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.

翻译：医疗健康领域的风险评估工具通常采用基于评分的点值系统，通过阈值将患者映射到有序的风险类别中。虽然电子健康记录（EHR）数据为这些工具的数据驱动优化提供了机会，但两个基本挑战阻碍了标准的监督学习：（1）由于干预导致的结果删失，标签通常仅适用于极端风险类别；（2）误分类成本具有不对称性，并随序数距离增加而增加。针对这些挑战，我们提出了一个混合整数规划（MIP）框架，该框架联合优化评分权重和类别阈值。我们的方法通过阈值约束防止标签稀缺类别的塌缩，并利用不对称、距离感知的目标函数。该MIP框架支持治理约束，包括符号限制、稀疏性以及对现有工具的最小修改，从而确保在临床工作流程中的实际可部署性。我们进一步开发了MIP问题的连续松弛形式，为更高效的MIP优化提供预热启动解。我们将所提出的评分优化框架应用于一个使用约翰·霍普金斯跌倒风险评估工具的住院患者跌倒风险评估案例研究。