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An agent-based model to study accountable care organizations

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An agent-based model to study accountable care organizations

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AN AGENT-BASED MODEL TO
STUDY ACCOUNTABLE CARE
ORGANIZATIONS

BY

PAI LIU

A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE
DOCTOR OF PHILOSOPHY
IN
INDUSTRIAL AND SYSTEMS ENGINEERING

May 2013

II

Acknowledgements
Pursuing a PhD is a journey and I owe my gratitude to all the people who helped me
through this great experience and supported me to the destination.

My deepest gratitude is to my advisor, Dr. Shinyi Wu. I am always feeling very fortunate
to have such a great advisor and valuable friend. She always encourages me to find my
best interest and provides me constructive and critical thinking. She is extremely patient
and supportive that helped me overcome many frustrating situations during my five years
at graduate school.

I am also grateful to my dissertation committee members: Dr. Carl Kesselman, Dr. Mike
Nichol, Dr. Alex Chen, and Dr. Azad Madni who have provided me great insight,
constructive criticisms, and supports for my dissertation.

Finally, I want to dedicate my special gratitude to my fiancé e for her constant love and
supports, to my parents for their many years’ love, care and education.

III

Abstract
Creating Accountable Care Organizations (ACOs) has been widely discussed as a
strategy to control rapidly rising healthcare costs and improve the quality of care;
however, little is known about how to build an ACO that can achieve these goals.
Implementation of an ACO is costly in terms of time and money and could cause safety
hazards because of immature design. Therefore, there is an urgent need for analytic
capacity and decision-support tools that can quickly evaluate different ACO models and
predict future outcomes to facilitate the ACO design and implementation process.

Industrial and Systems Engineering (ISE) methods have been used for system modeling
and optimization for years. However, traditional ISE approaches are facing challenges in
modeling the important features of an ACO which is composed of multiple interacting
stakeholders including payers, providers, and patients who are working to maximize their
own interests.

To meet the analytic demands of an ACO and address the modeling challenges, we first
developed an analytic framework to guide the analysis and modeling of an ACO. We then
demonstrated the framework through constructing an Agent-based simulation model to
study the ACO under the Shared Saving payment model for Congestive Heart Failure
IV

(CHF) care. The goal of the Agent-based simulation model is not to substitute an ACO
pilot program but to provide analytic supports for decision makers to make informed
decisions.

The Agent-based simulation model has identified the critical determinants for the
payment model design that can motive provider behavior changes to achieve maximal
financial and quality outcomes of an ACO. In particular, for the Shared Saving payment
model, the simulation model can determine the variable optimal shared saving rate as
well as the distribution of the shared savings to hospitals and primary care physicians
based on an ACO’s financial or quality targets. The results have shown the non-linear
provider behavior change patterns responding to the changes in payment model. The
model also has provided insight on how providers with different priorities respond
differently to a certain payment model, which indicates the payer may need to expand its
strategies to motivate all types of providers. The sensitivity analysis has shown that the
model outputs are most sensitive to the cost-effectiveness of the interventions that an
ACO implements to improve the outcomes.

This research contributes to healthcare service and policy research by providing an
analytical method that can help decision makers better understand the complexity and
V

risks of the design and implementation of an ACO and facilitate more informed decision
making. It contributes to the ISE community by addressing the modeling challenges to
better model a complex system and achieve a higher impact.

VI

Table of Contents
1. Introduction ................................................................................................................. 1
2. Literature Review........................................................................................................ 7
2.1. Opportunities for Costs Reduction and Quality Improvement............................. 7
2.2. ACO Model Design .............................................................................................. 9
2.2.1. Organizational Structure ............................................................................. 10
2.2.2. Payment Model ............................................................................................11
2.2.3. Measurement System .................................................................................. 15
2.3. Agent-based Model ............................................................................................ 17
2.3.1. Modeling Technique Comparison ............................................................... 18
2.3.2. ABM Application ........................................................................................ 21
2.4. CHF Care............................................................................................................ 22
3. Analytic Framework ................................................................................................. 25
3.1. Framework Overview ......................................................................................... 25
3.2. CHF ACO Model ............................................................................................... 27
3.2.1. Organizational Structure ............................................................................. 28
VII

