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A Six-Way Kidney Exchange

Kidney Transplants are typically thought to only involve a patient and a donor, but in recent years, kidney exchange chains have become more prominent as kidney databases are built, and algorithms optimized.  Recently, a 6-way kidney exchange occurred in California, as 6 donors and 6 patients were all brought together to transplant the kidneys to the right patients. What makes the operation incredible is the finding of these 6 pairs of people, and how multi-pair exchanges benefit everyone involved. Even if a patient finds family or a friend willing to donate a kidney, there are often complications involving the rejection of the donated kidney due to blood type and anti-bodies. Additionally, it is important for the donor to be alive as it reduced the change of rejection. The software that allowed for such an exchange is called MatchGrid and focuses on “choosing the greatest number of kidney transplants that can possibly occur at the same time, while still finding the most immunological commonalities between pairs.” At most, there can be 10 pairs of kidneys chained together, an amount that greatly surpasses normal kidney exchanges. The results of such software are easily seen as showcased by the story of one of the 6-way exchange patients. Within her blood type, only 10% of the population could be potential donors. The odds were clearly stacked against a match, but the more donor-patient pairs stringed together, the greater the chances of finding a potential kidney donor, as shown in what happened just a week ago. The faster this type of software is utilized, the greater the chances patients around the world have of being saved.

Kidney Exchange mirrors the topic of matching we have discussed in-depth during lecture, specifically matching markets without money. We can view Kidney Exchanges as essentially house allocation with mixed initial endowments, and binary-preference agents. The agents or patients, can be represented with binary preferences because all compatible kidneys are equally good, while all incompatible kidneys are equally bad. Of course, some matches must definitely be better than others, but overall, once a certain threshold of safety is met, any compatible kidneys can be treated equally. Kidney exchanges are essentially house allocations with mixed initial endowments because some patients enter the exchange with a donor, mirroring an initial endowment, while others are on the kidney transplant with no donor or initial endowment.  Research has shown that a three-way exchange adds many transplants, holding the majority of improvement, with four-way exchanges adding only a little efficiency. While five and six-way exchanges have yet to be studied in-depth, the 6-way exchange in California shows that 6-way exchanges can provide benefit in saving the lives of patients with high constraints and low chances of finding a match (the patient with 10% of the population as potential donors inside her blood type).  The biggest factors to consider however are whether the exchanges are pareto-efficient and strategyproof. The software MatchGrid uses strives to be pareto-efficient, but adds the constraint that the immunological commonalities between matches must be decent enough to minimize the rate of rejection. The immune response constraint is clearly needed and worth sacrificing some efficiency gain if it decreases the rejection rate of kidneys. There is no point in performing a kidney transplant with a high rejection rate, as the kidney could have been better utilized by another patient with a lower chance of rejection. Strategyproofing the mechanism remains another area of concern as hospitals could potentially be bribed to make patients appear sicker than they actually are in order to receive transplants earlier as seen in the Chicago case reported by Reuters in 2003. Overall though, software like MatchGrid represents a step in the right direction as patients are given greater chances at receiving their necessary transplant by optimizing the limited number of exchanges.




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