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Simultaneous variable selection and estimation for a partially linear Cox model.

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  • 1School of Mathematical Sciences, Capital Normal University, Beijing, PR China.

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This study introduces a new penalized method for variable selection and estimation in deep neural network partially linear Cox models. The approach simplifies computation and enhances interpretability for survival data analysis.

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Area of Science:

  • Biostatistics
  • Machine Learning
  • Survival Analysis

Background:

  • Deep neural networks (DNNs) are increasingly used in survival analysis.
  • Partially linear Cox models offer flexibility in modeling survival data.
  • Simultaneous variable selection and estimation remain challenging in complex models.

Purpose of the Study:

  • To develop a novel penalized approach for simultaneous variable selection and estimation in DNN-based partially linear Cox models.
  • To address the curse of dimensionality and improve interpretability of linear covariate effects.
  • To reduce computational burden by avoiding explicit tuning parameter selection.

Main Methods:

  • A two-step iterative algorithm is proposed.
  • Minimum information criterion is utilized for sparse estimation.
  • Convergence rates and asymptotic properties of the estimator are established.

Main Results:

  • The method effectively performs simultaneous variable selection and estimation.
  • It circumvents the curse of dimensionality.
  • The algorithm demonstrates reduced computational complexity compared to traditional methods.
  • Consistency of variable selection is proven.

Conclusions:

  • The proposed penalized approach offers an efficient and interpretable solution for DNN-based partially linear Cox models.
  • The method is validated through simulations and a real-world myeloma dataset analysis.
  • This work advances statistical modeling for complex survival data.