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A Group MCP Approach for Structure Identification in Non-Parametric Accelerated Failure Time Additive Regression Model

Author

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  • Sumin Hou

    (School of Economics, Jinan University, Guangzhou 510632, China)

  • Hao Lv

    (Department of Mathematics, Guangdong University of Education, Guangzhou 510632, China)

Abstract

In biomedical research, identifying genes associated with diseases is of paramount importance. However, only a small fraction of genes are related to specific diseases among the multitude of genes. Therefore, gene selection and estimation are necessary, and the accelerated failure time model is often used to address such issues. Hence, this article presents a method for structural identification and parameter estimation based on a non-parametric additive accelerated failure time model for censored data. Regularized estimation and variable selection are achieved using the Group MCP penalty method. The non-parametric component of the model is approximated using B-spline basis functions, and a group coordinate descent algorithm is employed for model solving. This approach effectively identifies both linear and nonlinear factors in the model. The Group MCP penalty estimation exhibits consistency and oracle properties under regularization conditions, meaning that the selected variable set tends to have a probability of approaching 1 and asymptotically includes the actual predictive factors. Numerical simulations and a lung cancer data analysis demonstrate that the Group MCP method outperforms the Group Lasso method in terms of predictive performance, with the proposed algorithm showing faster convergence rates.

Suggested Citation

  • Sumin Hou & Hao Lv, 2023. "A Group MCP Approach for Structure Identification in Non-Parametric Accelerated Failure Time Additive Regression Model," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4628-:d:1279024
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    References listed on IDEAS

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    1. 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.
    2. Jian Huang & Shuangge Ma & Huiliang Xie, 2006. "Regularized Estimation in the Accelerated Failure Time Model with High-Dimensional Covariates," Biometrics, The International Biometric Society, vol. 62(3), pages 813-820, September.
    3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    4. Li Liu & Hao Wang & Yanyan Liu & Jian Huang, 2021. "Model pursuit and variable selection in the additive accelerated failure time model," Statistical Papers, Springer, vol. 62(6), pages 2627-2659, December.
    5. Heller, Glenn, 2007. "Smoothed Rank Regression With Censored Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 552-559, June.
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