Real Numeracy

by George Taniwaki

The most common measure of kidney function is called the glomerular filtration rate (GFR). Traditionally, a GFR level of 90 or higher (measured in mL/min/1.73m^2) is considered normal. Kidney disease is categorized in stages from 1 to 5 with each stage defined by a GFR range. Patients with chronic kidney disease (CKD) generally progress though the stages until they reach stage 5. At this point they will require renal replacement therapy, meaning dialysis or a transplant. Details are given in the table below.

Traditional definitions of the five stages of kidney disease, they may not apply to kidney donors with one kidney

Patients with stage 4 and stage 5 are much more likely to also have hypertension (chronic high blood pressure) and are more likely to die from a cardiac event (heart failure). About 20% of patients in these categories die each year.

Estimated versus measured GFR

Before looking at the results of studies, let’s define GFR and how it is measured. Glomerular filtration rate is the volume of fluid (in mL) that can be filtered from the renal (kidney) glomerular capillaries per unit time (in min) adjusted for the body surface area (BSA) of the patient (that’s the reason the 1.73m^2 appears in the denominator; it represents the height of the average male of about 5 foot-8 inches).

The most accurate way to measure filtration rate is to use find a chemical that has a steady level in the blood, is completely filtered by the kidneys (arrow 1 in figure below) and is not reabsorbed (2) or secreted (3).

Schematic of function of kidney. Image from Wikipedia

The most common chemical used in GFR measurement is a protein called creatinine. It is a waste product from muscle cells and is produced at a fairly steady rate. As described in a Mar 2008 blog post, a test called the creatinine clearance rate (CCR) can be used to measure the amount of creatinine removed from the blood and excreted in the urine in a 24 hour period. A blood sample is taken to measure the concentration of creatinine in the plasma. These two measurements are used to calculate GFR. Since the concentration in both the urine and plasma are directly measured, this is called measured GFR or mGFR.

Collecting a 24 hour sample of urine is cumbersome and it is hard to get patients to do it correctly. (I’ve done it three times in the past two years while being evaluated as a kidney donor, so I’ve become accustomed to the routine.) To avoid the 24-hour urine collection, doctors estimate the GFR using just the serum concentration. These estimates are based on the person’s age (muscle mass declines with age), gender (women have less muscle mass then men), weight (thin people have less muscle mass), and race (blacks have higher muscle mass than whites). GFR calculated in this way is called estimated GFR or eGFR.

A scary story for donors

After their surgeries, some kidney donors are told they have low GFR, below 60 ml/min/1.73m^2, and thus have Stage 2 chronic kidney disease. A recent paper presented at the 26th Annual Congress Eur. Assoc. Urology reports that one year after undergoing a live donor nephrectomy, more than half of donors will have CKD as defined by the traditional stages. The paper is described in Renal and Urology News Mar 2011.

In the study, a team led by Nilay S. Patel examined data from 3,424 living donors in the United Kingdom who had preoperative and one-year follow-up data available. “The fall in GFR [following donation] has been underestimated to date,” said Dr. Patel. Potential donors should be informed of the risk of renal function decline following donation.

Well, this is rather scary. Is it safe to donate a kidney?

Rising GFR after donation

In the study above, Dr. Patel notes that after the initial decline in GFR, it appears to remain stable for at least five years. Further, donors rarely suffered adverse cardiovascular events or cardiac mortality.

Among the 784 donors with five years of follow-up data available, only 0.4% experienced non-fatal cardiac events and 0.05% died from cardiac events. New-onset hypertension was diagnosed in 10% of donors.

This is reassuring. Let’s take a look at the results from some other recent studies that investigated GFR after kidney donation.

A study of 237 Japanese donors is reported in Clin. Exper. Nephr. Aug 2010. The authors found that the median estimated GFR at the time of donation was 79, meaning that many donors could be considered to have stage 2 kidney disease. After one year, the average decrease in eGFR was down 40% to 48, meaning most (85%) Japanese kidney donors would be considered having stage 3 kidney disease.

This sounds bad. However, data collected over the next four years shows that on average, the eGFR rose by 1 mg/mL/1.73m^2 per year. This upward change was seen regardless of the absolute values of estimated GFR at the time of donation or one year afterwards. This is unexpected because GFR generally declines with age. Thus, among these Japanese kidney donors, low GFR was not a sign that kidney disease will progress.

A Swedish study published in Nephr. Dialy. Transpl. May 2011 (subscription required) and described in Renal and Urology News Mar 2011 confirms that people who donate kidneys experience an increase in estimated GFR for more than a decade after nephrectomy.

