Optimization-driven framework to understand healthcare networks cost and resource allocation

152 Pages·2016·13.08 MB·English

Cost and Resource Allocation
in Healthcare Delivery Systems
by
Maria Fernanda Bravo Plaza
Submitted to the Sloan School of Management
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Management
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted
Author ......
Sloan School of Management
August 1, 2015
Signature redacted
Certified by....
Retsef Levi
I I
J. Spencer Standish (1945) Prof. of Management, Sloan School of
Management
Thesis Supervisor
Signature redacted
A ccep ted by ...........................................................
Catherine Tucker
M TITUTE YDirector, Ph.D. Program, Sloan School of Management
JAN 2 6 2016
LIBRARIES
2
Cost and Resource Allocation
in Healthcare Delivery Systems
by
Maria Fernanda Bravo Plaza
Submitted to the Sloan School of Management
on August 1, 2015, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Management
Abstract
This thesis studies contemporary challenges arising at the market, system, and orga-
nization levels in the healthcare industry, and develops novel frameworks that allow
us to better understand cost and resource allocation for strategic decision making in
healthcare settings. The U.S. healthcare industry is going through a massive transfor-
mation process due to the increasing industry consolidation, and the implementation
of the recently enacted healthcare reform. These changes have completely transformed
the incentives in the industry, and traditional practices have become outdated, or are,
in general, inadequate to address the new challenges. Our frameworks combine real
data and statistical analysis with novel optimization-driven approaches (e.g., linear
programming, game theory) that capture the first order aspects of the dynamics of the
corresponding markets, systems, and organizations. Overall, this work has relied on
collaboration with industry partners in order to identify trade-offs, validate models,
and pursue practical innovation and implementation of the proposed frameworks.
In the first part, and motivated by real applications from the healthcare industry,
we consider a setting, where one firm provides a service to a second firm that is facing
stochastic demand for the service. The changes in the reimbursement system have
created new opportunities for business-to-business interactions between healthcare
systems and providers. Typical contracts in the healthcare industry are based on a
transaction fee per unit of service that is negotiated between the two parties. Unlike
traditional product-based 2-echelon supply chains, the two firms have opposing risks
with respect to the demand volume. We leverage this insight to design a conceptu-
ally simple two-price volume based contract, and analyze it within a game theoretic
setting. We show that a two-price contract can optimally ensure risk sharing. More-
over, although the resulting problem is non-convex, we are able to characterize the
unique equilibrium contract in closed form for a family of utility functions that cap-
tures firms' different risk behaviors, and general demand distributions. Moreover, at
equilibrium the new contract has two desirable properties: (1) it allows for better risk
reduction (measured by CVaR) for the two firms, and (2) it reduces the uncertainty
of the payment transaction.
3
In the second part, we study the strategic cost and resource allocation in large
healthcare delivery networks and how these networks can, efficiently, integrate their
operations in order to attain network's welfare objectives. Strategic problems, such
as resource allocation, capacity placement, and portfolio of services in multi-site net-
works, require the correct modeling of network costs, network's welfare objectives and
trade-offs, and operational constraints. Traditional practices related to cost account-
ing, specifically, the allocation of overhead and labor cost to individual activities, as a
way to account for the consumption of resources, are not suitable for addressing these
challenges. These practices often confound resource allocation and network building
capacity decisions. In this part, we develop a general methodological optimization-
driven framework inspired by network revenue management models, specifically linear
programming optimization, that allows us to better understand network costs and pro-
vide strategic solutions to the aforementioned problems. We report the application
of this framework on a real case study to demonstrate its applicability and important
insights derived from it.
Finally, in the third part of this thesis, we study the nature and sources of vari-
ability in surgical activities in a large pediatric hospital. We use machine learning
techniques to quantitatively show that surgery time variability is high among pedi-
atric cases and, against common belief, this is poorly explained by surgeon effect
or other commonly considered characteristics. Our studies suggest that pediatric
surgery time has higher inherent variability making pediatric ORs necessarily more
costly and harder to schedule than adult ORs. They must therefore be sourced
accordingly. These findings are novel and will be useful in the management of busy
pediatric operating theaters. For administrators and policymakers, it provides a basis
for understanding some of the added costs inherent in caring for children.