3.2.2. Payment Model ........................................................................................... 31
3.2.3. Measurement System .................................................................................. 32
3.3. Model Structure and Agent Overview ................................................................ 32
4. CHF Model and Agents Specification ...................................................................... 35
4.1. Patient Agent ...................................................................................................... 35
4.1.1. Generation of Simulated Patient Agent Population .................................... 35
4.1.2. Patient Agent State Transition Module ....................................................... 38
4.2. Provider Agent.................................................................................................... 50
4.2.1. The effects of the intervention .................................................................... 52
4.2.2. Provider Agent Decision Making Module .................................................. 54
4.3. Payer agent ......................................................................................................... 63
4.4. Healthcare cost ................................................................................................... 65
4.5. Model Implementation and Simulation Setting ................................................. 70
5. Simulation Result ...................................................................................................... 73
5.1. Baseline Model ................................................................................................... 74
5.2. Model Verification and Validation ..................................................................... 75
VIII

5.3. Scenario Analysis ............................................................................................... 78
5.4. Sensitivity Analysis ............................................................................................ 84
6. Discussion and Future Direction ............................................................................... 86
7. Conclusion ................................................................................................................ 94
8. References ................................................................................................................. 97

IX

List of Figures
Figure 1 Analytic Framework ........................................................................................... 25
Figure 2 Agent-based Model Structure ............................................................................. 33
Figure 3 Patient Agent Transition Model .......................................................................... 39
Figure 4 Patient Agent Model Overview .......................................................................... 41
Figure 5 the Theory of Planned Behavior ......................................................................... 56
Figure 6 Model Runtime Dashboard Screen Shot ............................................................ 73
Figure 7 Shared saving to the payer by shared saving rate ............................................... 80
Figure 8 CHF related hospitalization by shared saving rate ............................................. 81
Figure 9 Mortality rate by shared saving rate ................................................................... 81
Figure 10 SSP by SRH with the shared saving rate = 0.1 ................................................. 82
Figure 11 SSP by SRH with shared saving rate from 0.5-0.8 ........................................... 83
Figure 12 SSP by SRH with the shared saving rate = 0.9 ................................................. 84
Figure 13 Sensitivity analysis ........................................................................................... 85
Figure 14 Effects of provider type .................................................................................... 89

X

List of Tables
Table 1 Patient Agent Characteristics ............................................................................... 38
Table 2 CHF incidence rate by age ................................................................................... 43
Table 3 Risk coefficient for CHF incidence rate ............................................................... 44
Table 4 Data input for CHF survival curve ....................................................................... 45
Table 5 Age adjusted coefficients for CHF mortality ....................................................... 46
Table 6 Age adjusted coefficients for Non CHF mortality ............................................... 47
Table 7 Transition probability from the CHF diagnosed state to the CHF related
hospitalization ................................................................................................................... 48
Table 8 Diabetes incidence rate by race ............................................................................ 49
Table 9 Hypertension incidence rate by age and race ....................................................... 50
Table 10 Intervention Effect Factor .................................................................................. 53
Table 11 Healthcare Cost .................................................................................................. 70
1

1. Introduction
The healthcare costs in the United States have been rising rapidly for years. The total
healthcare expenditures reached $2.5 trillion in 2009, accounting for 17.9% of the
nation’s Gross Domestic Product (GDP) [1]. The rapid growth of healthcare costs has
placed increasing burdens on government finance and the whole country’s economy, and
controlling the rising costs has been a focus of current health reform. On the other side,
the quality of healthcare is far from optimal. According to the Agency for Healthcare
Research and Quality(AHRQ) National Healthcare Quality Report 2010, there are still
high rates of medical errors and low rates of delivering preventive care services [2].

One significant contributing factor to the high costs and low quality of care is the
fragmented healthcare delivery system where patients receive care from different
providers who then bill the payers individually under current Fee-for-Service payment
system, and no individual or organization holds accountability for the overall costs and
quality. Current health system lacks mechanisms and incentives for providers to provide
coordinated care, improve the quality and control the cost [3]. Therefore, the idea of
Accountable Care Organization (ACO) which is a group of providers who accept greater
accountability for the total costs and quality of care merged [4, 5]. Although the ACO has
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been outlined in the Patient Protection and Affordable Care Act enacted in 2010 [6] and
there have been growing nationwide discussions and supports for it, relatively little is
known about specifically how to design and implement an ACO, and how an ACO would
actually achieve its envisioned goals—curbing the rising healthcare costs and improving
the quality of care.

