Joint Score-Threshold Optimization for Interpretable Risk Assessment

TL;DR

This paper introduces a mixed-integer programming framework to optimize risk scoring systems in healthcare, addressing label scarcity and asymmetric misclassification costs for better clinical decision-making.

Contribution

It presents a novel joint optimization method for scoring weights and thresholds that accounts for practical constraints and data challenges in healthcare risk assessment.

Findings

Successfully applied to inpatient falls risk assessment at Johns Hopkins.

Prevents label-scarce category collapse through threshold constraints.

Supports governance constraints for practical clinical deployment.

Abstract

Risk assessment tools in healthcare commonly employ point-based scoring systems that map patients to ordinal risk categories via thresholds. While electronic health record (EHR) data presents opportunities for data-driven optimization of these tools, two fundamental challenges impede standard supervised learning: (1) labels are often available only for extreme risk categories due to intervention-censored outcomes, and (2) misclassification cost is asymmetric and increases with ordinal distance. We propose a mixed-integer programming (MIP) framework that jointly optimizes scoring weights and category thresholds in the face of these challenges. Our approach prevents label-scarce category collapse via threshold constraints, and utilizes an asymmetric, distance-aware objective. The MIP framework supports governance constraints, including sign restrictions, sparsity, and minimal modifications to incumbent tools, ensuring practical deployability in clinical workflows. We further develop a continuous relaxation of the MIP problem to provide warm-start solutions for more efficient MIP optimization. We apply the proposed score optimization framework to a case study of inpatient falls risk assessment using the Johns Hopkins Fall Risk Assessment Tool.