Thesis Supervisor: Retsef Levi
Title: J. Spencer Standish (1945) Prof. of Management, Sloan School of Management
4
Acknowledgments
Foremost, I would like to thank my advisor Retsef Levi for all the support and guid-
ance he provided me along my Ph.D. journey. During all these years, Retsef has
been insightful and encouraging not only academically, but also personally. He al-
ways believed in me, and inspired me to overcome my fears and challenges along the
way. In addition, Retsef has also been a great professional model. I really admire
his principles in the classroom and his high ethical standards, which I would like to
uphold as I move forward in my academic career. I am so grateful of having him as
my advisor.
I would also like to thank Vivek Farias, and Georgia Perakis for serving as part
of my thesis committee, and for supporting me in my goal of becoming a professor.
I collaborated with Vivek in Chapter 3 of this thesis, and I also was the teaching
assistant for his OM class. I really enjoyed these experiences, and learned a lot by
observing his performance in the classroom. Georgia has not only been a co-author
of the work in Chapter 2 of this thesis, but also a mentor. She has been caring
to a personal level beyond her role as the chair of the OM area, and provided me
thoughtful advice anytime I needed. In addition, I would like to thank the faculty at
Sloan Itai Ashlagi, and Karen Zheng for their advice and support in the completion
of this journey.
Another mentor I would like to thank is Dr. Mike McManus (from Boston Chil-
dren's Hospital). Mike has been an incredible collaborator and the source of invaluable
practical knowledge. He is a co-author of the work included in Chapter 4 of this the-
sis, and it has been a delightful experience to work with him. I am really grateful
for his support, and for enriching my understanding of the healthcare delivery in the
U.S. - I have learned so much through him!
I have been very lucky to encounter remarkable collaborators - Gonzalo Romero
and Marcus Braun (LGO) - during my time at MIT. Gonzalo is an insightful re-
searcher and I really enjoyed working with him in the project described in Chapter
2. Marcus and I worked together in the project described in Chapter 3. He is an
excellent professional, always very approachable, and really helpful.
To the Ph.D. program coordinators Hillary Ross and Sarah Massey - thank you
for making the Ph.D. years smooth and socially friendly. I really appreciated all
those remainders, and certainly enjoyed every single activity you organized for us. I
would also like to thank Ariel Brandner for her assistance; she has provided me help
far beyond her responsibilities. Thanks to all of you for making things happen in a
timely and flawless way.
This journey would not have been the same without the wonderful friends I made
along the way. My ORC friends Andre Calmon, Maxime Cohen, David Fagnan,
Paul Grigas, Swati Gupta, Vishal Gupta, Nathan Kallus, John Kessler, Will Ma,
Velibor Misic, Allison O'Hair, Yaron Shaposhnik, Joline Uichanco, Phebe Vayanos,
and Nataly Youssef. Your friendship has made these years the most memorable
time of my student life. Special thanks to Angie King, and Kris Johnson for their
endless support. Thank you girls for traveling this journey (and all the other journeys
5
we actually did!) with me, and thank you for being the closest to a family for
me here in the U.S. I would also like to give special thanks to Adam Elmachtoub
whose friendship has been invaluable to me. I think this thesis would not have
been written if it was not for his encouragement and support - Thank you Adam
for believing in me, and for making me believe in myself. To my office mates (and
office neighbors): Florin Ciocan, Gonzalo Romero, Yiwei Chen, Leon Valdes, Jason
Acimovic, Guillaume Saint-Jacques, and Cecilia Zenteno, thank you for your support
and innumerable advices along the way. The short (and long) breaks, and the random
conversations and laughs made days in the office much more fun. Special thanks to
Cecilia for the gym/zumba/pilates breaks! To my Chilean friends Charlie Thraves,
Francisco Unda, Leon, Mey, and Gaston, thank you for reminding me of our roots,
language, and silly humor. I would also like to thank my wonderful roommates Rashi
Gupta and Allison. Thank you girls for keeping up with me, and for the amazing
time we shared together!
Friends and relatives from Chile who have been really supportive throughout the
years: Ita, Kathy, Panchi, Javiera, Ines, and Vero. Thank you for your love and for
keeping me as part of your life despite the distance. In particular, I would like to
thank my aunt Piedad, who left our family in the middle of my Ph.D. journey, for
her unconditional love and care - you are always in my thoughts.