The researchers looked at 573 kidney donors who had a mean age of 47 years at the time of donation and with a mean time since donation of 14 years.

The findings suggest that for 30-year old donors, the median estimated GFR increases for 17 years, then remains constant for 8 years, and then declines thereafter. For a 50-year old donor, the median eGFR increases for 13 years and then declines. The gains were less pronounced for measured GFR. The data, developed using multiregression analysis are shown below.

Curves showing median eGFR (left) and median mGFR (right) for a typical 30-year-old donor (black line) and 50-year-old donor (gray line). Graphics from Nephr. Dialy. Transpl.

Difficulty in measuring GFR

Finally, there is some research that indicates that using the standard calculations for measured GFR and estimated GFR is not appropriate for kidney donors and are not reliable ways to determine if they have kidney disease. An article in Clin. J. Amer. Soc. Nephr. Jan 2010 reports that eGFR underestimated actual kidney function while  mGFR overestimated it. The error was larger the older the donor.

Mark Wedel, a retired MD and kidney transplant recipient, provides the following comment on these studies.

“I think the primary question [these studies raise] is whether or not this change is what one would expect [to occur in these donors] after having half their renal mass removed, and secondarily, does that GFR actually increase as the remaining kidney hypertrophies in response to the donation nephrectomy.

“I’m not aware of any serial data on renal mass following nephrectomy. Ideally, I’d like to see a study correlating GFR with renal mass plotted against time [since transplant].”

Comparing donors to patients

I have drawn two graphs below to represent the change in GFR for two people. On the left is GFR data plotted for a hypothetical 40-year-old woman. Her GFR declines for two years going from 98 to 78 before she is diagnosed as having kidney disease. At this point, which we will call year 0, she has stage 2 kidney disease. Over the following four years her GFR continues to decline and reaches 40 in year 4 meaning she is now at stage 3. If the trend continues we can expect her to reach stage 5 eventually.

On the right is GFR data plotted for another hypothetical 40-year-old woman. Her GFR is relatively flat for two years until she donates a kidney. At her first medical examination after her donation, the lab test show her GFR is 66. We will call this year 0. Her GFR is lower than the 78 level that was used to diagnose the woman in the paragraph above as having stage 2 kidney disease. Should she be concerned? Maybe, maybe not. Let’s see what happens over then next four years. In the case I have illustrated, her annual GFR test results are 76, 83, 88 and  86. These GFR values are still below normal and lower than her pre-nephrectomy values. However, they are trending upward rather than downward. Saying this woman has stage 2 or stage 1 kidney disease doesn’t seem accurate or useful in describing her situation.

This does not mean you can ignore the lab results. However, it means you need to look at the trend as well as the absolute value when evaluating GFR results after a kidney donation.

Note that the same analysis holds true for the kidney transplant recipient as well. Checking to see if GFR is trending upward or downward can play an important role in deciding if the transplant is successful.

Change in GFR for a hypothetical kidney patient (left) and a hypothetical kidney donor (right) both show below normal kidney function, but only the one on the left should be considered kidney disease. Graphics by George Taniwaki

[Update: Added byline. Fixed a numerical error and clarified the CKD level.]

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.]

This is a continuation of yesterday’s blog post on why national kidney exchanges are not reaching their full potential.

In yesterday’s post, we described how a single national kidney exchange would be efficient. By having a large pool of candidates, it will lead to both more matches and faster matches. But we observe some hospitals do not join an exchange. And even hospitals that do join an exchange still perform some or most of their matches in-house. Below are some reasons. Part 3 will outline some solutions.

Hospitals believe they will get more transplants doing swaps in-house

Everybody wants to do what is best for the patients. However, that is hard to know what that is in practice. Hospitals want to do what is best for their own patients, the ones they know and care for. It is difficult for doctors at a single hospital to judge what is collectively best for all the patients in the U.S. One of the problems facing a kidney exchange is that maximizing the number of transplants in the pool may not maximize the number of transplants within a hospital that is a member of the exchange.

Let’s say there are two transplant hospitals A and B. Hospital A has 3 pairs in its pool and can match all 3 of them. Hospital B has 4 pairs and can match 2, for a total of 5 transplants as shown below. Black lines show matches used while orange lines show matches that are not used.

Five transplants when hospitals don’t cooperate. Graphic based on Nat. Bureau Econ. Res.

Now let’s combine the pairs from the two hospitals in an exchange. If we do so, we find we can get a total of 6 transplants as shown in the figure below.