In 2011, the Centers for Medicare and Medicaid Services (CMS) published the final rule
of its Medicare Shared Savings Program which will implement ACOs with the Shared
Saving payment model [7]. Some private insurers also just launched or will launch their
ACO implementations in the near future [8]; however, there are large variations among
the CMS’s and other ACO models in terms of their designs of organizational structure,
participating providers, payment models, targeting conditions and patient population.
These ACO design parameters define an ACO model and need to be configured before
the ACO implementation.

For example, to design a payment model for an ACO, current popular payment model
frameworks include the Shared Saving model, Bundled (or Episode-based) payment, and
Risk-adjusted Capitation (or Comprehensive Payment) model. Once a payment
framework is chosen, there are many parameters and functions under it that need to be
3

configured. Taking the CMS shared saving program as example, the decision makers
need to specify how to calculate the saving, what portion of the saving will be shared to
providers, and how to distribute the shared saving among different providers who have
involved in the care process, etc..

Combining these ACO design parameters could reach hundreds of possible ACO models
to implement. On the other hand, an ACO implementation usually can only implement
one or very limited number of models at a time, and the implementation process is very
costly in terms of financial costs and time. Because little is known about how to design
an ACO model to achieve the desirable outcomes given a specific provider and patient
population environment that a payer is facing, the ACO model design becomes a very
complex and risky decision making process. Therefore, there is an urgent need for
analytic capacity and decision-support tool that can quickly screen and evaluate different
ACO models, optimize the ACO design parameters given specific goals and environment,
and predict future outcomes under different scenarios to facilitate the design and
implementation of an ACO model.

Industrial and System Engineering (ISE) has the potential to provide analytic solutions to
address this need. However, traditional ISE methodologies usually are not applicable to
4

model two important features of an ACO implementation: first, an ACO consists of
multiple, independent agents such as patients, providers, and payers working
independently to optimize their position; second, there are dynamic interactions and
communications among the agents in an ACO that can influence agent behaviors and
system outcomes. These modeling challenges are also highlighted in the AHRQ report for
critical areas of ISE research in healthcare [9] which calls for methodologies that can
incorporate different objectives and behaviors of multiple interacting stakeholders into
the model and make optimal recommendations for the overall system.

To address the need of analytic capacity for ACO implementation and the modeling
challenges, we first developed an analytic framework that layouts the model structure,
key stakeholders and components to be considered to model an ACO implementation.
Then, we demonstrated the framework through constructing an Agent-based simulation
model to study ACOs with a Shared Saving payment model aiming to deliver coordinated
high quality care to Medicare patients with Congestive Heart Failure (CHF). CHF is
selected over other diseases because it is the leading cause for hospitalization and high
healthcare costs for the elders [10]. Moreover, many studies have showed that the
outcomes of CHF care can be improved through implementation of evidence-based care
[11, 12]. The ACO is expected to create incentives and mechanisms to facilitate the
5

adoption and implementation of the evidence-based care.

The basic idea of the Shared Saving payment model is that providers are still paid under
the traditional FFS model, but if they can manage the total healthcare costs under a target
level, a portion of the difference between the target level and the actual costs, the saving,
will be shared to the providers. We chose the Shared Saving payment model over other
candidates in our model because first it is the payment model used in many current and
planned ACO implementations including the CMS Medicare Shared Savings Program;
Secondly, connected with the FFS model, the Shared Saving model serves as an
important bridge for the transition from the FFS model to more fundamental risk-sharing
payment models.

The CHF Agent-based simulation model we developed enables decision makers to test
different scenarios to understand the complexity and risks involved in the design of the
ACO and the Shared Saving payment model. Our model includes multiple interacting
self-interest agents to simulate behaviors of the key stakeholders in an ACO. We used the
model to answer the following questions as an illustration of the capability of the model:
1. How to set the key parameters in the Shared Saving model to maximize the utility of
the payer? The key parameters include the percentage of saving that will be shared to the
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providers (the shared saving rate) and the distribution of the shared saving among
different types of providers involved in the CHF care. 2. How providers’ diverse
individual preference can influence the outcomes of a certain payment model?

The goal of the Agent-based simulation model is not to substitute an ACO pilot program
but to facilitate the ACO design and implementation process by providing analytic
supports for the decision makers to make informed decisions on how to design an ACO
and the corresponding Shared Saving payment model to maximize the desirable
outcomes.

