External Risk Prediction Informed Bayesian Survival Analysis

2026-08-28

AI Summary

该研究通过贝叶斯生存分析框架，整合外部风险预测信息，解决了小到中等样本量下新生物标志物增量价值评估的问题。

Abstract

Prognostic factor evaluation and prediction model development are central to precision oncology, enabling patient risk stratification and individualized treatment selection. Unified predictions that synthesize information from existing models are valuable for comprehensive and consistent risk assessment. Many studies also seek to evaluate the incremental value of new biomarkers beyond established prognostic factors. However, such efforts are often constrained by small-to-moderate sample sizes. Motivated by these challenges, we consider Cox regression analysis in settings where individualized risk predictions from existing models are externally available without a transparent or interpretable structure, for example, through online calculators. We develop a Bayesian discretized survival time inference framework in which individualized predictions from potentially multiple external sources are integrated through a formulation based on Kullback-Leibler divergence, yielding informative priors. The divergence-based formulation serves as a surrogate for the external information likelihood, enabling principled incorporation of individualized predictions without requiring knowledge of the underlying external prediction models. Theoretical results show that the resulting posterior mean estimators are asymptotically more efficient than their internal-only maximum likelihood counterparts. However, using the divergence-based surrogate in place of the unavailable external likelihood renders posterior variance-based inference conservative. We propose a correction to address this overcoverage. We demonstrate the performance of the proposed approach through simulations and an application to prostate cancer trial data.

Problem

• prognostic factor
• prediction model
• small-to-moderate sample sizes
• external risk predictions
• Bayesian survival analysis

Innovation

• Bayesian Discretized Survival Time Inference
• Kullback-Leibler Divergence
• External Risk Predictions
• Informative Priors
• Asymptotic Efficiency