Fairness, Efficiency and Flexibility in Organ Allocation for
Kidney Transplantation
Dimitris Bertsimas Vivek F. Farias Nikolaos Trichakis
July 12, 2012
Abstract
We prop ose a scalable, data-driven metho d for designing national policies for the allocation
of deceased donor kidneys to patients on a waiting list, in a fair and efficient way. We focus
on policies that have the same form as the one currently used intheU.S.Inparticular,we
consider policies that are based on a point system, which ranks patients according to s o me
priority criteria, e.g.,waitingtime,medicalurgency,etc.,oracombinationthereof. Rather
than making specific assumptions about fairness principles or priority criteria, our metho d offers
the designer the flexibility to select his desired criteria and fairness constraints from a broad
class of allowable constraints. The metho d then designs a point system that is based on the
selected priority criteria, and a pproximately maximizes medical efficiency, i.e.,lifeyeargains
from transplant, while simultaneously enforcing selected fairness constraints.
Among the several case studies we present employing our method, one case study designs
apointsystemthathasthesameform,usesthesamecriteriaand satisfies the same fairness
constraints as the point system that was recently proposed byU.S.policymakers.Inaddition,
the point system we design delivers an 8% increase in extra life year gains. We evaluate the
performance of all policies under consideration using the same statistical and simulation tools
and data as the U.S. p olicymakers use. Other case studies perform a sensitivity analysis (for
instance, demonstrating that the increase in extra life yeargainsbyrelaxingcertainfairness
constraints can b e as high as 30%), and also pursue the design of policies targeted specifically
at remedying criticisms leveled at the recent point system proposed by U.S. policymakers.
We emphasize that our methodology is not amechanisticreplacementforprofessionalmedical
or ethical judgment but rather serves as a tool to circumvent exhaustive exp erimentation with
point systems given such input.
1. Introduction
Renal or kidney transplantation and maintenance dialysis are the only treatments for end-stage re-
nal disease (ESRD), a terminal disease affecting over 500, 000 people currently in the United States,
see USRDS (2009). Despite being a major surgical procedure, transplan tation is the treatment of
choice for ESRD patients, as a successful transplantation improves their quality of life. In particular,
dialysis treatment requires that the patient visits a dialysis center for at least 12 hours each week,
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Forthcoming in Operations Research
whereas transplantation typically allows the patient to resume r egular life activities. Furthermore,
amultitudeofresearchandclinicalstudieshavestatistically demonstrated that transplantation
also reduces the mortality risk for patients, see Suthan thiran and Strom (1994), Schnuelle et al.
(1998), Port et al. (1993), Ojo et al. (1994). Thus, a kidney transplant is considered by many as a
potentially life-saving gift.
The two sources of kidneys for transplantation are living donors (e.g.,familymembersorfriends
of the patient) and deceased or cadaveric donors. The majority of patients are unsuccessful in finding
living donors, and thus join a pool of patients wa iting for a deceased donor organ. Of course, while
in the living donor case the donation is typically made to a specific patient, in the deceased donor
case an important allocation problem arises. In particular,onceanorganisprocuredfroma
deceased donor, there can be thousands of medically compatible and available recipients the organ
can be allocated to. The problem becomes even more significant, if one accounts for the organ
shortage and the size of the pool of waiting patients in the United States: On October 20th 2010,
86, 391 patients were waiting for a kidney transplant. In 2009, there were 33, 671 new additions, but
only 16, 829 transplantations were performed, from which 10, 442 transplan ts were from deceased
donors. For more information and statistical details we refer the reader to UNOS (2010).
In recognition of the aforementioned allocation problem andthegrowingdifficultyofmatching
supply and demand, the U.S. Congress p assed the National Organ Transplant Act (NOTA) in 1984.
According to this legislation, deceased donor organs are viewed as national resources in the U.S.,
and as such, their allocation has to be based on fair and equitable policies. Moreover, the sale of
organs as well as money transfers of any nature in the acquisition of organs are strictly prohibited.
Instead, the policy for allocating the organs should utilizewaitinglistsandhavetheformofa
priority method.Thatmeansthatpatientsinneedofatransplantregisteronwaiting lists. Then,
once an organ is procured, all medically compatible patien tsarerankedaccordingtosomepriority
rules and the organ is successively offered to them according to their ranking, until it is accepted by
apatient. SubsequenttotheNOTA,theU.S.Congressestablished in 1984 the Organ Procurement
and Transplantation Network (OPTN) in order for it to maintain a national registry for organ
matching and develop allocation policies
Naturally, the aforementioned allocation policies are of central importance and have to accom-
plish ma jor ob jectives in alleviating human suffering, prolonging life and providing nondiscrimina-
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tory, fair and equal access to organs for all patients, independent of their race, age, blood group
or other peculiar physiological c haracteristics. Some of the main challenges in designing a kidney
allocation policy are the following:
• Fairness constraints:Whatdoesfairandequalaccesstoorgansmean?Duetothesubjective
nature of fairness, there is no single fairness criterion that is universally accepted by policy-
makers and academics alike. As such, a great challenge lies inidentifyingtheappropriate
fairness constraints that the allocation outcomes of a policy should ideally satisfy. An exam-
ple of such a constraint could be a lower bound on the percentage of organs allocated to a
particular group of patients – say, requiring that at least 47% of all transplants are received by
recipients of blo od type O. In the absence of such a constraintthesegroupswouldotherwise
be handicapped and not have access to organs because of their physiological characteristics.
AnumberofsuchcriteriahavebeenstudiedbyOPTNpolicymakers, see RFI (2008).
