A proposed new system for assigning kidneys to patients waiting for transplants would reduce the median waiting time for transplantation from approximately 24 to 14 months and improve equity for African-Americans and women, according to the author of a study published in a journal of the Institute for Operations Research and the Management Sciences (INFORMS®).
The proposal, an alternative to the system currently employed by the United Network of Organ Sharing (UNOS), would also increase the overall likelihood of transplantation from 45% to 61% and increase quality-adjusted life expectancy from 32.7 months to 33.9 months.
"We developed a mathematical model that describes the dynamics of the patient group with renal disease and superimposes a system that maximizes length and quality of life," explains Prof. Lawrence M. Wein of MIT, a co-author. "The model also minimizes inequity in waiting time and inequity in the likelihood of transplantation.
"Our model leads us to propose a new policy that assigns priorities using a mixture of efficiency points and equity points that are similar to the one used by UNOS. But we add a larger set of historical information about the patient and donor characteristics and their relationship to chance of a successful transplant. We also add points to reduce disparities between different groups." Using the proposed operations research system, when a new cadaveric kidney becomes available, a statistical model computes a health benefits score for each patient. This score takes into consideration both the patient and organ characteristics used by UNOS, as well as newly added factors that include prior transplants, body size, gender, and race. The health benefits score is higher for those patients that are most likely to gain maximum benefit from the organ. The score is then adjusted so that patients who repeatedly score low on the health benefits scale can gain equal access to transplantation.
The study, "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," is by Dr. Stefanos A. Zenios, Assistant Professor of Operations, Information, and Technology, Graduate School of Business, Stanford University; Dr. Glenn M. Chertow, Assistant Professor of Medicine, University of California San Francisco; and Dr. Wein, Professor of Management, Sloan School of Management, MIT. It appears in the July/August issue of Operations Research, an INFORMS publication. Professor Wein is editor of Operations Research.
A companion to this article, entitled "Evidence-Based Organ Allocation," appeared last year in The American Journal of Medicine.
Demographics Work Against African Americans & Women
The study considers transplant of cadaveric kidneys, which are kidneys taken from accident fatalities and others who died with kidneys suitable for transplantation. Currently, there is a shortage of cadaveric kidneys for transplant.
The UNOS system currently used gives each candidate a place on the waiting list based on a system that assigns points based on several factors. These include medical compatibility between potential donor and recipient, length of time waiting on the list, and rank in the waiting list. It also assigns extra points to children based on age.
The UNOS method of matching tissue types of donors and recipients has been the subject of heated debate for the better part of a decade, in large part because it generates inequities.
Examining the local transplant agencies coordinated by UNOS, the researchers found that African Americans have longer waiting times until transplantation because they have lower mortality rates as dialysis patients, they have a blood type mismatch with Caucasians coupled with a higher demand-to-supply ratio than Caucasians, and they score high rates of panel reactive antibodies, known as pra. A high pra rate shows a likelihood that the recipient will reject the donated organ.
Under the current system, African-American are nevertheless more likely to receive a transplant than Caucasians because they are younger and have lower mortality rates while waiting for an available organ transplant. This higher likelihood of transplantation allows African-Americans to experience greater quality and length of life than Caucasians, with an important caveat: African Americans have higher graft failure rates and higher mortality rates as transplant recipients.
Females are less likely to receive a transplant than males because, like African Americans, they have higher pra levels and lower mortality rates on the waiting list. Despite being less likely to receive a transplant, the low mortality rates for female dialysis patients and transplant recipients allow them to experience greater quality and length of life than men.
A contrast comes when examining the impact of age. Dialysis patients over 50 have higher mortality rates than younger patients and hence experience shorter waits until transplantation. Nevertheless, they have a much smaller likelihood of transplantation. This smaller likelihood of transplantation, coupled with the higher mortality rates on the waiting list and with functioning grafts, causes patients over 50 to experience lesser quality and length of life than patients under 50.
A New Balance of Equity and Efficiency
The authors of the current study sought to determine the organ allocation algorithm that does the best job of balancing equity and medical efficiency without discriminating against groups of patients.
In their analysis, the authors use an operations research technique known as the Monte Carlo simulation model - a gaming model - and other math models associated with operations research.
The authors examined factors such as gender, race, age, tissue type, prior transplants, blood type, and time of entry onto the waiting line. They also looked at patient and donor arrival dates, the distributions for the patient and donor characteristics, the pre-transplantation and post-transplantation mortality rates, the graft failure rates, and quality of life scores.
They compared four alternate ways of assigning kidneys: (1) a first come first served system, (2) the UNOS algorithm currently in use, (3) an efficiency-based algorithm whose goal is to improve life expectancy, and (4) a distributive efficiency algorithm meant to foster greater equity in the way that kidneys are assigned to African-Americans, women, and other candidates.
For each policy and scenario considered, a ten-year simulation was generated for the local Organ Procurement Organization (OPO) being studied. UNOS coordinates the activities of 72 OPO's in distinct geographical regions around the country.
The authors constructed the large-scale simulation model using data from over 30,000 transplants. The data used for the analysis was extracted from the UNOS Public-Use Data Set, published in 1995.
The Institute for Operations Research and the Management Sciences (INFORMS®) is an international scientific society with 12,000 members, including Nobel Prize laureates, dedicated to applying scientific methods to help improve decision-making, management, and operations. Members of INFORMS work in business, government, and academia. They are represented in fields as diverse as airlines, health care, law enforcement, the military, the stock market, and telecommunications. The INFORMS website is at http://www.informs.org .
Journal
Operations Research