Towards an Online Matching Mechanism for Kidney Paired Donation

摘要

Kidney paired donation (KPD) matches a recipient and his incompatible donor to another pair with a complementary incompatibility, such that the donor of the first pair gives to the recipient of the second and vice- versa. Recipients and their incompatible donors arrive one at a time seeking paired donation, but in order to use optimized matching, programs must require patients to wait many weeks or months for pairs to accumulate. On the other hand, if all recipients were instead matched immediately as they arrived, then the number of transplants achieved would be reduced by at least 20%, and the expected lifespan of the transplants would also suffer (1). We propose a radical alternative to our own optimization model of matching for paired donation. We will consider paired donation as a Markov Decision Process (MDP), a mathematical model for making a sequence of decisions in situations that evolve over time. Markov Decision Processes have been successfully employed, for example, to help liver recipients choose the best timing for their living donor transplantation (2). By calculating the best policy (sequence of decisions) for a kidney paired donation MDP, we can allow some, but not all, feasible paired donation matches to proceed to transplant immediately, while preserving the higher match rates achieved by optimization. Our results would offer clinical guidance, tailored to diverse KPD programs which differ in arrival rates and registry composition, about whether and which arriving incompatible pairs should wait before matching. The types of matches which should proceed immediately to transplant are those in which at least one of the pairs is a difficult-to-match pair. In contrast, pairs that are easier to match might be better reserved for a later arrival who will be looking for that particular needle in a haystack. Also, as large numbers of pairs accumulate in the pool, it will become more advantageous to match pairs immediately rather than add them to the pool.