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Group MCP for Cox Models with Time-Varying Coefficients

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  • Xie Xiaodong
  • Zheng Shaozhi

    (School of Economics, Jinan University, Guangzhou510632, China)

Abstract

Cox’s proportional hazard models with time-varying coefficients have much flexibility for modeling the dynamic of covariate effects. Although many variable selection procedures have been developed for Coxs proportional hazard model, the study of such models with time-varying coefficients appears to be limited. The variable selection methods involving nonconvex penalty function, such as the minimax concave penalty (MCP), introduces numerical challenge, but they still have attractive theoretical properties and were indicated that they are worth to be alternatives of other competitive methods. We propose a group MCP method that uses B-spline basis to expand coefficients and maximizes the log partial likelihood with nonconvex penalties on regression coefficients in groups. A fast, iterative group shooting algorithm is carried out for model selection and estimation. Under some appropriate conditions, the simulated example shows that our method performs competitively with the group lasso method. By comparison, the group MCP method and group lasso select the same amount of important covariates, but group MCP method tends to outperform the group lasso method in selection of unimportant covariates.

Suggested Citation

  • Xie Xiaodong & Zheng Shaozhi, 2017. "Group MCP for Cox Models with Time-Varying Coefficients," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 476-488, October.
    • Handle: RePEc:bpj:jossai:v:4:y:2017:i:5:p:476-488:n:7
    DOI: 10.21078/JSSI-2016-476-13
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    References listed on IDEAS

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    1. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    2. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    3. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    4. Tibshirani Robert J., 2009. "Univariate Shrinkage in the Cox Model for High Dimensional Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-18, April.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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