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Adaptive Conformal Prediction via Bayesian Uncertainty Weighting for Hierarchical Healthcare Data

Marzieh Amiri Shahbazi, Ali Baheri, Nasibeh Azadeh-Fard

TL;DR

This work tackles the challenge of uncertainty quantification for hospital LOS predictions in hierarchically structured healthcare data by marrying Bayesian hierarchical uncertainty with distribution-free conformal calibration. The proposed Hybrid HRF framework combines hierarchical random forests, Bayesian posterior predictive uncertainty, and group-aware conformal calibration to deliver coverage-guaranteed yet adaptively narrow intervals. Empirical results on a large HCUP dataset show near-target coverage (94.3% vs 95%) with substantial interval width adaptation: 21% narrower intervals for low-uncertainty cases and conservative widening for high-uncertainty cases, while well-calibrated uncertainties alone underperform without conformal validity. This modular approach enables risk-stratified clinical decision support and scalable deployment across diverse hospitals, though it notes under-coverage in the most uncertain cases and suggests practical mitigations such as stratified calibration and enhanced oversight.

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.

Adaptive Conformal Prediction via Bayesian Uncertainty Weighting for Hierarchical Healthcare Data

TL;DR

This work tackles the challenge of uncertainty quantification for hospital LOS predictions in hierarchically structured healthcare data by marrying Bayesian hierarchical uncertainty with distribution-free conformal calibration. The proposed Hybrid HRF framework combines hierarchical random forests, Bayesian posterior predictive uncertainty, and group-aware conformal calibration to deliver coverage-guaranteed yet adaptively narrow intervals. Empirical results on a large HCUP dataset show near-target coverage (94.3% vs 95%) with substantial interval width adaptation: 21% narrower intervals for low-uncertainty cases and conservative widening for high-uncertainty cases, while well-calibrated uncertainties alone underperform without conformal validity. This modular approach enables risk-stratified clinical decision support and scalable deployment across diverse hospitals, though it notes under-coverage in the most uncertain cases and suggests practical mitigations such as stratified calibration and enhanced oversight.

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.
Paper Structure (14 sections, 3 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 14 sections, 3 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. Paper Organization
  5. Methodology
  6. Problem Formulation
  7. Hierarchical Random Forest Foundation
  8. Hierarchical Conformal Prediction Framework
  9. Bayesian Hierarchical Random Forest
  10. Hybrid HRF (Bayesian Conformal) Framework
  11. Validation Metrics and Experimental Framework
  12. Experiments
  13. Discussion
  14. Conclusion

Figures (4)

  • Figure 1: Coverage performance across methods
  • Figure 2: Conditional coverage by uncertainty quintiles. (A) Bayesian HRF: uniformly poor (12.7%--15.5%). (B) Conformal HRF: Q1--Q4 near-perfect (96.2%--99.7%), Q5 under-coverage (81.7%). (C) Hybrid HRF: Q1--Q4 strong (93.9%--97.1%), Q5 improved (90.9%).
  • Figure 3: Cross-validation stability across 5 folds
  • Figure 4: QQ plots showing distributional improvement: (a) Raw uncertainties with systematic deviations, (b) Calibrated uncertainties approaching normality.