优化医疗风险评分的打分权重与阈值，提升可解释性与实用性。
Joint Score-Threshold Optimization for Interpretable Risk Assessment
- 用混合整数规划联合优化评分权重和分类阈值。
- 在标签稀缺情况下防止低风险类别崩溃，且考虑误判代价随等级距离增加。
- 支持临床部署的约束条件，适合医疗系统实际应用。
医疗风险评估工具通常采用基于分值的评分系统，通过阈值将患者划分为有序的风险等级。尽管电子健康记录（EHR）数据为工具的优化提供了机会，但标准监督学习面临两大挑战：(1) 标签仅对极端风险等级可用（因干预截断结果），(2) 误分类代价具有非对称性且随等级距离递增。本文提出一种混合整数规划（MIP）框架，联合优化评分权重与分类阈值以应对上述问题。该方法通过阈值约束防止标签稀缺类别的崩溃，并采用非对称、距离敏感的目标函数。MIP框架支持治理约束，包括符号限制、稀疏性要求及对现有工具的最小修改，确保临床流程中的可部署性。此外，我们还开发了该MIP问题的连续松弛版本，用于提供高效的热启动解。我们将该评分优化框架应用于约翰霍普金斯医院跌倒风险评估工具的案例研究。
原文摘要 · Abstract (English)
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.
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