The objective of this collaborative research project is to provide much more accurate valuations of potential paired kidney exchanges (PKEs). Given an arbitrary-sized PKE, consider the question of when (in terms of patient health) an exchange should occur. An exchange is only possible if every patient in the exchange desires it. This problem is naturally formulated as an infinite-horizon stochastic game. Analyzing this stochastic game reveals several unique features (e.g. the exchange probabilities completely characterize the equilibria, and one can restrict attention to equilibria in which only one patient randomizes). One can then demonstrate a one-to-one correspondence between the equilibria of this game and the feasible points of a certain mixed-integer program. Extensions include iterative approaches to this game, as well as modeling extensions, such as cadaveric kidney arrivals and altruistic donors. This goal will be accomplished in three ways: 1) By comparing quality-adjusted life expectancies, it will value exchanges where the patients and donors are well matched more than others; 2) It will consider dynamic patient health; and 3) It allows patients to determine when the transplantations should occur.
Given the severe shortage of kidneys and the potential of paired kidney exchanges, this research can lead to much better matching between patients and donors. Medical researchers, graduate students and undergraduate students will benefit from this research as it blends important aspects of operations research, medicine, and economics.
Live-donor kidney exchange (or kidney paired donation) has become a transplant modality within the last decade, in which when a willing but incompatible donor of a patient donates to the compatible patient of a similar incompatible donor-patient pair, while the donor of the second pair donates to the patient of the first pair, who happens to be compatible. The PI had contributed to the optimal organization of kidney exchanges so that as many patients as possible can be saved and helped foundation of several exchanges. Because of this, he was nominated for an Edelman Award, and this effort has been being published as a paper. Besides this, in the main several studies funded by the current grant, the PI and his coauthors (Murat Kurt, Andrew Schaefer, Mark Roberts) study the operational and economic consequences of pre-emptive transplants being also used in kidney exchange. Pre-emptive transplants save patients without even going through dialysis and are known to increase the expected quality adjusted life of the patient as the side effects of dialysis can be harmful for overall health of a patient. Currently in a kidney exchange, the optimization process involves integer programming for maximizing the number of patients matched subject to institutional and exchange feasibility constraints or maximizing the sum of weights, each of which is assigned to a possible exchange cycle subject to such constraints. Currently these weights are determined in an experience-based metric and some weights are quite arbitrary. This study comes up with welfare weights for such maximization process. The weights themselves are determined as the sum of the expected quality -adjusted life years of the patients in each exchange cycle. It is assumed that once an exchange cycle is determined, because of the pre-emptive nature of these transplants, patients will be involved in a self-centric behavior to choose actually when to agree for when actual exchange to be conducted. In practice, if the committed exchange does not go through for various reasons within a time frame, the patients and donors are returned to the exchange pool and are matched again through the same optimization process. Hence, we use a stochastic game-theoretic approach to pin down how patients would behave in such a situation in a timing game. An exchange can go through if all patients agree at a time. We characterize the equilibria of these games through mathematical programming and simulate the welfare losses because of this coordination game feature with respect to societal optimum. The total welfare in best equilibria emerge as a scientifically determined weight for the whole exchange and could be better than ad-hoc weights currently used or can be used in combination with such weights. Then these weights can be fed back to the optimization process to determine in the first place which exchange cycles to choose and who to match. This approach can also be fine-tuned for other objectives. A subsequent study (in progress) considers in parallel the existence of other transplant modalities such as "list exchange" and redoes the study. Another paper (in progress) is based on the technique introduced to solve such mathematical programs in determining equilibria. This turns out to be a new technique in applied math and operations research. The PI has focused on two related studies as well. In the first study the PI and his coauthor (Tayfun Sonmez) explore the effects of the inclusion of "compatible" pairs to kidney exchange. Compatible pairs are those whose donor is actually compatible and directly donate to the patient. However, by going through exchange they can "save" an additional (or more) incompatible pair, which otherwise would not be saved. Because of the specifics of blood-type compatibility and tissue-type compatibility, the PI's earlier studies have predicted that the number of pairs who receive live-donor transplant can increase by 20-30 percent wrt. status-quo where compatible pairs almost never participate in exchange. This paper focuses on the structure of efficient matching’s and incentive compatible mechanisms when only the simplest forms of the exchanges are feasible i.e. exchanges with only two pairs. The paper extends Galai-Edmonds Decomposition Theorem to the case when compatible pairs also participate in exchange. This extension and comparative statics for what happens when an additional compatible pair arrives help us to understand what are the best ways of organizing such exchanges. In particular, it is shown that it is possible to use the minimum necessary number of compatible pairs and freely choose the incompatible pairs to form an efficient matching, i.e. these sets are separable from each other. Another study focused on organizing real-life "matching markets": the Pennsylvania Adoption Exchange for children. The PI used a similar "weight" determination idea for recommending matches between a child and family with his coauthors (Vince Slaugh, Mustafa Akan, and Onur Kesten), this system is now used in PA.
