. doi: 10.4236/ojs.2012.25072.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] S. C. Cheng, L. J. Wei and Z. Ying, “Analysis of Transformation Models with Censored Data,” Biometrika, Vol. 82, No. 4, 1995, pp. 835-845. doi:10.1093/biomet/82.4.835
[2] K. Chen, Z. Z. Jin and Z. L. Ying, “Semiparametric Analysis of Transformation Model with Censored Data,” Biometrika, Vol. 89, No. 3, 2002, pp. 659-668. doi:10.1093/biomet/89.3.659
[3] D. Zeng and D. Y. Lin, “Efficient Estimation in the Accelerated Failure Time Model,” Journal of the American Statistical Association, Vol. 102, No. 480, 2007, pp. 1387-1396. doi:10.1198/016214507000001085
[4] D. Zeng and D. Y. Lin, “Efficient Estimation of Semiparametric Transformation Models For Counting Processes,” Biometrika, Vol. 93, No. 3, 2006, pp. 627-640. doi:10.1093/biomet/93.3.627
[5] R. Tibshirani, “The Lasso Method for Variable Selection in the Cox Model,” Statistics in Medicine, Vol. 16, No. 4, 1997, pp. 385-395. doi:10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3
[6] J. Fan and R. Li, “Variable Selection for Cox’s Proportional Hazards Model and Frailty Model,” Annals of Statistics, Vol. 30, No. 1, 2002, pp. 74-99.
[7] H. H. Zhang and W. Lu, “Adaptive-Lasso for Cox’s Proportional Hazards Model,” Biometrika, Vol. 94, No. 3, 2007, pp. 691-703. doi:10.1093/biomet/asm037
[8] W. Lu and H. H. Zhang, “Variable Selection for Proportional Odds Model,” Statistics in Medicine, Vol. 26, No. 20, 2007, pp. 3771-3781. doi:10.1002/sim.2833
[9] Q. Li, C. J. Huang, D. Li and T. T. Fu, “Semiparametric Smooth Coefficient Models,” Journal of Business & Economic Statistics, Vol. 20, No. 3, 2002, pp. 412-422. doi:10.1198/073500102288618531
[10] W. Zhang, S. Lee and X. Song, “Local Polynomial Fitting Semivarying Coef?cient Model,” Journal of Multivariate Analysis, Vol. 82, No. 1, 2002, pp. 166-188. doi:10.1006/jmva.2001.2012
[11] J. Fan and T. Huang, “Profile Likelihood Inferences on semiparametric Varying-Coefficient Partially Linear Models,” Bernoulli, Vol. 11, No. 6, 2005, pp. 1031-1057. doi:10.3150/bj/1137421639
[12] I. Ahmad, S. Leelahanon and Q. Li, “Efficient Estimation of a Semiparametric Partially Linear Varying Coefficient Model,” Annals of Statistics, Vol. 33, No. 1, 2005. pp. 258-283. doi:10.1214/009053604000000931
[13] H. Wang, Z. Zhu and J. Zhou, “Quantile Regression in Partially Linear Varying Coefficient Models,” Annals of Statistics, Vol. 37, No. 6B, 2009, pp. 3841-3866. doi:10.1214/09-AOS695
[14] R. Li and H. Liang, “Variable Selection in Semiparametric Regression Modeling,” Annals of Statistics, Vol. 36, No. 1, 2008, pp. 261-286. doi:10.1214/009053607000000604
[15] W. Lu and H. H. Zhang, “On Estimation of Partially Linear Transformation Models,” Journal of the American Statistical Association, Vol. 105, No. 490, 2010, pp. 683- 691. doi:10.1198/jasa.2010.tm09302
[16] H. H. Zhang, W. Lu and H. Wang, “On Sparse Estimation for Semiparametric Linear Transformation Models,” Journal of Multivariate Analysis, Vol. 101, No. 7, 2010, pp. 1594-1606. doi:10.1016/j.jmva.2010.01.015
[17] J. Fan and R. Li, “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of American Statistical Association, Vol. 96, No. 456, 2001, pp. 1348-1360. doi:10.1198/016214501753382273
[18] H. Zou and R. Li, “One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models,” Annals of Statistics, Vol. 36, No. 4, 2008, pp. 1509-1533. doi:10.1214/009053607000000802
[19] X. He, W. K. Fung and Z. Y. Zhu, “Robust Estimation in Generalized Partial Linear Models for Clustered Data,” Journal of the American Statistical Association, Vol. 100, No. 472, 2005, pp. 1176-1184.
[20] X. He, Z. Y. Zhu and W. K. Fung, “Estimation in a Semiparametric Model for Longitudinal Data with Unspecified Dependence Structure,” Biometrika, Vol. 89, No. 3, 2002, pp. 579-590. doi:10.1093/biomet/89.3.579
[21] K. Chen and X. Tong, “Varying Coef?cient Transformation Models with Censored Data,” Biometrika, Vol. 97, No. 4, 2010, pp. 969-976. doi:10.1093/biomet/asq032
[22] H. Wang, G. Li and G. Jiang, “Robust Regression Shrinkage and Consistent Variable Selection via the LAD-LASSO,” Journal of Business & Economics Statistics, Vol. 25, No. 3, 2007, pp. 347-355. doi:10.1198/073500106000000251
[23] J. D. Kalb?eish and R. L. Prentice, “The Statistical Analysis of Failure Time Data,” 2nd Edition. Wiley, Hoboken, 2002. doi:10.1002/9781118032985

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.