In 2012 from a pool of 90,000 people who were waiting for a transplant, just 10% of them are “highly sensitized” meaning that they are immunologically incompatible with about 80% of donors sharing the same blood type. Given this situation, one would expect that this percentage would not be far from the percentage of highly sensitized people that prevails in the kidney exchange networks. Unfortunately, it isn’t the case, in 2012 the percentage of “highly sensitized” people in the 4 exchange networks with which Itai Ashlagi and Alvin E. Roth, the authors of the paper briefly summarized in this entry worked, showed that the proportion was actually of 50 – 80 percent of highly sensitized patients.
At first, kidney exchange networks allowed only exchanges between two patient-donor pairs due to logistical constraints, afterwards, three and four way exchanges were considered also efficient as patient pools grew larger. This exchanges are organized as cycles and chains, and these procedures allow many of the actual kidney transplants.
Apparently, kidney exchange networks should maximize the number of transplants allocating them efficiently by the use of matching algorithms but in reality, as mentioned before the total number of transplants is not maximized because of the high percentage of highly sensitized patients in the pools.
Ashlagi and Roth show that the usefulness of chains is closely related with highly sensitized percentages of patients as hospitals enroll in the exchanges just their hardest to match patients and keep the easy to match ones and so making it harder to make an efficient match. The authors propose various reasons to explain why hospitals would prefer not to enroll all their patients in the exchanges, being some of them that they’d like to avoid logistic difficulties to coordinate with other hospitals or to avoid paying for the tests required to do the transplant but according to the authors, the main reason is that it is not individually rational for hospitals to enroll all their pairs since there’s no guarantee that that each hospital will perform the same number of transplants if it submits all its pairs than by keeping some of them and performing the transplants with their own patients internally.
The authors also propose a simple model to explain such a situation, suppose there’s hospital A that has two donor-patient pairs, say a1 and a2 which he can transplant internally. Then suppose that the hospital submits both of its pairs to the exchange network but the algorithm solution that allows the most number of transplants doesn’t include pair a2 which is transplanted at hospital A. It’s evident that hospital A would have incentives not to submit both pairs and perform both of the transplants internally instead of just one.
To finish my contribution, I quote one of the concerns of the authors which is proven in their paper:
“The initial papers on kidney exchange focused on incentives for patients and their surgeons, but the current problems facing kidney exchange arise from the fact that hospitals have become the main players, and have different strategy sets than individuals, since directors of transplant centers deal with multiple patient-donor pairs. “
Itai Ashlagi and Alvin E. Roth
Rogelio Antonio Melo Juárez
New Challenges in Multihospital Kidney Exchange
Author(s): Itai Ashlagi and Alvin E. Roth
Source: The American Economic Review, Vol. 102, No. 3, PAPERS AND PROCEEDINGS OF
THE One Hundred Twenty Fourth Annual Meeting OF THE AMERICAN ECONOMIC
ASSOCIATION (MAY 2012), pp. 354-359
Published by: American Economic Association