kidney swap

Kidney swaps II

The Wall Street Journal reports (subs. required) that the kidney swap idea I wrote about earlier is beginning to be implemented. Here are they key points:

Last year, 43% of kidneys transplanted in the U.S. came from living donors, up from 28% a decade ago.

But a biological barrier often blocks a transplant from a relative. In about a third of all would-be pairs, blood types are incompatible. In others, the sick person has antibodies that can initiate a rejection of the donated organ. It’s heartbreaking “to have the treasure of the live donor and then have that not go forward because of a biological obstacle,” says Massachusetts General Hospital transplant surgeon Francis DelMonico.

Occasionally, transplant centers spot a way out: One New England father with blood type A couldn’t donate a kidney to his daughter with blood type B. So he gave a kidney to a teenager with blood type A, and the teenager’s sister gave a kidney for the man’s daughter.

Such swaps, however, typically occur only when happenstance alerts surgeons to the possibility. Economist Alvin Roth and co-authors have devised an algorithm, however, that computes all the possible swaps and which is incentive-compatible.

…when Dr. Saidman gave the economists details on 45 pairs in which the would-be donor was unable to give a kidney to the intended recipient. Even though each of the 45 had a donor willing to spare a kidney, all were stuck waiting for the right person to die. With swaps involving two kidneys, the economists found, eight transplants were possible. If swaps involving three kidneys were possible, then 11 transplants were possible.

Addendum: Alert readers will note that kidney swaps are quite similar to organ clubs an idea for saving lives that has been implemented by Lifesharers.

Kidney swaps

Your spouse is dying of kidney disease. You want to give her one of your kidneys but tests show that it is incompatible with her immune system. Utter anguish and frustration. Is there anything that you can do? Today the answer is yes. Transplant centers are now helping to arrange kidney swaps. You give to the spouse of another donor who gives to your spouse. Pareto would be proud. Even a few three-way swaps have been conducted.

But why stop at three? What about an n-way swap? Let’s add in the possibility of an exchange that raises your spouse on the queue for a cadaveric kidney. And let us also recognize that even if your kidney is compatible with your spouse’s there may be a better match. Is there an allocation system that makes all donors and spouses better off (or at least no worse off) and that maximizes the number of beneficial swaps? In an important paper (Warning! Very technical. Requires NBER subscription.) Alvin Roth and co-authors describe just such a mechanism and show that it could save many lives. Who says efficiency is a pedestrian virtue?

See here for more on how to alleviate the shortage of transplant organs.

The Global Kidney Exchange Programme

In my WSJ review of Al Roth’s excellent book Who Gets What—and Why I wrote about Roth’s proposal to extend the idea of kidney swaps globally:

It’s often the case that a living donor is willing to give a kidney to a loved one, but the loved one can’t accept it because of immunity mismatch. But if a pair of such mismatched donors could be found (call them A and A´ and B and B´), then perhaps a match could be found by a crisscross pairing: Donor A could give to recipient B´ and donor B could give to recipient A´, thus solving the mismatch problem and saving lives.

…Today such multi-way exchanges are becoming common….Mr. Roth, however, wants to go further….why not open U.S. transplants to the world? Imagine that A and A´ are Nigerian while B and B´ are American. Nigeria has virtually no transplant surgery or dialysis available, so in Nigeria patient A’ will die for certain. But if we offered a free transplant to him, and received a kidney for an American patient in return, two lives would be saved.

The plan sounds noble but expensive. Yet remember, Mr. Roth says, “removing an American patient from dialysis saves Medicare a quarter of a million dollars. That’s more than enough to finance two kidney transplants.” So offering a free transplant to the Nigerian patient can save money and lives.

It’s hard to think of a better example of gains from trade (or a better PR coup for the U.S. on the world stage).

Recently, Rees et al., (including Roth) announced the first such global kidney exchange:

We report the 1‐year experience of an initial Filipino pair, whose recipient was transplanted in the United states with an American donor’s kidney at no cost to him. The Filipino donor donated to an American in the United States through a kidney exchange chain. Follow‐up care and medications in the Philippines were supported by funds from the United States. We show that the logistical obstacles in this approach, although considerable, are surmountable.

