The kidney paired donation (KPD) program provides an innovative solution to overcome incompatibility challenges in kidney transplants by matching incompatible donor-patient pairs and facilitating kidney exchanges. To address unequal access to transplant opportunities, there are two widely used fairness criteria: group fairness and individual fairness. However, these criteria do not consider protected patient features, which refer to characteristics legally or ethically recognized as needing protection from discrimination, such as race and gender. Motivated by the calibration principle in machine learning, we introduce a new fairness criterion: the matching outcome should be conditionally independent of the protected feature, given the sensitization level. We integrate this fairness criterion as a constraint within the KPD optimization framework and propose a computationally efficient solution using linearization strategies and column-generation methods. Theoretically, we analyze the associated price of fairness using random graph models. Empirically, we compare our fairness criterion with group fairness and individual fairness through both simulations and a real-data example.

翻译：肾脏配对捐赠（KPD）项目通过匹配不相容的供体-患者对并促进肾脏交换，为克服肾移植中的不相容性挑战提供了创新解决方案。为解决移植机会获取不均的问题，目前存在两种广泛使用的公平性标准：群体公平性与个体公平性。然而，这些标准未考虑受保护的患者特征——即法律或伦理上认可的需要防止歧视的特征（如种族和性别）。受机器学习中校准原则的启发，我们提出一种新的公平性标准：在给定致敏水平的条件下，匹配结果应与受保护特征条件独立。我们将此公平性标准作为约束条件整合到KPD优化框架中，并利用线性化策略与列生成方法提出一种计算高效的解决方案。在理论上，我们通过随机图模型分析了相关的公平性代价。在实证方面，我们通过模拟实验和真实数据案例，将本公平性标准与群体公平性及个体公平性进行了对比分析。