Six transplants when hospitals cooperate. Graphic based on Nat. Bureau Econ. Res.

Hospital B goes from 2 transplants to 4. But notice that Hospital A drops from 3 transplants to 2. The patient in Pair A1 no longer gets a kidney and Hospital A performs one fewer profitable transplant. Hospital B and patients in pair B1 and B2 benefit at the expense of Hospital A and the patient in Pair A1. Thus, Hospital A has an incentive to withhold its pairs from the exchange and perform the swaps in-house.

If every hospital performs all the easy matches in-house, then the exchange will contain fewer pairs. This will make finding matches harder. Even worse, the exchange will only contain hard-to-match pairs, making it even less likely that patients in the exchange will find a match. Hard to match pairs will be patients with O blood type (for more see this Mar 2010 blog post) and patients with high levels of antibodies to human leukocyte antigens (for more see this Feb 2011 blog post.)

Note that most hospitals may not even realize that they are withholding pairs from the exchange. If a patient and donor match (which is likely if the donor is blood type O), the hospital will just proceed with the transplant without even considering entering them into an exchange. By transplanting their easy-to-match O donor pairs directly, they leave the national pools with a surplus of O patients and a shortage of O donors.

Hospitals believe there is less delay doing swaps in-house

Another reason hospitals may prefer to handle swaps in-house is the perceived high administrative cost and delay caused by placing patients in an exchange.

For example, the United Network for Organ Sharing (UNOS is the national organization responsible for the distribution of deceased donor kidneys) has started a pilot program to create a national living donor kidney exchange. It taken over two years to develop a consensus of how to operate the program. Finally, in November of last year it conducted its first match run which found 3 sets of matches. Only one of them was accepted and resulted in 2 transplants. Since then it has not had a single match offer accepted and no further transplants have occurred. (See Jan 2011 blog post for details.)

Hospitals are quickly learning that a majority of offers made by the national exchanges do not lead to a transplant. With a lack of success in a national exchange, hospitals would be negligent to not try to help their patients by conducting matches within their own patient pools or form small regional pools.

Here’s an explanation why I think match offers may not lead to a transplant. Imagine a swap that involves three sets of patients-donor pairs. For each of the three transplants, the surgeon has to approve of the donor. If any one is rejected, then the entire swap fails. Then all transplant pairs require a cross-match test for compatibility. Again, if any one fails or cannot be completed within the required time limit, then the swap fails. Finally, all six surgeries must be scheduled. If any of surgeries cannot be scheduled within the required time windows, then the swap will fail. If each of the 3 step for each of the 3 transplant has a 7% chance of failure, then the cumulative chance of success for a 3-way swap is only about 50 percent (1 – 0.07)^9 = 0.52.

All of the steps above are easier to coordinate if they are conducted within a single hospital. An important key to success for a national exchange is to remind every transplant center how important it is to get the approvals and tests completed in a timely manner and to drive these transplants to completion.

Hospitals believe there are lower medical risks doing swaps in-house

Finally, some hospitals fear that participating in an exchange will expose them to higher risk donors. Each hospital does a very thorough examination of donors prior to accepting them into the transplant program. Accepting a donor that they did not evaluate exposes them to two risks, one real and the other perceived.

Let’s cover the perceived risk first. A surgeon at the transplant hospital probably believes the evaluation of donors done at her hospital is excellent and trusts all members of the transplant team. However, in an exchange, the donor comes from another hospital. The surgeon may not personally know the evaluation team at the donor hospital. She may not be familiar with the evaluation criteria used at that hospital. In fact she may believe that the testing done there may not be  is not as rigorous as its own.

I believe that this concern will be alleviated over time as hospitals become more comfortable with the concept of cross-hospital exchanges. There are only 268 transplant centers in the U.S. and most of them use a very similar criteria when evaluating donors. Even if the hospitals use different criteria for acceptance, the equipment they use are very similar so the test results themselves should be comparable across hospitals.

The real risk is that a patient and her surgeon may be subjected to is that the donor hospital may not be as careful in evaluating a donor in an exchange, knowing that it will not be responsible for the outcome of the transplant. This type of risk is known as moral hazard. It is one of the factors that led to the recent financial crisis. Banks reduced the effort made to ensure mortgages were properly evaluated when they knew they would not be responsible for losses caused by any future loan defaults. This is a real risk and has to be managed. One solution is to make sure a certain percentage of matches made in the national exchange include pairs in the same hospital. This should encourage hospitals to do a good job of evaluating donors, since they won’t know which transplants will remain in-house.