Naturally, some people aren’t happy because of “ethical” objections. Minerva, Savulescu and Peter Singer write in defense of the program:

Lurking behind all the arguments against the GKE is the assumption that people who are poor are incapable of autonomous choices. So, if they appear to choose to act in ways that benefit not only themselves, but people in HICs, they must have been coerced, exploited, or commodified.

…Poverty does not necessarily make a person unable to choose to donate a kidney to a loved one, nor does it make someone incapable of weighing the pros and cons of an option like that offered by the GKE. Poverty does narrow down the options available to people, and often forces them to settle for an option that is not as good as a wealthy person would choose. That, however, is irrelevant to the ethics of the GKE if that programme provides a better option to patients in LMICs who need a kidney than any other option currently available to them.

…It would be tragic if such misguided objections were to prevent the GKE from realising its potential to reduce suffering and save the lives of rich and poor patients alike.

Hat tip: Frank McCormick.

Kidney Gift Vouchers

I am not expecting a market in kidneys anytime soon but ever more sophisticated barter is slowly improving kidney allocation. Most recently, UCLA has started a program where a kidney donation may be swapped for a kidney gift certificate good for a kidney transplant at a time of the recipient’s choosing.

The program allows for living donors to donate a kidney in advance of when a friend or family member might require a kidney transplant.

…“It’s the brainchild of a grandfather who wanted to donate a kidney to his grandson nearing dialysis dependency, but the grandfather felt he would be too old to donate in a few years when his grandson would likely need a transplant.”

Nine other transplant centers across the U.S. have agreed to offer the gift certificate program, under the umbrella of the National Kidney Registry’s advanced donation program. Veale anticipates that more living donors will come forward to donate kidneys, which could trigger chains of transplants. Then, when a patient redeems his or her gift certificate, the last donor in the chain could donate a kidney to that recipient.

Improving allocation is important but the real constraint today is supply. This program may help with that on the margin, however, because altruistic donors could donate and keep a gift certificate as insurance in case any of their family members one day needed an transplant. More fundamentally, however, increasing supply will require some form of compensation or incentive such as no-give, no-take.

Kidney Donor Chains

Virginia Postrel has an excellent piece in the online Atlantic on the shortage of transplant organs, it includes a very good discussion of both the promise and limitations of kidney swaps and donor chains.  Imagine that Mrs. Smith and Mr. Jones each need a kidney transplant.  Mr. Smith is willing but due to an incompatible blood type unable to donate a kidney to his wife.  Similarly, Mrs Jones is willing but unable to donate a kidney to her husband.  In a kidney swap, Mr. Smith donates to Mr. Jones and Mrs. Jones donates to Mrs. Smith.  Everyone is happy.

Donor chains extend this idea.  We start with an altruistic donor willing to give to anyone – by careful arrangement it's then possible to produce many transplants.  Recently, a single donor led to a chain of ten transplants!

Despite the promise of these techniques they are being underutilized.  Amazingly, the National Kidney Registry, which coordinates swaps and chains, has donors who are waiting to give.  A clear reminder that $500 bills aren't always picked up as quickly as we would like. 

Even the maximal use of swaps and chains won't solve the crisis, however. For that we are going to need better incentives to encourage more donors.

The Hidden World of Matchmaking and Market Design

Roth Cover

Al Roth’s Who Gets What and Why: The Hidden World of Matchmaking and Market Design is an excellent addition to the pantheon of popular economics books. It’s engagingly written, covers new material and will be of interest to professional economists as well as to the broader audience of intelligent readers.

review the book more extensively for the Wall Street Journal. (Google the title, Matchmaker, Make Me a Market to get beyond the paywall for non-subscribers). Roth is well known for helping to design kidney swaps–when donor A and patient A’ and donor B and patient B’ are mismatched it may yet be possible for A to give to B’ and B to give to A’.

Mr. Roth, however, wants to go further. The larger the database, the more lifesaving exchanges can be found. So why not open U.S. transplants to the world? Imagine that A and A´ are Nigerian while B and B´ are American. Nigeria has virtually no transplant surgery or dialysis available, so in Nigeria patient A’ will die for certain. But if we offered a free transplant to him, and received a kidney for an American patient in return, two lives would be saved.

