Resource Allocation Models in Healthcare Decision Making

199 Pages·2017·1.78 MB·English

by  Abdelhalim Hiassat

Resource Allocation Models in
Healthcare Decision Making
by
Abdelhalim Hiassat
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Doctor of Philosophy
in
Management Sciences
Waterloo, Ontario, Canada, 2017
(cid:13)c Abdelhalim Hiassat 2017
Examining Committee Membership
The following served on the Examining Committee for this thesis. The decision of the
Examining Committee is by majority vote.
External Examiner MEHMET A. BEGEN
Associate Professor
Co-Supervisor F. SAFA ERENAY
Assistant Professor
Co-Supervisor OSMAN Y. OZALTIN
Assistant Professor
Internal Member JAMES H. BOOKBINDER
Professor
Internal Member QI-MING HE
Professor
Internal-external Member ALI ELKAMEL
Professor
ii
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis,
including any required final revisions, as accepted by my examiners.
I understand that my thesis may be made electronically available to the public.
iii
Abstract
We present models for allocating limited healthcare resources efficiently among target
populations in order to maximize society’s welfare and/or minimize the expected costs. In
general, this thesis is composed of two major parts.
Firstly, we formulate a novel uncapacitated fixed-charge location problem which con-
siders the preferences of customers and the reliability of facilities simultaneously. A central
planner selects facility locations from a set of candidate sites to minimize the total cost of
opening facilities and providing service. Each customer has a strict preference order over a
subset of the candidate sites, and uses her most preferred available facility. If that facility
fails due to a disruptive event, the customer attends her next preferred available facility.
This model bridges the gap between the location models that consider the preferences of
customers and the ones that consider the reliability of facilities. It applies to many health-
care settings, such as preventive care clinics, senior centers, and disaster response centers.
In such situations, patient (or customer) preferences vary significantly. Therefore, there
could be a large number of subgroups within the population depending on their preferences
of potential facility sites. In practice, solving problems with large numbers of population
subgroups is very important to increase granularity when considering diverse preferences
of several different customer types. We develop a Lagrangian branch-and-bound algorithm
and a branch-and-cut algorithm. We also propose valid inequalities to tighten the LP
relaxation of the model. Our numerical experiments show that the proposed solution al-
gorithms are efficient, and can be applied to problems with extremely large numbers of
customers.
Secondly, we study the allocation of colorectal cancer (CRC) screening resources among
individualsinapopulation. CRCcanbeearly-detected, andevenprevented, byundergoing
periodic cancer screenings via colonoscopy. Current guidelines are based on existing med-
ical evidence, and do not explicitly consider (i) all possible alternative screening policies,
and (ii) the effect of limited capacity of colonoscopy screening on the economic feasibility of
the screening program. We consider the problem of allocating limited colonoscopy capacity
for CRC screening and surveillance to a population composed of patients of different risk
groups based on risk factors including age, CRC history, etc. We develop a mixed inte-
iv
ger program that maximizes the quality-adjusted life years for a given patient population
considering the population’s demographics, CRC progression dynamics, and relevant con-
straints on the system capacity and the screening program effectiveness. We show that the
current guidelines are not always optimal. In general, when screening capacity is high, the
optimal screening programs recommend higher screening rates than the current guidelines,
and the optimal screening policies change with age and gender. This shows the significance
of incorporating screening capacity into the decisions of optimal screening policies.
v
Acknowledgements
Firstly,Iwouldliketoexpressmyimmensegratitudetomytwoco-supervisors. Dr.Fatih
SafaErenayhasbeenmybiggestsupportandsourceofmotivation. Hisvastknowledgeand
high intelligence are surpassed only by his kindness and courtesy. Dr. Erenay’s door was
always open whenever I had a question or needed help. While I wish him better students
in the future, I certainly could not have imagined having a better supervisor for my doc-
toral studies. Dr. Osman Ozaltin has been my model scholar for his exceptional knowledge
and unparalleled robustness. His clear vision and humbling questions have significantly
improved this thesis. Despite being away for the better part of my studies, he always made
himself available for my never-ending questions. Both supervisors valued learning, and
allowed me to make mistakes. For that, I am ever grateful.
The members of the Examining Committee have improved this thesis and made it more
organized and easier to read through their comments and suggestions. I am grateful for