Chapter 2 is the literature review of the ACO, the method of Agent-based model, and the
evidence-based care for CHF. In chapter 3, we will present the analytic framework that
can guide the modeling and analysis of ACO implementation. In chapter 4, we will
introduce our CHF Agent-based simulation model to study ACO models with the Shared
Saving payment model for CHF care. In chapter 5, we will present the simulation results
with scenario analysis and sensitivity analysis. At last, we will discuss our findings and
future directions in chapter 6 and conclude in chapter 7.
7

2. Literature Review
This literature review chapter includes four parts. First, we will explore the opportunities
for costs reduction and quality improvement which are the motives for the creation of an
ACO. Then we will discuss in more details about the ACO design parameters. Thirdly,
we will review the methodology of Agent-based modeling and compare it with other
system modeling techniques. Finally, we will review the evidence-based are for CHF.

2.1. Opportunities for Costs Reduction and Quality Improvement
Before the idea of ACO, the Health Maintenance Organization (HMO) was proposed and
widely implemented to curb the rising healthcare costs. However, the concerns for the
traditional HMO model include that it may reduce or delay necessary care and put too
much restrictions on patients’ choice of providers. Because of these concerns, HMO now
becomes less popular and is replaced in many places by the less restricted Preferred
Provider Organization (PPO). However, the PPO usually lacks incentives for providers to
control costs and it also restricts patient’s choice by discouraging patients from seeking
care out of the network. On the other hand, there are many opportunities in current health
system for costs reduction and quality improvement without rationing healthcare services.
For example, many preventable events, such as avoidable hospital readmission and
8

duplicate tests, are due to the fragmentation of the healthcare system. We have listed
some widely discussed opportunities for improvement:
 Emphasis on primary care with focuses on prevention and monitoring could
lead to early diagnosis and treatment. The case management program can
provide continuous education and support for patients who have chronic
diseases [13].
 Comprehensive discharge planning and post-discharge follow-up provided by
multidisciplinary teams including a combination of clinic follow up, telephone
monitoring, and home visit can effectively reduce the chance of readmission
[11].
 Improving the efficiency of care delivery through wastes reduction. For
example, scheduling and operation improvement can reduce hospital operating
rooms turnover time [12].
 Reducing the duplicate tests, unnecessary referrals to specialists and drug
overuse through better care coordination and information sharing.
 Switching to more cost-effective treatments and medications based on
comparative effectiveness research and evidence-based guidelines. For example,
it is more cost-effective for some traditional inpatient treatments to be
conducted at outpatient facilities. The use of generic drugs can also bring down
9

the medication cost.
 Implementation of Health Information Technology (HIT) has the potential to
improve operational efficiency, reduce medical errors, provide shared data
support for better decision making and improve provider communication [14].
 Reducing adverse events in Hospital such as hospital-acquired infection and
complications could reduce readmission, length of stay and the overall inpatient
costs [15].

However, current healthcare delivery system and payment model generally lack
mechanisms and incentives for providers to take these opportunities [16]. Therefore, the
ACO aims to create the mechanisms and incentives to motive providers to pursuit these
opportunities and hold more accountability for the healthcare costs and quality. The key
challenges are how to design and implement the ACO model to achieve these goals.

2.2. ACO Model Design
In this section, we will discuss in more details about considerations faced by decision
makers when design an ACO model, what the key ACO design parameters are and what
options are available for each parameter. We categorized the ACO design parameters into
three sets: organizational structure, payment model, and measurement system.
10

2.2.1. Organizational Structure
There is little evidence to show what kind of organizational structure, such as what type
of providers should be included and how they are organized, could lead to a more
successful ACO implementation. Elliot Fisher et al. [4] proposed to create an ACO based
on the existing virtual care delivery pattern comprising hospitals and physicians who
refer their patients to the hospitals. On the other side, one report [17] argued that ACO
initially should be primary care focused, and hospitals and specialists are not necessary
parts. Current ACO demonstrations mainly build on existing provider organizations such
as the Independent physician Association (IPA), multispecialty group, Physician–Hospital
Organizations (PHO), Integrated Health System or a combination of them [8]. Starting
from existing organizations is reasonable as these organizations already have developed
some capability of managing care for the patient population they are serving. Some of
them may already have the experiences of coordinated care and are equipped with
infrastructures an ACO needs such as HIT.

However, these existing organizations are significant different in terms of their structure,
ownership, scales and patient population served. Therefore, it is hard to find an absolute
answer about which organizational structure would have higher chance to achieve
desirable outcomes for an ACO. The point is that the outcomes of an ACO do not just
11

depend on one set of ACO design parameters but all the ACO design parameters as well
as the providers and patient population involved.

