This is the final blog entry on solving the problem of getting hospitals to cooperate and allow a national kidney exchange to match all their live donors. You can see part 1 here and part 2 here.

Solutions

There are several ways to encourage hospitals to submit all their pairs to the exchange rather than withhold some. One mentioned in a paper by Itai Ashlagi and Alvin Roth in Nat. Bur. Econ. Res. Jan 2011 is to use a lottery that rewards hospitals with more matches if they enter their easy-to-match pairs into the exchange. Hospitals that enter more O blood type donors will be rewarded by getting more matches for their O blood type patients. (As noted earlier, currently most transplant centers do not place their matched patient-donor pairs in exchanges. This must change for exchanges to reach their full potential.)

The solution suggested by Mr. Ashlagi and Mr. Roth reduces the number of total transplants compared to full cooperation with no incentive, but produces more transplants than under the current practice of noncooperation.

Some other possible solutions could involve incentives that don’t reduce the total number of transplants. For instance, the exchange could publicize the count of paired matches made for each hospital internally vs through the exchange (basically shaming the hospitals that don’t fully participate). Even if the transplant centers do not reveal the total number of pairs to the exchange, this number is publicly available. Each transplant hospital is required to report the total number of swaps it performs to the United Network for Organ Sharing (UNOS). The exchange knows how many swaps it facilitated. The difference between the UNOS’s count of live unrelated donors and the exchange’s count of pairs entered will be the number of transplants the hospital conducted internally.

Another solution that doesn’t affect the total number of transplants is to reward cooperating hospitals with first choice of donors if there are multiple matches.

Finally, exchanges can do a better job of handling preferences and constraints requested by the participating hospitals. Rather than having a collection of regional exchanges in order to meet the needs of a set of hospitals, a single national exchange can include preferences for maximum shipping time/distance, maximum donor age, minimum and maximum donor kidney size, maximum HLA mismatches, etc. for each hospital and even each patient. It can give preferences to juvenile patients, patients with high cPRA, patients who have been waiting more than six months in the exchange, etc. The exchange can use these constraints to find the favored matches without sacrificing the total number of transplants.

Conclusions

One would expect the kidney exchange market to evolve into a natural monopoly with one exchange gaining all the participants by offering the highest likelihood of a match in the shortest possible time.

However, we are not seeing that at this time because of difficulty in getting exchanges and participating hospitals to work cooperatively and quickly. These problems can be resolved and I expect kidney exchanges to grow until nearly all live donor transplants are mediated through them.

I hope that regional kidney exchanges do not form and instead the problems in the national exchanges are solved. The formation of regional exchanges would split up the pool of potential matches. Finding the easy matches locally and the pushing the hard matches to another pool will lead to suboptimal number of transplants. This is a serious issue because it means some patients will die while waiting for a transplant.

[Disclosure: I do volunteer work for the National Kidney Registry, one of the several exchanges that are the subject of this three-part blog post.]

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