Fair Matching in Dynamic Kidney Exchange

TL;DR

This paper explores balancing fairness and efficiency in dynamic kidney exchange by designing algorithms that prioritize time-critical patients, demonstrating a tradeoff favoring time fairness over sensitization fairness.

Contribution

It introduces two algorithms, SENS and TIME, analyzing their effectiveness and proposing a batching method to balance fairness in dynamic kidney exchanges.

Findings

Prioritizing time-critical patients offers a 9.18% advantage over sensitized patients.

Time fairness considerations improve matching outcomes in dynamic environments.

A batching algorithm effectively balances fairness needs in practical solvers.

Abstract

Kidney transplants are sharply overdemanded in the United States. A recent innovation to address organ shortages is a kidney exchange, in which willing but medically incompatible patient-donor pairs swap donors so that two successful transplants occur. Proposed rules for matching such pairs include static fair matching rules, which improve matching for a particular group, such as highly-sensitized patients. However, in dynamic environments, it seems intuitively fair to prioritize time-critical pairs. We consider the tradeoff between established sensitization fairness and time fairness in dynamic environments. We design two algorithms, SENS and TIME, and study their patient loss. We show that the there is a theoretical advantage to prioritizing time-critical patients (around 9.18% tradeoff on U.S. data) rather than sensitized patients. Our results suggest that time fairness needs to be considered in kidney exchange. We then propose a batching algorithm for current branch-and-price solvers that balances both fairness needs.