A Bayesian Bootstrap Method for Survival Models

2026-07-30

AI Summary

This study addresses the challenge of quantifying uncertainty in survival analysis arising from censored data, small sample sizes, and population heterogeneity. The authors propose a model-agnostic Bayesian framework that circumvents reliance on a full likelihood specification and avoids sensitivity to parametric distributional assumptions. The approach integrates Bayesian bootstrapping with generalized Bayesian (Gibbs) posterior updating: nonparametric survival estimates are generated via Dirichlet-weighted resampling to capture sampling uncertainty, while prior information is incorporated through a loss-based updating rule to yield robust posterior inference. The framework is compatible with the Cox proportional hazards model, preserving the interpretability of hazard ratios. Simulation studies and real-data applications demonstrate its ability to effectively quantify uncertainty and flexibly leverage prior knowledge. An accompanying open-source R package, BayesBoots, has been released.

Abstract

Survival analysis is widely used for analyzing time-to-event data, and often uncertainty quantification remains challenging in the presence of censoring, limited sample sizes, and heterogeneous populations. Existing Bayesian survival methods provide a framework for incorporating prior information but typically require specification of a full probabilistic likelihood, making inference sensitive to distributional assumptions and sometimes computationally demanding. We propose a Bayesian approach for survival analysis that combines the Bayesian bootstrap with generalized Bayesian (Gibbs) updating. The Bayesian bootstrap first generates a distribution over survival estimators through Dirichlet weights, providing a nonparametric characterization of sampling uncertainty. Prior information for model parameter is then incorporated using a loss function within the generalized Bayesian framework, yielding an inference for posterior distribution. The proposed methodology is model-agnostic and can be applied to a broad class of survival estimators. As an illustration, we develop the framework for the Cox proportional hazards model, producing posterior inference for regression coefficients while preserving the familiar properties and interpretation of hazard ratios. Simulation studies demonstrate that the proposed approach provides robust uncertainty quantification and effectively incorporates prior information. An application to right-censored survival data further illustrates its practical utility. An open-source R package, BayesBoots, implements the proposed methodology.

Problem

• survival analysis
• uncertainty quantification
• censoring
• Bayesian methods
• nonparametric

Innovation

• Bayesian bootstrap
• generalized Bayesian inference
• survival analysis
• nonparametric uncertainty quantification
• Cox proportional hazards model