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Selection of effects in Cox frailty models by regularization methods.

Andreas Groll1, Trevor Hastie2, Gerhard Tutz1

  • 1Department of Statistics, Ludwig-Maximilians-University Munich, Akademiestraße 1, 80799 Munich, Germany.

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This study introduces a new penalization method for Cox frailty models to identify relevant covariates in high-dimensional survival data. The approach effectively distinguishes between time-varying, time-constant, and irrelevant effects, simplifying complex influence structures.

Keywords:
Cox frailty modelLASSOPenalizationTime-varying coefficientsVariable selection

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • High-dimensional data presents challenges in regression, requiring methods to identify influential covariates.
  • The Cox frailty model is crucial for analyzing survival data with heterogeneity.
  • Accounting for time-varying covariate effects is essential in survival analysis.

Purpose of the Study:

  • To investigate and select relevant effect structures within the Cox frailty model.
  • To develop a penalization approach for distinguishing time-varying, time-constant, and irrelevant covariate effects.
  • To achieve a sparse representation of relevant effects in survival models.

Main Methods:

  • A novel penalization approach is proposed for the Cox frailty model.
  • The method differentiates between time-varying, time-constant, and irrelevant covariate effects.
  • Simulation studies are used to evaluate the performance of the proposed method.

Main Results:

  • The proposed penalization method successfully identifies relevant covariate effects.
  • The approach effectively distinguishes between different types of covariate influences over time.
  • Simulations demonstrate the method's efficacy in handling high-dimensional survival data.

Conclusions:

  • The developed penalization strategy simplifies complex influence structures in survival data.
  • The method provides a robust tool for feature selection in Cox frailty models.
  • Application to time-to-pregnancy data shows significant reduction in model complexity.