New Challenges in Multihospital Kidney Exchange.

The growth of kidney exchange presents new challenges for the design of kidney exchange clearinghouses. The players now include directors of transplant centers, who see sets of patientdonor pairs, and can choose to reveal only difficult to match pairs to the clearinghouse, while withholding easy to match pairs to transplant locally. This reduces the number of transplants. We discuss how the incentives for hospitals to enroll all pairs in kidney exchange can be achieved, and how the concentration of hard to match pairs increases the importance of long, nonsimultaneous nondirected donor chains. New challenges in multi-hospital kidney exchange By ITAI ASHLAGI AND ALVIN E. ROTH∗ A kidney transplant is the treatment of choice for end stage renal disease, but over 90,000 patients are waiting for a cadaver kidney in the U.S., and fewer than 11,000 such transplants are performed annually. Live donation is also possible, and there are now more live than deceased donors each year in the U.S., although they still account for fewer than 6,500 transplants a year (since living donors only donate one kidney). And having a healthy willing live donor is not enough: sometimes a donor’s kidney is incompatible with the intended recipient, either because of blood type or immunological incompatibilities. Incompatibility between donor and intended recipient creates the demand for kidney exchange (aka kidney paired donation): an incompatible patient-donor pair can donate a kidney to a compatible recipient and receive a kidney from a compatible donor. The first kidney exchange was in Korea (J.Y. Kwak et al. (1999)), where the high frequency of blood types A and B make exchanges due to blood type incompatibility readily available (an A-B pair exchanging with a B-A pair, where XY denotes a patient of blood type X and donor of blood type Y), more than in the U.S. where blood type B is relatively rare. The first kidney exchange in the U.S., in New England in 2000, also involved two blood type incompatible pairs (see Bradley C. Wallis et al. (2011) for history and references). And for most patients on the waiting list for cadaver kidneys, blood type determines compatibility with a given donor. Only 10% of those 90,000 patients are “highly sensitized,” meaning they are immunologically incompatible with more than 80% of donors with compatible blood type. But the patients enrolled in the most active kidney exchange networks are much more highly sensitized: in the four exchange networks ∗ Ashlagi: Sloan School of Management, MIT, Cambridge, MA 02138, [email protected]. Roth: Department of Economics, Harvard University and Harvard Business School, Cambridge, MA, 02138, [email protected]. We are grateful to Mike Rees, for many helpful conversations, and to Parag Pathak and Scott Kominers for helpful discussion. with which we have worked, the percentage of highly sensitized patients is from 50%-80% of those enrolled (Ashlagi, David Gamarnik and Roth (2011)). The present paper considers why this is the case, and its consequences. While the first proposal for organizing kidney exchange on a large scale involved exchanges organized as both cycles and chains, logistical constraints required that the initial exchanges conducted by the New England Program for Kidney Exchange, the Alliance for Paired Donation and other networks were between just two patient-donor pairs (Roth, Tayfun Sönmez and M. Utku Ünver (2004,2005a,b) ).1 Subsequent work suggested that as patient pools grew larger, expanding the infrastructure to allow only slightly larger, 3and 4-way exchanges would be efficient (Roth, Sönmez and Ünver (2007a)). But the prevalence of highly sensitized patients among those enrolled in kidney exchange has brought long chains back into the picture in an important way, after the introduction of nonsimultaneous chains initiated by a non-directed donor (Roth et al. (2006), Michael Rees et al. (2009)). Chains now contribute many of the kidney exchanges performed by all of the largest multi-hospital networks except the UNOS pilot program. The usefulness of chains turns out to be closely related to the highly sensitized patient population. And one of several causes of the high percentage of highly sensitized patients is that many large transplant centers are withholding their easy-to-match patient-donor pairs, and only enrolling their hard-to-match pairs. This reduces the total number of transplants that can be achieved, particularly for the most highly sensitized patients.2 (Another reason the patient pool 1In addition to those two large kidney exchange clearinghouses, kidney exchange today is practiced by a growing number of hospitals and consortia. Computer scientists have become involved, and an algorithm of David J. Abraham, Avrim Blum and Toumas Sandholm (2007) designed to handle large populations was briefly used in the APD, and has been used in the UNOS (United Network for Organ Sharing) pilot program for a national exchange. 2For example, the UNOS kidney exchange program was be-