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The Cox-Pólya-Gamma algorithm for flexible Bayesian inference of multilevel survival models.

Benny Ren1,2,3, Jeffrey S Morris4, Ian Barnett4

  • 1Regeneron Pharmaceuticals, Inc., Tarrytown 10591, United States of America.

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|September 19, 2025
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Summary

We introduce the Cox-Pólya-Gamma algorithm for Bayesian multilevel Cox regression, enhancing survival analysis. This method simplifies incorporating complex multilevel structures into survival models, improving clinical predictions.

Keywords:
Bayesian inferenceCox modelKaplan-Meierfrailty modelmultilevel modelsurvival analysis

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Area of Science:

  • Statistics
  • Biostatistics
  • Computational Statistics

Background:

  • Bayesian Cox semiparametric regression is crucial in clinical settings.
  • Elliptical information geometry offers potential for Bayesian inference in survival analysis.
  • Existing methods struggle with multilevel modeling in Cox models.

Purpose of the Study:

  • To propose a novel algorithm for Bayesian multilevel Cox semiparametric regression.
  • To address challenges in monotonicity-constrained modeling of cumulative hazards.
  • To integrate survival analysis with hierarchical Gaussian models.

Main Methods:

  • The Cox-Pólya-Gamma algorithm is developed for Bayesian multilevel Cox models.
  • Two strategies leverage elliptical geometry: Poisson process approximation and dimension reduction.
  • Iterative Gaussian sampling and Gibbs sampling are employed for computation.

Main Results:

  • The algorithm efficiently handles monotonicity constraints and multilevel regression.
  • Computational efficiency is achieved through approximations and dimension reduction.
  • Uniform ergodicity conditions for the algorithm are explored.

Conclusions:

  • The Cox-Pólya-Gamma algorithm provides a unified framework for Bayesian multilevel survival analysis.
  • The approach simplifies complex modeling, applicable in diverse clinical settings.
  • Software and demonstrations confirm the method's utility with real-world data.