Joint Score-Threshold Optimization for Interpretable Risk Assessment Under Partial Supervision

2025-10-24

AI Summary

Medical risk assessment commonly relies on point-based ordinal scoring systems, yet data-driven optimization using electronic health record (EHR) data faces two key challenges: (1) partial supervision—only extreme risk categories (e.g., low/high) can be reliably annotated; and (2) asymmetric misclassification costs—errors farther apart in the ordinal scale incur higher penalties. This paper proposes an interpretable joint optimization framework that simultaneously learns scoring weights and risk thresholds. It innovatively integrates mixed-integer programming with soft-label relaxation, enforces a minimum threshold separation constraint to prevent category collapse, and incorporates sign constraints, sparsity regularization, and clinically grounded modification limits. The method preserves ordinal structure under partial labeling, significantly improving robustness and classification performance while ensuring clinical deployability and decision trustworthiness.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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) partial supervision arising from intervention-censored outcomes, where only extreme categories can be reliably labeled, and (2) asymmetric misclassification costs that increase with ordinal distance. We propose a mixed-integer programming (MIP) framework that jointly optimizes scoring weights and category thresholds under these constraints. Our approach handles partial supervision through per-instance feasible label sets, incorporates asymmetric distance-aware objectives, and prevents middle-category collapse via minimum threshold gaps. We further develop a CSO relaxation using softplus losses that preserves the ordinal structure while enabling efficient optimization. The framework supports governance constraints including sign restrictions, sparsity, and minimal modifications to incumbent tools, ensuring practical deployability in clinical workflows.

Problem

• Optimizing scoring systems under partial supervision and censored outcomes
• Addressing asymmetric misclassification costs in ordinal risk assessment
• Developing interpretable clinical tools with governance constraints for deployment

Innovation

• Joint optimization of scoring weights and thresholds
• Handles partial supervision via feasible label sets
• Prevents category collapse with minimum threshold gaps