Table Of ContentOPTIMAL POLICIES FOR THE ACCEPTANCE OF
LIVING- AND CADAVERIC-DONOR LIVERS
by
Oguzhan Alagoz
MS in Industrial Engineering, Middle East Technical University,
2000
Submitted to the Graduate Faculty of
the Department of Industrial Engineering in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Pittsburgh
2004
UNIVERSITY OF PITTSBURGH
DEPARTMENT OF INDUSTRIAL ENGINEERING
This dissertation was presented
by
Oguzhan Alagoz
It was defended on
July 12, 2004
and approved by
Andrew J. Schaefer, Assistant Professor, Department of Industrial Engineering
Matthew Bailey, Assistant Professor, Department of Industrial Engineering
Cindy L. Bryce, Assistant Professor, School of Medicine
Lisa M. Maillart, Assistant Professor, Weatherhead School of Management
Mainak Mazumdar, Professor, Department of Industrial Engineering
Mark S. Roberts, Associate Professor, School of Medicine
Dissertation Director: Andrew J. Schaefer, Assistant Professor, Department of Industrial
Engineering
ii
OPTIMAL POLICIES FOR THE ACCEPTANCE OF LIVING- AND
CADAVERIC-DONOR LIVERS
Oguzhan Alagoz, PhD
University of Pittsburgh, 2004
This dissertation considers the problem of optimally timing liver transplantation to maximize
patient life expectancy. Transplantation is the only viable therapy for end-stage liver diseases
(ESLD) such as hepatitis B. In the US, patients with ELD are placed on an organ waiting
list when they need a transplant. When organs become available they are offered to the
patients on this waiting list. This dissertation focuses on the decision problem faced by
these patients: which offer to accept and which to refuse? This decision depends on two
major components: the patient’s current and future health, as well as the current and future
prospect for organs. A recent analysis of liver transplant data indicates that 60% of all livers
offered to patients for transplantation are rejected.
This problem is formulated as a discrete-time Markov decision process (MDP). This study
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describes three different MDP models, each representing different approaches for modeling
the organ acceptance question. The Living-Donor-Only Model considers the problem of
optimal timing of living-donor liver transplantation, which is accomplished by removing an
entire lobe of a live donor’s liver and implanting it into the recipient. In this model, the
waiting list has no effect on the decision process.
The Cadaveric-Donor-Only Model considers the problem of accepting/refusing a cadav-
eric liver offer when the patient is on the waiting list and has no available living donor. In
this model, the effect of the waiting list is incorporated into the decision model implicitly
through the probability of being offered a liver.
The Living and Cadaveric Donor Model is the most general model, which combines the
first two models. That is, the patient is both listed on the waiting list and has an available
living donor. The patient can accept a cadaveric liver offer, decline the cadaveric liver offer
and use the living-donor liver, or can decline both and continue to wait. This is the most
realistic problem faced by patients who have an available living donor.
This dissertation derives the structural properties of all three models, including several
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sets of conditions that ensure the existence of intuitive structured policies such as control-
limit policies. This dissertation solves all three models using real data. The computational
experiments show that the optimal policy is typically of control-limit type.
Keywords: Control-limit policy, Markov decision processes, medical decision making, organ
transplantation, service operations.
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To my wonderful parents, Zeliha and Ilhami Alagoz
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ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to my advisor and mentor, Professor Andrew
Schaefer for directing this study and supporting me through my PhD education. He has
always been available for me. Many thanks to him for his generous support, advice, flexibility,
inspiration and motivation.
My sincere thanks and appreciation go to my committee member, Professor Lisa Maillart
for her help in conducting this research and preparing this manuscript. Her technical and
editorial advice were essential to the completion of this dissertation. I really enjoyed working
with her throughout this study.
I would also like to thank my committee member, Professor Mark Roberts for his valuable
comments and enthusiasm throughout this study. I am also indebted to the rest of the mem-
bers of my dissertation committee, Matthew Bailey, Cindy Bryce and Mainak Mazumdar for
their valuable suggestions and insights. I am grateful to my former advisors Professor Meral
Azizoglu and Professor Bryan Norman for encouraging me to pursue an academic career.
I am also grateful to my friends in the Computational Optimization Lab who mentally
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supported me throughout my study. Among them, special thanks to Nan Kong, Jennifer
Kreke and Steven Shecthter, for their valuable insights and comments about my research.
Thanks to my undergraduate helpers Danielle Williams and Laura Henderson for their help
in preparing this manuscript. Thanks also to my colleagues in the Industrial Engineering
Department, Ozlem Arisoy, Halil Bayrak, Mehmet Can Demirci, Salil Desai, Emre Eser,
Mehmet Gokhan, Gorkem Saka and Zhouyan Wang for their friendship. Thanks also to my
long-time friends Hakan Yildiz, Kemal Akkaya and Hakan Ferhatosmanoglu for their moral
support throughout my PhD education.
I thank the wonderful staff of the Industrial Engineering Department, Lisa Bopp, Richard
Brown, Minerva Hubbard and Jim Segneff, for providing technical support throughout my
study.
Lastly, I am forever indebted to my wonderful parents Zeliha and Ilhami, to my dear
sister Bilgehan and to my dear brother Mehmet Sezgin. I would have never finished this
dissertation without their endless love, encouragement and unconditional support.
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TABLE OF CONTENTS
1.0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Current Liver Allocation System . . . . . . . . . . . . . . . . . . . . . . . 15
2.0 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 Markov Decision Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 MDP Applications in Medical Decision Making . . . . . . . . . . . . . . . 34
2.3 Previous Simulation Models on Liver Allocation System . . . . . . . . . . 38
2.4 Previous Research on the Optimal Use of Organs . . . . . . . . . . . . . . 41
3.0 PROBLEM FORMULATION . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.0 DATA SOURCES AND SUPPLEMENTARY MODELS . . . . . . . . 59
4.1 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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4.2 Natural History Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2 A Simulation Model to Predict the Progression of ESLD . . . . . . 70
4.2.3 Computational Tests . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.4 Conclusions and Limitations . . . . . . . . . . . . . . . . . . . . . 87
4.3 Post-transplant Survival Model . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4 Computation of the Organ Refusal Rates and Arrival Probabilities . . . . 91
5.0 LIVING-DONOR-ONLY MODEL . . . . . . . . . . . . . . . . . . . . . . 96
5.1 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3 Computational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.1 Estimating Parameters . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.2 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.0 CADAVERIC-DONOR-ONLY MODEL . . . . . . . . . . . . . . . . . . . 138
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