their time and effort spent in reading the manuscript, and for showing up for an exam in
August.
The courses I have taken (or audited) at the University of Waterloo have been instru-
mental in my development and in shaping this thesis. I would like to thank the instructors
of these courses for making hard concepts easy to understand and introducing me to new
topics and ideas: Hossein Abouee Mehrizi, Steve Drekic, Samir Elhedhli, Bon Koo, Osman
Ozaltin, Frank Safayeni, Anindya Sen, Levent Tuncel.
I also would like to thank my group-mates who helped in challenging my ideas and gen-
erating new ones. The long and frequent talks with Mustafa, Najmaddin, Bahar, Gizem,
Onur, Tagi, and Burak have sharpened my understanding and enhanced my knowledge.
I am thankful for the joyful times and the anxiety about future plans our meetings have
brought. I had enjoyed a practically private office on campus thanks to my amazing office-
mate, Ata. When he was around, which was not too often, he was constantly considerate
and understanding.
I had the opportunity to be an instructor and a teaching assistant for a number of
courses during my studies. I was inspired by my students every time I was in class. I
vi
have learned a lot about myself and about the subjects that I was teaching. Thanks to
all of my students, instructors, and teaching assistants that I worked with for making
my job interesting and possible. Thanks to Dr. Samir Elhedhli for nominating me to be
an instructor, which has both slowed my research progress and significantly enriched my
experience.
I am grateful for the support of the staff of the Department of Management Sciences
at the University of Waterloo. A special thanks to Wendy Fleming, Lisa Hendel, Shelley
Vossen, and Kathy Tytko for all the administrative help throughout the years.
My friends in Waterloo made my life slightly less boring. Tarek has made my first days
less scary. Thanks to my roommates Selva, Arty, and Burak for being so neat and clean
that I did not want to try my luck a fourth time. Thanks to Gizem and Onur for the
delicious food and car rides. Thanks to Ibrahim and Tagi for organizing football games.
Also, thanks to Khaled for being a food and cooking partner, a FIFA opponent, and an
immigration advisor. I also want to thank my friends in Jordan, UAE, USA, and elsewhere
for staying in touch despite the long distance and torturous time zones.
Last but definitely not least, thanks to my family for keeping me sane and teaching
me everyday what unconditional love is. Being away from them is always the hardest
challenge. I would have never been here without their support and unlimited belief in me.
A man cannot wish for more.
vii
Dedication
She always kept chocolate in her room. My brothers realized she would always give if I
were the one asking. I always feared the time she wouldn’t.
For the trick that never failed... to my mother.
He rarely expressed his feelings. It was that extra tight hug when I was back home from
the airport that told everything. It was an untold secret.
For the promise still kept hours before his passing... to my late father.
viii
Table of Contents
List of Tables xiii
List of Figures xvi
List of Abbreviations xvii
List of Symbols xix
1 Introduction 1
1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Resource Allocation Models in Healthcare . . . . . . . . . . . . . . . . . . 4
1.2.1 Facility Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Cancer Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Target Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Connection of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
ix
2 Reliable Facility Location Model with Customer Preference 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 Review of Related Literature . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Preliminary Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.3 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Solution Techniques: Preliminary Model . . . . . . . . . . . . . . . . . . . 28
2.4 Computational Results and Analyses: Preliminary Model . . . . . . . . . . 34
2.4.1 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.2 Basic Analysis: CB-LBB . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.3 Stack Queue Tree: Stack-LBB . . . . . . . . . . . . . . . . . . . . . 46
2.4.4 Priority Queue Tree: PQ-LBB . . . . . . . . . . . . . . . . . . . . . 52
2.5 Modified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.6 Solution Techniques: Modified Model . . . . . . . . . . . . . . . . . . . . . 66
2.6.1 Tighter LP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.6.2 Lagrangian Branch-and-Bound Algorithm . . . . . . . . . . . . . . 68
2.6.3 Branch-and-Cut Algorithm . . . . . . . . . . . . . . . . . . . . . . . 73
2.7 Computational Results and Analyses: Modified Model . . . . . . . . . . . 76
2.8 Applications on Healthcare . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.8.1 Cancer Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.8.2 Senior Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.8.3 Emergency Response . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
x