The plan sounds noble but expensive. Yet remember, Mr. Roth says, “removing an American patient from dialysis saves Medicare a quarter of a million dollars. That’s more than enough to finance two kidney transplants.” So offering a free transplant to the Nigerian patient can save money and lives.

It’s hard to think of a better example of gains from trade (or a better PR coup for the U.S. on the world stage).

One of the most interesting aspects of the book is that Roth has created a new typology of market failure but a very different way of addressing such market failures. Read the whole review for more.

Noble Matching

In honor of the Nobel prizes to Al Roth and Lloyd Shapley, here is a primer on matching theory. Matching is a fundamental property of many markets and social institutions. Jobs are matched to workers, husbands to wives, doctors to hospitals, kidneys to patients.

The field of matching may be said to start with the Gale-Shapley deferred choice algorithm. Here is how it works, applied to men and women and marriage (n.b. the algorithm can also work for gay marriage but it’s a little easier to explain and implement with men and women). Each man proposes to his first ranked choice. Each woman keeps her top-ranked suitor but defers accepting the proposal. Each woman also rejects her lower ranked suitors. Each rejected man proposes to his second ranked choice. Each woman rejects again any lower-ranked suitors, which may include previous suitors who have now become lower-ranked. The process repeats until no further proposals are made; each woman then accepts her top-ranked suitor and the matches are made.

A similar process works when proposal receivers may accept more than one suitor, not that useful for marriage in most of the United States but very useful for when students are applying to schools and each school accepts many students.

Now what is good about this algorithm? First, Gale and Shapley proved that the algorithm converges to a solution for a very wide range of preferences. Second, the algorithm is stable in the sense that there is no man and no woman who would rather be matched to each other than to their current match. There are of course, men who would prefer to marry other women and there are women who would prefer to marry other men but no mutually preferable match is possible. Thus, the algorithm produces a stable match.

The application to men and women is somewhat fanciful, although Match.com should clearly adopt this idea!, but the application to students and schools is very real. Gale and Shapley concluded their paper by writing:

It is our opinion, however, that some of the ideas introduced here might usefully be applied to certain phases of the admissions problem.

Indeed, this is exactly what has happened. Students in New York and in Boston are now matched to schools using versions of this algorithm. Even before Gale and Shapley the algorithm had been used, without much theorizing, by doctors allocating residents to hospitals and since Gale-Shapley and Roth the idea has been used much more extensively all over the world .The algorithm, by the way, has been picked up and extended by computer scientists notably including Knuth.

I said above that the men propose to the women–this matters because when the women propose to the men you also get a stable match but it may be a somewhat different match and in general it is better to be the one proposing. Matching becomes more difficult when, as in modern times, both men and women may propose. Fortunately, in many problems, such as with students and schools, the proposers and receivers can be fixed.

Another question is whether the algorithm can be strategically manipulated. In an Impossibility Theorem with much the same flavor as Arrow’s Theorem and the Gibbard-Satterthwaite theorem, Roth and Roth and Sotomayor proved that there is always some possibility for manipulation but the G-S algorithm can be said to minimize the opportunity for strategic manipulation; in particular for the proposers, men or say students applying to schools. it is a dominant strategy to reveal one’s true preferences.

The importance of a stable matching algorithm can be seen in what happens when such algorithms are not used. In trying to allocate residents to hospitals, for example, what typically happens when a stable algorithm is not used is unraveling and chaos. Unraveling occurs when offers are made earlier and earlier in an attempt to get a jump on the competition. Prior to the currently used National Residency Matching Program, for example, hospitals were making offers to residents up to two years in advance! All kinds of chaos arose as hospitals would make exploding offers, accept now or the offer explodes! Such offers would inevitable lead to recriminations and backing out of the offers as better matches were sought.

What Roth has done is extend the Gale-Shapley algorithm to more complicated matches and to actually design such algorithms to solve real problems. In the 1970s, for example, the medical residency algorithm began to run into trouble because of a new development, the dual career couple. How to match couples, both doctors, to hospitals in the same city? By the 1990s assortative matching in the marriage market was beginning to derail matching in the doctor-hospital market! Roth was called in to solve the problem and moved from being a theorist to a market designer. Roth and Peranson designed the matching algorithm that is now used by Orthodontists, Psychologists, Pharmacists, Radiologists, Pediatric surgeons and many other medical specialties in the United States.