• Efficiency:Asasuccessfultransplantationtypicallyprolongsthelife of a patient, wh ile also
improving his quality of life, the policy needs to ensure thatthenumberofqualityadjusted
life year gains garnered by transplantation activities is ashighaspossible. Thisisalsoin
line with the view of organs as national resources. Again, this objectiv e is of paramount
importance to the current policy design, see OPTNKTC (2008).
• Prioritization criteria:Thepolicyneedstobebasedonmedicallyjustifiedcriteriaand phys-
iological characteristics of patients and organs. However,ethicalrulesdisallowtheuseof
criteria that can be deemed as discriminatory (e.g.,race,gender,etc.).
• Simplicity:Patientsneedtomakeimportantdecisionsabouttheirtreatment options, together
with their physicians. To this end, they need to be able to estimate the probability of receiving
an organ, or at least understand the allocation mechanism. For that reason, the priority
method that is used needs to be simple and easy to communicate.
• Implementation:Supposethatonehasselectedthedesiredfairnessconstraints, prioritization
criteria and a simple priority method. Ho w does he then balance the emphasis put on the
different prioritization criteria, so as to design a policy whose allocation outcomes would
maximize efficiency, while satisfying the fairness constraints?
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All the above challenges were faced by the OPTN policymake rs in 2004, when they initiated
the development of a new national allocation policy that willeventuallyreplacethecurrentone. In
2008, the OPTN released a concrete proposal in a Request for Information publication (RFI (2008))
that is currently under consideration by the U.S. DepartmentofHealthandHumanServices.
In this work, we deal with the implementation challenge in designing a national allocation
policy, while accounting for all the other challenges above.Inparticular,wefocusonperhapsthe
simplest, most common and currently in use pr iority method, namely a point system. We make
the following contributions:
1. We presen t a novel method for designing allocation policies based on poin t systems in a
systematic, d ata-driven way. Our method offers the fl exibility to the policymaker to select
the fairness constraints he desires, as w e ll as the prioritization criteria on which the point
system will be based on. The method then outputs a conforming point system policy that
approximately maximizes medical efficiency, while satisfying the fairness constraints.
2. To validate our method, w e use it to design policies under different scenarios of interest to
policymakers. Under a particular scenario, we design a policy that (a) matches the fairness
constraints of the recently proposed policy by U.S. policymakers, and (b) is based on the
same criteria and simple scoring rule format. Critically though, it achieves an 8% increase in
an ticipated extra life year gains, as demonstrated by numerical simulations, which are based
on the statistical and simulation tools currently in use by U.S. policymakers (see below).
3. We use our method to perform a sensitivity analysis that explores the consequences from
relaxing or introducing fairness constraints – for instance, what is the impact of reducing the
percentage of transplants to patients on dialysis for greater than 15 years by 1%? In the
case of some constraints, relaxations of fairness constraints can result in life year gains on the
order of 30%. As such, we believe this is a valuable tool in the policy design process.
4. We develop a means of designing approximately optimal policies in problems of dynamic
allocation that are massively high dimensional. In particular, these are allocation problems
where the number of “classes” of objects being allocated, andthenumberof“bins”these
objects may be allocated to are themselves intractably large. To the best of our knowledge,
this approach is novel.
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Performance in all our numerical studies is evaluated using the same statistical and simulation tools,
as w ell as data, as the U.S. policymakers use. Those tools and datasets were obtained directly from
their developers, namely the United Network for Organ Sharing (UNOS), which is the non-profit
organization that operates the OPTN, and the Scientific Registry of Transplant Recipients (SRTR).
1.1. Literature Review
The mod el-based analysis of the organ allocation p rocess hasattractedsignificantinterestinthe
academic literature. One of the first papers in this vein is by Ruth et al. (1985), in which the
authors develop a simulation model to study the problem. Shechter et al. (2005) also introduce
adiscreteeventsimulationmodelfortheevaluationofpotential changes to the liver allocation
process. In this work, we utilize the simulation model developed by the SRTR, see KPSAM (2008).
The organ allocation process was also analyzed by Righter (1989) and Da vid and Yechiali (1995)
via a stochastic assignment problem formulation. In their work, they analyze st ylized models that
fit into that framework. In this work, we also utilize an assignment problem formulation, but only
for the training p h ase of our methodology: the output allocation policies of our framew ork are
rather simple, based on scoring rules and in full compliance with policies that U.S. policymakers
consider, unlike the above referenced w ork. In a similar vein, Zenios et al. (2000) introduce a fluid
mo d el approximation of the organ allocation process that allows them to explicitly account for
fairness and medical efficiency in the allocation. Our framework accounts for fairness in accordance
with the considerations of policymakers. Zenios (2002), Roth et al. (2004), Segev et al. (2005) and
Ashlagi et al. (2011) study the problem of living donation andtheallocationofkidneys. Kongetal.
(2010), Sandikc i et al. (2008) and Akan et al. (2011) also tac kle the problem of liver allocation.
Another stream of research focuses on the decision-making behavior of patients, by dealing with
organ acceptance policies. David and Yechiali (1985) model the candidate’s problem as an opti-
mal stopping problem. Similar acceptance policies are developed by Ahn and Hornberger (1996),
Howard (2002), Alagoz (2004) and Alagoz et al. (2007). The present paper will test policies on a
simu lator developed by SRTR for OPTN; this simulator assumesaspecific,exogenousacceptance
mo d el for patients built from historical data. While the acceptance model ignores endogeneity, it
allows us to simulate outcomes in precisely the manner policymakerscurrentlydo.
Recent work by Su and Zenios (2005, 2004) attempts to combine the abo ve streams of research
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