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Variable Selection for Nonlinear Cox Regression Model via Deep Learning

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  • Kexuan Li

Abstract

Variable selection problem for the nonlinear Cox regression model is considered. In survival analysis, one main objective is to identify the covariates that are associated with the risk of experiencing the event of interest. The Cox proportional hazard model is being used extensively in survival analysis in studying the relationship between survival times and covariates, where the model assumes that the covariate has a log-linear effect on the hazard function. However, this linearity assumption may not be satisfied in practice. In order to extract a representative subset of features, various variable selection approaches have been proposed for survival data under the linear Cox model. However, there exists little literature on variable selection for the nonlinear Cox model. To break this gap, we extend the recently developed deep learning-based variable selection model LassoNet to survival data. Simulations are provided to demonstrate the validity and effectiveness of the proposed method. Finally, we apply the proposed methodology to analyze a real data set on diffuse large B-cell lymphoma.

Suggested Citation

  • Kexuan Li, 2025. "Variable Selection for Nonlinear Cox Regression Model via Deep Learning," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 12(1), pages 1-21, January.
    • Handle: RePEc:ibn:ijspjl:v:12:y:2025:i:1:p:21
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    References listed on IDEAS

    as
    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. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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