Most famously, Roth has worked on improving kidney allocation. I first wrote about this in 2004 (see also these posts):

Your spouse is dying of kidney disease. You want to give her one of your kidneys but tests show that it is incompatible with her immune system. Utter anguish and frustration. Is there anything that you can do? Today the answer is yes. Transplant centers are now helping to arrange kidney swaps. You give to the spouse of another donor who gives to your spouse. Pareto would be proud. Even a few three-way swaps have been conducted.

But why stop at three? What about an n-way swap? Let’s add in the possibility of an exchange that raises your spouse on the queue for a cadaveric kidney. And let us also recognize that even if your kidney is compatible with your spouse’s there may be a better match. Is there an allocation system that makes all donors and spouses better off (or at least no worse off) and that maximizes the number of beneficial swaps? In an important paper (Warning! Very technical. Requires NBER subscription.) Alvin Roth and co-authors describe just such a mechanism and show that it could save many lives. Who says efficiency is a pedestrian virtue?

Since that time we have seen many such swaps including this record of 60 people and 30 kidneys. Truly a noble match.

Minor editing Oct. 23.

Repugnance is Repugnant

Many people find the idea of selling human organs for transplant to be repugnant which is why Roth argues that we should focus more on improving efficiency through kidney swaps.  I’m all in favor of swaps and have also suggested that one argument in favor of no-give, no-take rules is that they are ethically acceptable to more people than organ sales.

Nevertheless, I think Roth assumes too quickly that repugnance is a constraint to be respected rather than an outrage to be denounced and quashed.  People’s repugnance at inter-racial dating or homosexual sex is no reason to prevent free exchange – the same is true for organ donations.  Repugnance itself can be repugnant.

Is it not repugnant that some people are willing to let others die so that their stomachs won’t become queasy at the thought that someone, somewhere is selling a kidney?

What people think repugnant can change rather quickly with changes in the status-quo.  Adam Smith said that in his time there were "some very agreeable and
beautiful talents of which the possession commands a certain sort of
admiration; but of which the exercise for the sake of gain is
considered, whether from reason or prejudice, as a sort of public
prostitution."  What were these talents that people in Smith’s time thought akin to prostitution?  Acting, opera singing and dancing.  How primitive, how peculiar.

In the not to distance future I think people will look back
on the present and think us
primitive and peculiar.  Letting thousands of people die while organs that could have saved their lives were buried and
burned.  So much unnecessary pain; all for fear of a little exchange.  How primitive, how peculiar.  How repugnant.

The Shortage of Transplant Organs

The Wall Street Journal has a front-page article and a debate between Julio Elias and Alvin Roth on alleviating the shortage of transplant organs.  This interactive graphic was good at explaining the idea of kidney swaps.  Elias and Roth should have discussed no-give, no-take rules and Lifesharers

I will be speaking to Congressional and agency staff about the organ shortage this Thursday at noon (this event is not open to the public.)

Addendum: Transplant surgeon Arthur Matas, mentioned in the WSJ article, is no
libertarian but argues for live kidney sales in a new Cato Policy
Report
.

Nobel Prizes: Al Roth and Lloyd Shapley

Great choices. Al Roth for matching and the design of new types of markets. Lloyd Shapley for fundamental contributions to game theory and mathematical economics including the Gale-Shapley algorithm which is a cornerstone of the matching methods Al Roth pioneered. I am especially pleased about this because of Roth’s great work on improving kidney allocation. Here is Roth’s blog, Market Design and here he is giving a talk at Google. Here is what I wrote in 2010 about Roth

Roth has applied heavy-duty theory to the very practical problems of matching doctors to residency programs, children to schools, economists to departments and kidneys to patients in a way that is stable, incentive-compatible, and maximizes the gains from exchange.  In my view, Roth is the most influential economist working today. Influential among other economists?  Yes.  But what I really mean is influential in the world.

Previous posts on MR about Roth (also here). Roth’s papers.

More soon.