Last but certainly not least, I would like to thank my family - Patricia Plaza
(mom), Eduardo Bravo (dad), Sebastian Bravo (brother), Matias Bravo (brother),
and Georgios Mallas (fiance) - for their unconditional love, and infinite support. I
would definitely not be concluding this journey without them. Georgios has been an
incredible partner, supportive, caring, and understanding from the very first day. His
every day love and support has been essential for the successful completion of my
Ph.D., and for been able to pursue my next goal of becoming a professor - thank you
for encouraging and helping me in these challenging times, and for making every day
a special one. My brothers have been my companions in life and, as the youngest
sister; I have always looked up to them. Matias' free spirit and Sebastian's reasoning
character made a perfect personality mix! - Thank you guys! My most profound
gratitude is for my parents. I have no words to describe how grateful I am for all
the effort that they put to educate me and my brothers. They taught me from the
very beginning the importance of education, and have supported me in every goal I
have endeavored, even when this implied to be far away from them - thank you for
your love and inspiration, the person who I am today, and my achievements, are all
because of you.
Fernanda Bravo
6
Contents
1 Introduction 15
1.1 Market level: A risk-sharing pricing contract in B2B service-based sup-
ply ch ains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2 System level: Optimization-driven framework to understand health-
care networks cost and resource allocation . . . . . . . . . . . . . . . 19
1.3 Organization level: The nature and sources of variability in pediatric
surgical case duration . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1
2 Risk-Sharing Pricing Contract in B2B Service Supply Chains: An
Application to Healthcare 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Model framework, and assumptions . . . . . . . . . . . . . . . 25
2.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Modeling approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1 Pricing contracts . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2 Valuation of an alternative new contract . . . . . . . . . . . . 35
2.2.3 Financial constraints: acceptable levels of risk . . . . . . . . . 38
2.3 Characterization of the new contract . . . . . . . . . . . . . . . . . . 40
2.3.1 B2B dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.2 Service Provider's problem . . . . . . . . . . . . . . . . . . . . 41
2.3.3 Service Requester's problem . . . . . . . . . . . . . . . . . . . 47
2.3.4 Statistical properties of the equilibrium new contract . . . . . 50
7
2.4 Equilibrium numerical analysis . . . . . . . . . . . . . . . . . . . . . 51
2.4.1 Influence of the SP's loss aversion and reservation utility in the
equilibrium contract . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.2 Influence of the SR's rate of loss aversion and demand at risk
in the equilibrium contract . . . . . . . . . . . . . . . . . . . . 55
2.5 C onclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5.1 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3 Optimization-Driven Framework to Understand Healthcare Networks
Cost and Resource Allocation 61
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.1 Our framework . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Current cost accounting and resource allocation practices . . . . . . . 66
3.3 G eneral mo del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 Elements of the model . . . . . . . . . . . . . . . . . . . . . . 72
3.3.2 Mathematical formulation . . . . . .. . . . . . . . .. . . 76
3.3.3 Alternative applications of our framework . . . . . . . . . . . 79
3.4 C ase study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.1 Data collection and estimation of model parameters . . . . . . 82
3.4.2 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5 C onclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4 The Nature and Sources of Variability in Pediatrics Surgical Case
Duration 95
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 M ethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 Data description and current prediction method . . . . . . . . 97
4.2.2 Analysis 1: Case time variability and performance of the stan-
dard m ethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8
4.2.3 Analysis 2: Prediction of surgery duration based on commonly
used factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.1 Analysis 1: Case time variability and performance of the stan-
dard m ethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.2 Analysis 2: Prediction of surgery duration based on commonly
used factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.1 Lim itations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5 Concluding Remarks 107
A Proofs Chapter 2 109
A.1 Proof of Lemma 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 Proof of Lemma 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A.3 Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 114
A.4 Proof of Corollary 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.5 Proof of Theorem 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 117
A.6 Proof of Corollary 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.7 Proof of Theorem 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B Additional Material Chapter 3 127
B.1 Data description and estimation of parameters . . . . . . . . . . . . . 127
C Figures and Tables Chapter 4 139
9
10