Bayesian inference for Cox regression models using catalytic prior distributions.

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• The Cox proportional hazards model (Cox model) is widely used for survival data.
• Standard inference methods in Cox models face challenges with small sample sizes relative to model dimensions.
• Existing methods may not sufficiently stabilize complex parametric models in high-dimensional settings.

Purpose of the Study:

• To propose a novel Bayesian approach, the Cox catalytic prior, for enhancing Cox model inference.
• To address the limitations of standard maximum partial likelihood inference in small sample, high-dimensional scenarios.
• To provide a stable and consistent estimation method for Cox models.

Main Methods:

• Formulation of the Cox catalytic prior using synthetic data and a surrogate baseline hazard.
• Generation of synthetic data from the predictive distribution of a simpler fitted model.
• Derivation of an approximate marginal posterior mode as a regularized log partial likelihood estimator.

Main Results:

• The proposed Cox catalytic prior is proven to be proper under mild conditions.
• The resulting estimator demonstrates consistency.
• Simulation studies show superior performance compared to standard maximum partial likelihood inference and comparable results to existing shrinkage methods.

Conclusions:

• The Cox catalytic prior offers a robust and effective Bayesian approach for Cox model inference, particularly in challenging small sample size scenarios.
• The method provides a stable and consistent estimator, outperforming traditional techniques.
• The approach is applicable to real-world survival data analysis.