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Partially linear structure selection in Cox models with varying coefficients.

Heng Lian1, Peng Lai, Hua Liang

  • 1Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore. henglian@ntu.edu.sg

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This study introduces a novel double shrinkage method for analyzing censored survival data, improving coefficient estimation and variable selection in partially linear proportional hazards models. The approach enhances accuracy for complex covariate interactions in survival analysis.

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Partially linear proportional hazards models are used for censored survival data to explore nonlinear covariate interactions.
  • Current methods for specifying the partially linear structure are often ad-hoc, relying on visual inspection of full varying-coefficient models.
  • There is a need for a more systematic approach to coefficient estimation, identification, and variable selection in these models.

Purpose of the Study:

  • To develop a statistically rigorous method for coefficient estimation and constant coefficient identification in partially linear proportional hazards models.
  • To incorporate variable selection within a coherent estimation framework using a double-penalization procedure.
  • To address the limitations of ad-hoc specification methods for partially linear structures in survival data analysis.

Main Methods:

  • A double shrinkage approach is proposed for coefficient estimation and constant coefficient identification.
  • A double-penalization procedure is introduced for variable selection within a unified estimation framework.
  • Asymptotic properties, including consistency, sparesistency, constansistency, and asymptotic normality, are established under mild assumptions.

Main Results:

  • The proposed double shrinkage and double penalization method provides consistent and efficient estimation for partially linear proportional hazards models.
  • The method successfully identifies constant coefficients and performs variable selection simultaneously.
  • Numerical simulations demonstrate the effectiveness of the proposed approach.

Conclusions:

  • The developed double shrinkage approach offers a robust and statistically sound method for analyzing censored survival data with partially linear structures.
  • The method facilitates accurate coefficient estimation, constant coefficient identification, and variable selection, outperforming traditional ad-hoc techniques.
  • The approach is validated through simulations and demonstrated on a real-world breast cancer dataset, highlighting its practical utility.