The Operational Impact of Registry size, Cycle length, and Blood Type Distribution in Multi-Registry Kidney Exchange Programs

Kidney exchange programs have been developed to overcome the compatibility challenges for patients with incompatible donors in kidney transplantation. A registry of such incompatible donor-recipient pairs is created, and compatibility is achieved through the exchange of donors. Single-center kidney exchange registries do not have a significant pool size for achieving the full benefits of the kidney exchange program. Thus, multi-registry exchange transplants seem to be a natural way forward. There are various challenges in multi-registry exchange programs, such as different constraints for each registry, varying bounds on cycle lengths, and data sharing among registries. Researchers have proposed different merging mechanisms, including a sequential merger, a full merger with fair allocations, and a full merger without any restrictions. To form a stable multi-registry sharing mechanism, registries should be individually rational both in the long run as well as in the short run. In this paper, an Integer Programming model for a multi-registry exchange program has been proposed with individual rationality constraints for each registry. A simulation study is conducted to compare the benefits of multi-registry programs with individual registry allocations on Indian data, and multiple analyses have been done. It was concluded that registries with lower arrival rates could benefit 7-9\% in terms of the number of transplants and 4-6\% in terms of quality of matches in a typical kidney exchange registry. Registries with harder-to-match patients will benefit significantly more than registries with easier-to-match patients.