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Fairness-aware kidney exchange and kidney paired donation

Mingrui Zhang, Xiaowu Dai, Lexin Li

TL;DR

This work addresses unequal access to kidney transplants in kidney paired donation by introducing a calibration-inspired fairness criterion: the matching outcome should be conditionally independent of a protected feature given the sensitization level. The authors integrate this criterion as a linear fairness constraint within the KPD optimization and develop an efficient column-generation-based algorithm to solve it, complemented by theoretical price-of-fairness results under random-graph models and empirical assessments via simulations and UNOS data. They demonstrate that the new criterion achieves substantially more equitable access across protected groups within each sensitization level, while incurring only modest efficiency loss, and provide methods to predict individual selection probabilities in dynamic pools. Overall, the paper offers a scalable, theoretically grounded framework for fairness in kidney exchanges with practical implications for policy and implementation in real-world programs.

Abstract

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.

Fairness-aware kidney exchange and kidney paired donation

TL;DR

This work addresses unequal access to kidney transplants in kidney paired donation by introducing a calibration-inspired fairness criterion: the matching outcome should be conditionally independent of a protected feature given the sensitization level. The authors integrate this criterion as a linear fairness constraint within the KPD optimization and develop an efficient column-generation-based algorithm to solve it, complemented by theoretical price-of-fairness results under random-graph models and empirical assessments via simulations and UNOS data. They demonstrate that the new criterion achieves substantially more equitable access across protected groups within each sensitization level, while incurring only modest efficiency loss, and provide methods to predict individual selection probabilities in dynamic pools. Overall, the paper offers a scalable, theoretically grounded framework for fairness in kidney exchanges with practical implications for policy and implementation in real-world programs.

Abstract

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.

Paper Structure

This paper contains 31 sections, 4 theorems, 73 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Kidney paired donation programs
  3. Fairness concerns in KPD programs
  4. Fairness in general decision-making problems
  5. Our contributions
  6. Review of KPD program in an optimization framework
  7. KPD program without fairness
  8. Classical formulation
  9. Extension: incorporating recourse strategies
  10. No-recourse strategy.
  11. Internal-recourse strategy.
  12. Subset-recourse strategy.
  13. KPD program with fairness constraint
  14. Group fairness
  15. Individual fairness
  16. ...and 16 more sections

Key Result

Proposition 1

Consider the random graph model in Section sec::theory, and fix any sequence $\varepsilon_N \downarrow 0$. For each $N$, let $\mathrm{Opt}(G_N)$ be the optimum of the unconstrained problem eq::theory-no-fairness, and let $\mathrm{Opt}^{\mathrm{prio}}_{\varepsilon_N}(G_N)$ be the optimum of the const

Figures (5)

  • Figure 1: Illustration of exchange cycles shown with solid arrows. Transplantations along the dashed arrows cannot proceed due to incompatibility.
  • Figure 2: Simulation results under random graph models. The average selection rates within each subgroup are calculated over 100 data replications. The error bars represent the mean $\pm$ 1 standard deviation of the absolute differences in selection rates.
  • Figure 3: Simulation results based on UNOS data. The average selection rates within each subgroup are calculated over 100 data replications. The error bars represent the mean $\pm$ 1 standard deviation of the absolute differences in selection rates.
  • Figure S1: Simulation results with subset-recourse strategy under random graph models. The average selection rates within each subgroup are calculated over 100 data replications. The error bars represent the mean $\pm$ 1 standard deviation of the absolute differences in selection rates.
  • Figure S2: Simulation results with subset-recourse strategy based on UNOS data. The average selection rates within each subgroup are calculated over 100 data replications. The error bars represent the mean $\pm$ 1 standard deviation of the absolute differences in selection rates.

Theorems & Definitions (8)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Lemma S1
  • proof : Proof of Lemma \ref{['lem2']}
  • proof : Proof of Proposition \ref{['prop2']}
  • proof : Proof of Proposition \ref{['cor1']}
  • proof : Proof of Proposition \ref{['prop3']}