The need for kidney exchange arises when someone who wishes to donate a kidney to a particular recipient is incompatible with that recipient. Two or more such incompatible patient-donor pairs can sometimes both receive transplants through an exchange,when the donor in one pair is compatible with the recipient in the other (or in cycles involving more incompatible pairs). Stemming in part from previously funded NSF research, organized kidney exchanges, such as the New England Program for Kidney Exchange (NEPKE) have become active in the United States, and now multiple regional kidney exchanges exist and are growing, and a national exchange is being contemplated (following the passage of the Charlie W.Norwood Living Organ Donation Act in 2007). The growth of kidney exchange to include many hospitals has raised new practical and theoretical questions and this award funds research that develops new methods in mechanism design to answer these questions.
The first issue is incentives. When kidney exchange programs started, the first models incorporated patient-donor pairs and their surgeons. However, the success of regional exchanges has demonstrated that transplant centers (hospitals) must also be included in the strategic analysis. Transplant centers deal with multiple patient-donor pairs, and their strategy sets include the possibility of withholding some pairs from the kidney exchange and revealing only those pairs that the hospital cannot match on its own. The team has observed exactly this in practice, and preliminary research results suggest that there is no way to get hospitals to reveal all their pairs while still using a efficient kidney exchange matching algorithm. Additional research explores the incentive properties of matching mechanisms in large populations. The PIs seek to demonstrate that existing mechanisms do not have good incentive properties even in large populations, but that alternative mechanisms can be designed that would have both good incentives and good efficiency properties when there are many patient-donor pairs in the pool, as would be the case in a successful national exchange.
The second part of the project concerns efficiency. The PIs adapt the classical (undirected) random graph results of Erdos and Rényi (1959, 1966) to graphs that model the compatibility between patient-donor pairs, and use these to explore the behavior of large kidney exchanges, with many pairs. The first part of this work will look at general populations of patients and donors, and the second part will consider the differently structured large graphs that result when there is a large population of extremely sensitized patients who have low probability of finding a donor. (This will involve modeling the compatibility graph in more detail; instead of one node for each patient and her donors, there will have to be separate nodes for patients and donors, since the connectedness of donors will be unaffected by the patient?s low probability of finding a compatible kidney, so that, once such a kidney is found, the pair will be well connected.) We will also consider different kidney exchange strategies, including the management of possibly long chains of donations.
Broader Impacts: There are over 80,000 patients on the waiting list for cadaver kidneys in the U.S. In 2009, 33,678 patients were added to the waiting list,10,441 transplants of cadaver kidneys were performed, 4,456 patients died while on the waiting list, and more than 1,941 others were removed from the list as ?Too Sick to Transplant?. There were also 6,387 transplants of kidneys from living donors in the US. There is a severe shortage of kidneys for transplant. Kidney exchange is in recent years the still small but fastest growing source of live kidney donors. Improvements in the methods used to match donors and recipients will save lives. The PIs will collaborate with transplant centers and regional alliances to take the newly developed methods into application.
