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Fairness-aware kidney exchange and kidney paired donation

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.