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

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.