In addition to donor evaluation risk, accepting a kidney from another hospital also entails transportation risk. Performing a transplant completely within a single hospital means that the kidney travels a few feet between the donor and the recipient.

The trauma a kidney undergoes is divided between warm ischemia time (the time it takes from when blood stops flowing to the organ to the time it is packed in ice) and cold ischemia time (the time it takes to transport the chilled organ from donor’s operating room to the recipient’s operating room and reattach it). The warm ischemia time causes the most damage. It will be a few minutes and it won’t differ whether a kidney is recovered within the same hospital as the patient or in a different one. The cold ischemia time for an in-house exchange can be as short as 10 to 15 minutes. However, if the donor operation takes place in New York while the transplant operation is in Los Angeles, the cold ischemia time may be as long as ten hours if there are flight delays.

Some transplant centers will not accept live kidneys that have been transported by air. I believe this is an unnecessary restriction. All transplant centers accept deceased donor kidneys recovered from outside their hospital. These kidneys are often delivered by commercial or charter aircraft, sometimes with cold ischemia times of over 20 hours. (For more on shipping kidneys, see this Dec 2010 blog post and an upcoming blog post.)

The third and final blog post provides ideas to solve these issues.

One of the latest innovations in helping patients with end-stage renal disease (ESRD) find live donors is the kidney swap. A kidney swap starts with a kidney patient who knows a person willing to donate but is not tissue compatible (let’s call them pair 0). If that patient finds another pair in a similar situation (let’s call them pair 1), then there is a chance the two pairs may be able to swap donors to produce a compatible match. If this happens both patients get a transplant and both donors can provide the gift of life, though not to their originally intended recipient (see image below).

An example kidney swap. Graphic by George Taniwaki

It is generally too difficult for patients to find partners for a kidney swap on their own (for a rare counterexample see Globe and Mail Feb 2011). Thus, these swaps are usually facilitated by the hospital where the patients are registered on the transplant waiting list. A transplant nephrologist at that hospital will periodically scan the list of patients with unmatched donors (done by computer nowadays) and see if any pairs potentially match. If any do, a transplant surgeon will review the matches to approve/reject the surgeries, a blood lab will run cross-match tests to ensure the patients’ immune systems will not react to the potential donors’ organs, and a transplant coordinator will schedule the surgeries.

These kidney swaps are a growing source of kidney transplants and now account for over 300 transplants a year in the U.S. (for more details on the rise in kidney swaps, see this Jun 2010 blog post).

However, unless the hospital had a large pool of unmatched pairs (say over 20 pairs), it would be unlikely to find matches for its sensitized patients who require more closely matched kidneys. To find matches for these patients, it needs a bigger pool to choose from. Thus, smaller hospitals began to band together to form kidney exchanges. There are now several such exchanges in the U.S., each vying to become the largest in order to maximize the chance of finding a match and thus minimizing the wait time for participating patients.

Natural monopoly

If size of pool was the only factor that led to more transplants getting done faster, then the exchange with the largest pool, even if it was only slightly larger than the others, would provide more matches and do them faster. Hospitals that were members of other exchanges (or doing swaps in-house), would see the success at this exchange and would switch to it, making the pool even larger, leading to even more matches faster. Eventually, all hospitals would join this one exchange to take advantage of the gains in performance and all the other ones (including the in-house exchanges) would be driven out of the market.

However, we don’t see this. For instance, an article in SFGate  Apr 2011 highlights a 5-way swap that California Pacific Medical Center just completed, its largest single-swap ever. Yet California Pacific also is a member of the largest kidney exchange in the U.S.

A five-way swap. Graphic from SFGate

In a similar vein, I recently attended a seminar held by one of the transplant centers in Seattle. The director of kidney transplant program stated that the center had performed several swaps in the past year, all in-house. They were also working with all the other transplant centers in the northwestern U.S. (4 in Seattle, 1 in Spokane, and 3 in Portland) to form a regional exchange. This would be in addition to the in-house exchanges and national exchanges that all these transplant centers participate in.

These stories highlight the growing interest in kidney exchanges among transplant centers. But they also point to a failure by the national kidney exchanges to meet the needs of their member hospitals.

I believe there are three reasons we see this reluctance by transplant centers to rely on large national kidney exchanges for all their swaps. They are the fear in missing some  transplants, fear of loss of efficiency and control, and fear of medical risks. I will describe each of these in the next blog entry.