Adaptive Conformal Prediction via Bayesian Uncertainty Weighting for Hierarchical Healthcare Data

TL;DR

This paper introduces a hybrid Bayesian-conformal prediction framework that provides distribution-free coverage guarantees and risk-adaptive precision for healthcare data, enabling more reliable and tailored clinical decision-making.

Contribution

It combines Bayesian hierarchical models with conformal calibration to achieve adaptive, risk-aware uncertainty quantification with valid coverage in healthcare predictions.

Findings

Achieves 94.3% coverage close to the 95% target.

Provides narrower intervals for low-uncertainty cases by 21%.

Highlights the underperformance of Bayesian uncertainties alone in coverage.

Abstract

Clinical decision-making demands uncertainty quantification that provides both distribution-free coverage guarantees and risk-adaptive precision, requirements that existing methods fail to jointly satisfy. We present a hybrid Bayesian-conformal framework that addresses this fundamental limitation in healthcare predictions. Our approach integrates Bayesian hierarchical random forests with group-aware conformal calibration, using posterior uncertainties to weight conformity scores while maintaining rigorous coverage validity. Evaluated on 61,538 admissions across 3,793 U.S. hospitals and 4 regions, our method achieves target coverage (94.3% vs 95% target) with adaptive precision: 21% narrower intervals for low-uncertainty cases while appropriately widening for high-risk predictions. Critically, we demonstrate that well-calibrated Bayesian uncertainties alone severely under-cover (14.1%), highlighting the necessity of our hybrid approach. This framework enables risk-stratified clinical protocols, efficient resource planning for high-confidence predictions, and conservative allocation with enhanced oversight for uncertain cases, providing uncertainty-aware decision support across diverse healthcare settings.