Chain of lives: kidney exchange in Forbes

Itai Ashlagi and David Gamarnik in Forbes: Kidney Transplants: How To Extend A Chain of Life

"What is the best way to use the kidney of an altruistic donor so that the greatest number of patients get transplants?

"To answer this question, we gathered data from a kidney exchange clearinghouse. Included was detailed information about patients’ blood and tissue types, which told us how hard it would be to find matches for them. We analyzed the data using the tool of graph theory, an approach used in mathematics and computer science to understand relationships among pairs of objects. This tool is used to find the largest number of matches achievable in each exchange program. Working with us were two pioneers of kidney exchange, Michael Rees, a transplant surgeon at the University of Toledo, and Alvin Roth, an economics professor at Harvard Business School.

"We found that long chains and long cycles of donations are essential to helping the greatest number of patients. This is especially true for patients whose blood or tissue types make them difficult to match. The percentage of hard to match patients in kidney exchange programs is very high since easy to match patients can often find a donor without the aid of the exchange program (even when enrolling the program they can be matched quickly while hard to match patients accumulate over time). But lengthy chains will benefit hard to match patients while not harming easy to match patients who are in kidney exchange programs, we found."

Here's the paper reporting the results in detail:
Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange"