A Beautiful Application: Using Economics to Make Kidney Exchanges More Efficient and Fair

Mohammad Akbarpour knew the mathematics well. He had worked in network theory. He’d spent time on maximum matching problems.

The year was 2012. Akbarpour was a doctoral student taking a class with Alvin Roth, the legendary Stanford economics professor, and the question before him was how to get the most kidneys to the most people in need of a transplant and, that way, give them the best chance at a longer, healthier life.

“We were using these tools that I was very familiar with to solve this important social problem,” recalls Akbarpour, now an associate professor of economics at Stanford GSB. “I had never seen such a beautiful application of the math.”

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Illustration by Eiko Ojala

In the U.S. alone, nearly 100,000 people are on a waiting list to receive a kidney. Roughly 8,000 of them are removed every year because they become too sick to undergo major surgery or die before an organ becomes available. Many others are on dialysis, surviving the slow decline of kidney function with dramatically reduced quality of life.

For those without private insurance, Medicare’s end-stage renal disease program pays for dialysis and transplantation — at a cost that amounts to 1% of the annual federal budget (a stunning $49.2 billion in 2018). Given the moral and economic significance of the problem, the natural question is how to optimize the system of allocation — how to get the most bang for the buck.

This is a question that Akbarpour has spent a good deal of time contemplating. It is also a question that two of his colleagues at Stanford GSB, Paulo Somaini and Stefanos Zenios, have studied from various angles. Roth himself shared the 2012 Nobel Memorial Prize in Economic Sciences in part for his work on kidney exchanges.

For Jonathan Levin, the Philip H. Knight Professor and Dean of Stanford GSB, this work exemplifies the two-way exchange between research and practice that is so foundational at the school: Research informs practice; practice, in turn, raises new questions for researchers to answer. And though the challenges remain technically daunting and ethically fraught, behind the equations and models and theories lies the simple, rewarding fact that improvements to the system, however marginal, save lives.

Winners and Losers

Ever since the 1960s, when a combination of surgical technique and pharmaceutical innovation made kidney transplants viable, demand has exceeded supply. In 1995, roughly 42,000 people were waiting for a kidney; in 2004, the figure was 77,000. Today it’s about 100,000, with 40,000 people joining the waiting list every year and roughly 20,000 transplants taking place.

“There is a great level of awareness among doctors that they are working with a limited resource,” Somaini says. “This is part of the reason they started talking to economists: Economics is about, and has always been about, how best to use scarce resources.”

A handful of operations specialists and economists, Roth among them, got involved with kidneys in the late 1990s and early 2000s. They realized that insights from game theory and queuing theory could be used to maximize the number of available kidneys and allocate them more efficiently.

“Efficiency, though, is a difficult concept in this case,” Somaini says. Striving to simply improve the combined years of life gained through kidney transplantation favors the healthy over the sick, the young over the old, as these recipients tend to live longer once they get a new kidney. Other changes to increase efficiency, while productive on their face, may end up discriminating against people by race, say, or blood type.

“When you adjust some distributional mechanism, then, generally, one group of people wins and another loses,” Somaini says. “You need to find a way to balance the demands of efficiency against the demands of equity.”

On top of this complication, transplants take place through two channels: living and deceased donation. Living donation occurs when someone who is alive decides to donate a kidney to another person who needs one — often a family member or friend, sometimes a stranger. (This is possible because most people are born with two healthy kidneys but can survive perfectly well with one.) Deceased donation, which made up about 70% of the kidneys transplanted in 2020, occurs when somebody who has previously decided to be an organ donor dies. Each of these routes operates in its own way, and each raises distinct challenges.

When Economics and Ethics Collide

The United Network for Organ Sharing is the nonprofit organization responsible for both managing the waiting list nationwide and formulating a ranking policy that governs how deceased-donor kidneys are distributed. The current matching algorithm works by creating scores based on a few dimensions, such as how long a patient has been on the waiting list, or how well a donated kidney pairs with the potential recipient’s tissue and blood type. If a good match is found (a high score), then the recipient, in consultation with her doctor, is given the choice of whether or not to accept the kidney.

A 2014 tweak to the algorithm began offering the highest-quality kidneys to candidates who were estimated to have the greatest post-transplant survival time, as a way to avoid transplanting kidneys with the greatest longevity potential into people who are nearing the end of their lives.

Recent work by Somaini and two of his colleagues examined whether adjustments to this algorithm could improve overall outcomes. What would happen if different sets of people were prioritized for different kinds of kidneys? In one extreme case, they looked at what would happen if you tried to simply maximize the longevity of patients among the entire transplant pool. Doing this led to an increase in median survival time of five years — from nine years to 14 years — but the gain was realized through a dramatic reshuffling of who does and doesn’t get kidneys; the sickest people on the waiting list were often passed over. As Somaini put it, “I was wearing my economist hat when looking at that option, not my ethicist hat.”

For Levin, this tension is part of what makes the question of kidney allocation so interesting. “This issue sits at the intersection of economics and ethics — not an area that economists typically spend their time in and yet here we’re forced to,” he says. “We’re in this world where we have to think about how to solve the problem facing those with kidney failure in a way that feels morally right.”

Zenios, who has studied deceased donation for almost two decades, has discovered a number of avenues that could improve outcomes. In a 2004 paper, for instance, he and two coauthors modeled the effect of having patients declare upfront their willingness to accept kidneys of varying quality. Some patients might opt to wait for kidneys of only the highest quality; others may be willing to accept any kidney that becomes available. By creating separate waiting lists within the main waiting list, this approach could increase by up to 15% the number of kidneys available for transplant and decrease by 30% the number of people who die while on the waiting list.

In a more recent study, Zenios and his colleagues find support for the 2014 policy shift that offers the healthiest kidneys to the healthiest patients. They suggest making the same shift at the other end of the waiting list, offering less-healthy patients priority for lower-quality kidneys. They also note that giving people priority based on how long they’ve been on the waiting list, though an intuitive metric, negatively affects outcomes; finding a metric to replace this one could lead to substantial improvements.

In the World of Living Donors

This is only one part of the equation. Akbarpour studies the other part: the world of living donors. Like his colleagues, Akbarpour has puzzled over how best to stretch this scarce resource.

About 20 years ago, Roth and two collaborators recognized and developed an innovation in the world of living kidney donation. Transplants historically involved one person giving their kidney to another person. That was it. Instead of one-to-one matching, Roth and his colleagues formalized a platform for paired exchanges. Suppose Donor A wants to give a kidney to Recipient B, but they are not a good match; and suppose Donor Y wants to give to Recipient Z, but they are not a match. If you pair them together, it’s possible that Donor A can give to Recipient Z, and Donor Y to Recipient B; now you’ve got two transplants instead of zero.

Even more powerful, Roth expounded a system in which non-directed donors — the small fraction of people who give a kidney to a stranger because they think it’s a good thing to do — can kick off transplant “chains” that generate dozens of transplants, all falling like dominoes from the first one.

But making these chains and paired exchanges happen as effectively as possible is difficult. For starters, the pool of potential donors and recipients is dynamic, which means decisions about who gets transplanted today will affect the state of the network — and who can and cannot receive a kidney — tomorrow. (Akbarpour’s PhD dissertation, under Roth, explored this problem.) Additionally, hospitals have their own incentives to match patients in-house rather than with another hospital, so they often don’t place patients and donors on the network for paired exchange. “A mix of mathematical, logistical, and incentive problems make this an interesting challenge,” Akbarpour says.

Nonetheless, Akbarpour sees several changes that could squeeze more transplants from the current supply of living donors. One simple fix would be to expand the paired exchange pool.

The U.S. currently has multiple “kidney exchange platforms,” Akbarpour says. From an economic perspective, this is inefficient; the larger the pool, the greater the potential for matches. Uniting different regional exchanges would improve transplant numbers. If done carefully, the potential pool of paired exchanges could even be expanded internationally.

Recent work by Stanford’s Itai Ashlagi, an associate professor in the School of Engineering at Stanford and a close collaborator with Roth, allowed for a three-way kidney exchange between Israel and Abu Dhabi, for instance. These transplants were made possible because the matching algorithm was able to draw candidates from a cross-border pool of patients. Akbarpour, too, has researched the potential benefits of global kidney chains.

“Another space where we could improve things is if we can convince people who are already planning to donate a kidney to join the exchange,” Akbarpour says. The main rationale for this is that donors with O-type blood can donate to anybody, but recipients with O-type blood can receive kidneys only from somebody else with O-type blood. As a result, there is a disproportionately large group of people with O-type blood waiting for kidneys. But if, for example, a mother with O-type blood who planned to give a kidney to her daughter with non- O-type blood could instead be convinced to take part in a paired exchange, then her daughter could still receive a kidney — perhaps one that is better matched — and someone with O-type blood who would otherwise have remained on the waiting list would receive a kidney from the mother.

Finally, Akbarpour suggested using kidneys from deceased donors to start transplant chains, a practice that is currently banned in the U.S. “Right now, the number of chains we can initiate is limited by the number of altruistic donors,” he says. This is a tiny portion of all kidney donors. “Imagine if we could multiply that by a factor of 10,” Akbarpour says.

What If Donors Were Paid?

Even with that multiplication, though, and even with refinements to the matching algorithm for deceased donors, the waiting list would continue to grow. When it comes to kidney transplants, supply — no matter how well managed — simply does not meet demand. Thus, looming behind all of this work is the question of whether more people can be convinced to donate their organs upon death, and whether more people might agree to give up a kidney while still alive.

For economists, one textbook answer to a mismatch between supply and demand relates to pricing. What would happen if living donors were compensated for giving a kidney? Although the practice is illegal in the U.S. (and every other country besides Iran) and repugnant to many, Akbarpour has researched the idea. He has found that such a system would effectively reduce wait times and increase transplants; the evidence from Iran is unambiguous. But he has not taken a position on whether these outcomes sufficiently outweigh potential drawbacks.

In the U.S., concerns about a paid market for kidneys typically fit into four big categories, he says. One, it will exacerbate economic inequality by placing kidneys on the list of items the rich can afford and the poor cannot. Two, it will create a system of the poor selling to the rich. Three, it is intrinsically immoral to sell body parts. And four, it will spur trafficking and black markets.

“If I were a policymaker considering a market, I would go after these one by one,” Akbarpour says. “I think most of them are at least debatable, if not solvable.”

Fears that the rich will be able to buy kidneys and the poor will not can be addressed by creating a monopsony: a market in which there is a single purchaser, in this case the federal government, which procures all donated kidneys at a fixed price. After that, they are allocated according to the system currently in place, which prioritizes the neediest recipients rather than the wealthiest. This would give everybody access to kidneys and save the government money, since a transplant costs far less over time than dialysis does.

Worries that the poor alone would be motivated to sell their kidneys are more difficult to address, Akbarpour says. At its core, this would be a question of establishing an acceptable price. If you consider the extreme case of donors being paid $10 million in exchange for a kidney, “then even I’m going to subscribe,” he says. Although poorer people would likely be overrepresented no matter what, paying the right amount could mitigate the most egregious disparities.

On the third issue of whether people should be allowed to sell body parts, “I don’t think there is any regulation that can solve that problem,” Akbarpour says. This represents a fundamental divide over convictions, not policy design.

Finally, there is the question of trafficking and the black market. A properly regulated legal market for kidneys would actually reduce the need for a black market, Akbarpour contends. Assuming that the waiting list in the U.S. would shrink as more donors step forward, people in need of a kidney would be less desperate and less willing to fly overseas to purchase one. In fact, it could be argued that the dysfunction of the current system feeds the existence of an overseas black market.

In the end, Akbarpour says, policymakers should at least acknowledge there is a huge cost for not having a paid system — the thousands of people who die each year, the billions that Medicare pays for dialysis, and the inequities that already exist around who does and does not get a kidney. “These present us with complicated trade-offs,” he says.

And it is the work of academics over the past two decades, starting with Roth, that has helped to nudge transplantation toward a position that is both more ethical and more efficient, suggests Levin: Academics present a new theoretical approach to distribution, the idea gets implemented in practice, unforeseen challenges arise, and the problem is returned to academics for refinement.

“This ongoing feedback loop from theory to practice and back to theory has proved a really nice model for the application of academic ideas,” Levin says. “And in this particular problem of kidney allocation, the payoff is saving people’s lives. That’s an inspiring challenge.”