Adaptation, Comparison and Practical Implementation of Fairness Schemes in Kidney Exchange Programs

TL;DR

The paper tackles fairness in Kidney Exchange Programs by moving beyond a pure utilitarian objective to probabilistic policies over exchange plans. It develops conic-program formulations for various fairness schemes and leverages column generation to handle exponentially many feasible exchanges, enabling practical evaluation on benchmark KEP instances. By introducing SWP and NSWP frameworks, the work demonstrates that balancing utility and fairness yields low price of fairness while maintaining high transplant counts, and it offers actionable methodologies for policy-makers. Key contributions include a unified modeling of multiple fairness concepts, a scalable solution approach, and insights into when fairness schemes improve or trade off against utility, with future work focusing on dynamics and richer patient features.

Abstract

In Kidney Exchange Programs (KEPs), each participating patient is registered together with an incompatible donor. Donors without an incompatible patient can also register. Then, KEPs typically maximize overall patient benefit through donor exchanges. This aggregation of benefits calls into question potential individual patient disparities in terms of access to transplantation in KEPs. Considering solely this utilitarian objective may become an issue in the case where multiple exchange plans are optimal or near-optimal. In fact, current KEP policies are all-or-nothing, meaning that only one exchange plan is determined. Each patient is either selected or not as part of that unique solution. In this work, we seek instead to find a policy that contemplates the probability of patients of being in a solution. To guide the determination of our policy, we adapt popular fairness schemes to KEPs to balance the usual approach of maximizing the utilitarian objective. Different combinations of fairness and utilitarian objectives are modelled as conic programs with an exponential number of variables. We propose a column generation approach to solve them effectively in practice. Finally, we make an extensive comparison of the different schemes in terms of the balance of utility and fairness score, and validate the scalability of our methodology for benchmark instances from the literature.

Figures (7)

• Figure 1: Example of a KEP graph
• Figure 1: Comparison of the NSWP fairness schemes with respect to the values of each fairness objective
• Figure 2: Pareto front (blue dots) and the NSWP optimal objective (given by the gray area). The SWP optimal objective plane is depicted with $\lambda = (1, 1)$.
• Figure 3: Comparison of SWP, NSWP and the utilitarian approach in terms of the value for each fairness objective
• Figure 4: Ratio of instances solved for each model over time

Theorems & Definitions (13)

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