External Risk Prediction Informed Bayesian Survival Analysis
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.
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BibTeX
@misc{jeon2026external,
title = {{External Risk Prediction Informed Bayesian Survival Analysis}},
author = {Yena Jeon and Yunxiang Huang and Hang J. Kim and Susan Halabi and Mi-Ok Kim},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28887},
eprint = {2608.28887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28887},
}
RIS
TY - UNPB
TI - External Risk Prediction Informed Bayesian Survival Analysis
AU - Yena Jeon
AU - Yunxiang Huang
AU - Hang J. Kim
AU - Susan Halabi
AU - Mi-Ok Kim
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28887
UR - https://arxiv.org/abs/2608.28887
AB - 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.
ER -