23rd Annual
Society for Health Systems Conference and Expo
Student Competition Submission Form
The Peabody Orlando
February 17 – 19, 2011
Atlanta, Georgia
SECTION 1: Student Information
First Name: Murat
Last Name: Kurt
Title: PhD Candidate
School: University of Pittsburgh, Department of Industrial Engineering
Address: 3700 O’Hara Street, 1048 Benedum Hall
City: Pittsburgh
State: PA
Zip: 15261
Email Address: muk7@pitt.edu
Telephone: 412-296 0661
Fax: 412-624 9831
Website: www.pitt.edu/~muk7
SECTION 2: Presenter Biography: Murat Kurt, MS, is a PhD candidate in Industrial Engineering Department at the
University of Pittsburgh. His main research interest is decision making under uncertainty with a primary focus on
applied stochastic dynamic optimization to carefully calibrated healthcare problems. His dissertation research
concentrates on the timing of paired kidney exchanges under patient autonomy. In addition to his dissertation
research, he also has active interests in applying dynamic decision models to the optimal treatment planning of Type 2
diabetes and optimal maintenance and replacement of stochastically deteriorating systems.
SECTION 3: Presentation Proposal: Optimizing the Timing of Paired Kidney Exchanges under Patient Autonomy
(Please see the next page for the abstract)
ABSTRACT
Optimizing the Timing of Paired Kidney Exchanges under Patient Autonomy
End-stage renal disease (ESRD), the ninth-leading cause of death in the U.S., typically occurs when the kidneys have less than 10
% of their normal functionality. There are two viable treatment alternatives for ESRD patients: Dialysis and transplantation. Although
dialysis is the most common therapy for ESRD patients, transplantation is the preferred choice of treatment, as it provides improved
long-term survival rates and a higher quality of life, but the demand for kidneys for transplantation far exceeds the supply. Paired
kidney exchange (PKE), a cross-exchange of organs among incompatible patient-donor pairs, is an emerging clinical modality to
alleviate the shortage in the supply of kidneys. PKEs have grown rapidly over the last two decades and it has been estimated that
they can reduce the waiting time for transplantation as well as the length of dialytic therapy by leading to 3,000 more kidney
exchanges per year. In a PKE, all exchange surgeries occur simultaneously so that no donor may renege after his/her intended
recipient receives a kidney.
While potential kidney exchanges have been formulated as finding matchings in a graph there has not been any consideration of
the timing of transplantation and the effects of disease severity on patients' decisions. As current practice in PKE aims to maximize
only the number of transplants in an exchange pool ignoring disease severity, the underlying edge weights are simply modeled, and
the question of determining proper edge weights remain unclear.
Due to insufficient supply of kidneys for transplantation, most ESRD patients undergo transplantation after a variable period of
dialysis. In contrast, as a more cost-effective strategy, preemptive living-donor renal transplantation is carried out before the
initiation of dialysis. It provides better long-term survival rates than the conventional post-dialysis transplantation and a better quality
of life by avoiding the morbidities and complications associated with dialysis, but despite such advantages, the timing and welfare
consequences of preemptive kidney transplantation have not been explored within the context of PKEs.
This paper concentrates on the timing of PKEs under patient autonomy and intersects with three methodological disciplines: Game
theory, Markov decision processes (MDP) and integer programming. We develop a clinically realistic game-theoretic dynamic
decision model to analyze the patients' transplant timing decisions in prearranged PKEs, and address open policy questions by
investigating the influence of the severity of ESRD on matching pairs with incompatible donors.
We consider an arbitrarily sized group of matched incompatible patient-donor pairs for whom the only feasible exchange of kidneys
is a cyclic exchange (see the figure below for a depiction of a cyclic N-way exchange). We assume the patients are self-interested
and have dynamically evolving uncertain health statuses. As transplantation surgeries take place simultaneously in a typical PKE so
that no donor may renege after his/ her intended recipient receives the organ, we model the patients' transplant timing decisions as
a noncooperative non-zero-sum stochastic game in which each patient aims to maximize his/her own life expectancy.
An illustration of a cyclic N-way kidney exchange. Donor i (Di) is only compatible with Patient i+1 (P i+1) for i=1,2,…,N-1
and Donor N (DN) is only compatible with Patient 1 (P1).
We conduct a competitive equilibrium analysis for the PKE game. As stationary strategies can address dynamic interactions by
constraining each patient to choose his/her actions in a time-independent and state-contingent manner, and are more consistent
with rationality of the patients and clinical practice, we restrict our analyses to stationary strategies. Specifically, we identify
necessary and sufficient conditions for a profile of the patients' stationary strategies to be a Nash equilibrium for the PKE game. As
pure strategies have a more intuitive appeal to patients and physicians for clinical practice, we refine these conditions to
characterize pure equilibria of this game. As different equilibria may imply different payoff outcomes, due to vast multiplicity of
equilibria that the PKE game can admit, a complete characterization of such equilibria is computationally prohibitive. As such, we
consider equilibrium selection within the class of stationary strategies and as a compromise between the patient autonomy and
social welfare we investigate a socially efficient stationary equilibrium. In particular, given the society's wish is to maximize the sum
of the patients’ quality-adjusted life expectancies, we motivate the welfare-maximizing equilibrium selection question: Which
stationary equilibrium maximizes the sum of the patients' quality-adjusted life expectancies in the PKE game? For non-zero-sum
discounted stochastic games there is no systematic of selecting the best stationary equilibrium with respect to a given optimality
criteria. Therefore, from an algorithmic point of view our goal of characterizing welfare-maximizing stationary equilibria requires a
deeper exploration of the model structure and an elaborate technique for an optimization over the space of stationary equilibria. To
this end, we explore key structural properties of the stationary equilibria of the PKE game and exploit them to construct a family of
mixed-integer linear programming (MIP) models to choose among stationary equilibria.
We illustrate our model using a large clinical data set. Our experiments empirically confirm that randomized strategies do not yield a
significant social welfare gain over pure strategies. We quantify the social welfare loss due to patient autonomy and demonstrate
that matching patients at similar stages of disease provides more preferable outcomes in terms of the social welfare gained by
matching patients based on their life expectancies and the social welfare lost by patient autonomy. We also highlight that
maximizing the number of transplants may be socially undesirable.