When a person donates a kidney to a broad pool of potential recipients, the altruistic act can kick off a long chain of donations that leads to more transplants for hard-to-match patients, a mathematical analysis concludes.
Many people needing kidney transplants have a willing donor, but they can’t take the kidney because it’s not compatible with their blood type or immune system. Paired exchanges, where incompatible donor/recipient pairs swap kidneys with another incompatible pair, is one trick for getting kidneys into hard-to-match patients. Another trick is a donor chain: A person gives a kidney to a clearinghouse or kidney exchange, which can set off a chain of donations.
Within the kidney transplant community, there’s been an ongoing debate over whether long chains ultimately mean more transplants. “The mathematical question was, are we really transplanting more people?” says Alvin Roth, an expert in game theory and market design at Harvard. “The answer is yes, a lot more.”
Long chains, which can involve more than 10 transplants, can result in 30 percent more transplants than a cycle of three exchanges, Roth and his colleagues calculated. That benefit varies depending on the number of difficult-to-match patients and the size of the kidney pool. These chains especially benefit patients that are hard to match and don’t harm patients who easily find a match, the researchers report in a July National Bureau of Economic Research working paper.
Hopeful transplant recipients can be difficult to match when they are what doctors call highly sensitized: The patient builds up antibodies that will attack most foreign tissue. Roth and his colleagues collected data from kidney clearinghouses on the number of these highly sensitized patients typically found in a kidney exchange pool. Because easy-to-match pairs often don’t enter pools, hard-to-match, sensitized patients can accumulate.
The researchers then developed an algorithm that finds the greatest number of matches for a pool of a given size with a given number of sensitized patients.
“It turns out to not be an easy problem. It’s very hard computationally,” says MIT’s Itai Ashlagi, who conducted the analysis along with Roth, MIT’s David Gamarnik, and Michael Rees, a transplant surgeon at the University of Toledo and medical director of the Alliance for Paired Donation, which arranged the first non-simultaneous chain of 10 kidney transplants.
There can be a considerable gap between mathematical simulations of kidney exchanges and the real world, says transplant surgeon and biostatistician Dorry Segev of Johns Hopkins, who comes down on the side of shorter chains are better. While long chains are very appealing — such as the 30-donor, 30-recipient chain completed late last year in 17 hospitals across the country — there’s always the danger that a potential donor will change their mind or no longer be medically able to give up a kidney, which can disrupt the chain. “The longer the chains are, the higher chance they will fall apart,” says Segev.
The new paper does highlight the importance of unifying kidney exchange programs, says Segev. Creating one large pool and coordinating transplant efforts nationwide would surely mean more transplants. “Right now, your experience depends very much on what center you work with,” he says. “We’re still in the Wild West of kidney donation.”