2.2.2. Payment Model
The second important set of ACO design parameters is the payment model. To better
explain the design of a payment model and its relationship with providers’ accountability,
we need to discuss two types of risks: the performance risks and insurance risks. As
discussed in [17], performance risks emerge under the circumstances that providers didn’t
treat patients in appropriate ways. For example, a high cost inpatient treatment occurs due
to a hospital-acquired infection. Insurance risks emerge under the circumstances such that
patients get older or have pre-existing conditions which are not controlled by providers.

As have been well discussed, the traditional Fee-for-Service (FFS) payment is accused of
encouraging the quantity not the quality of care. Under the FFS model, the more
preventive care and higher quality of care a provider delivers, the less revenue he/she
may receive. The traditional FFS is a big barrier to let providers take more accountability
for costs and quality of care as they bear neither the performance risks nor the insurance
risks under FFS. On the contrary, the traditional capitation payment model gives
12

providers incentives to avoid sick patients and to reduce services that could be necessary,
which is the consequences of letting providers take both the insurance risks and the
performance risks. Miller et al [17] argued that the ACO payment model should be
designed as risk-sharing that providers only take the performance risks while insurers
bear the insurance risks. Currently, many risk-sharing payment models have been
proposed to target this problem. The mostly discussed ones are the Shared Saving,
Bundled Payment, and Risk-adjusted Capitation. We will discuss these three types of
payment model next.

The Shared Saving is a payment model that providers in an ACO are still paid under the
FFS model, but if they can manage the total healthcare costs under a predefined target
level, a portion of the difference between the target level and the actual costs, the saving,
will be shared to the providers. To design a Shared Saving model, the payer and the
providers need to answer questions like: how to calculate the saving, what percentage of
the saving can be shared to the providers and how to distribute the shared saving among
providers. The target level should be risk adjusted and can be negotiated by comparing
with providers’ previous cost data or the costs of a comparable group of providers and
patient populations.

13

The advantages of the Shared Saving model are that it provides incentives for providers
to controlled overall costs and it is relatively easier to design and implement. The
problems of the Shared Saving model include the shared saving may or may not cover
providers’ investment in improving the quality and efficiency. In addition, if the saving is
determined by comparing providers’ performance with their previous records, it may
punish current high performers as there is less space for them to further improve. Given
these problems, the Shared Saving model is still a good choice of payment model to start
an ACO for its simplicity in design and implementation, and it can serve as a transitional
option for an ACO to develop more fundamental risk-sharing payment model.

Another key payment model drawing national attentions is the Bundled Payment, or
Episode-based payment. The basic idea of the Bundled Payment is using one single
budget for all the services provided by different providers within an episode of care.
Currently, there is no absolute answer on how to define an episode which could vary by
conditions and procedures. It is also one of the biggest challenges for the design of a
Bundled payment. The CMS has proposed four bundled payment models with different
episode definitions [18]. For example, the CMS model 1 has bundled all the costs
occurred during a patient’s acute hospital stay and the CMS model 2 includes the costs
generated from both the acute care hospital stay and the post-acute care associated with
14

the stay.

Another example is Geisinger Health System's ProvenCare payment. For some selected
surgeries, it defined a single bundled payment including the services fees of surgeons and
other providers, the inpatient stay, and 90 days of follow-up care [19]. Prometheus
Payment Inc. has built a severity-adjust model to estimate and adjust the cost of an
episode based on the patient’s condition and risk factors [20]. It matches the idea that
providers should only be required to take performance risks. The Bundled Payment, by
its nature, gives all the providers involved in an episode of care incentives to coordinate,
controlled costs and improve quality of care. The problems with the Bundled Payment
include that first it gives no incentive for providers to prevent an episode happening at the
first time. Second, it is more difficult and vague to define an episode for chronic diseases
than acute ones. The bundled payment is more complicated and harder than the Shared
Saving payment in terms of design and implementation.

The last risk-sharing payment model we will discuss is the Risk-adjust Capitation, or
called Comprehensive Payment or Globe Payment. It can be seen as an extension of the
bundled payment to all conditions and longer period of time. The key difference between
the Risk-adjust Capitation and traditional capitation payment model is the payment is
15

adjusted by patients’ risk factors in order to take the insurance risks from providers.
However, due to its complexity, it requires an ACO to have higher capability and larger
scales to be able to handle the uncertainty and risks.

Beyond these payment models, the payer and the ACO could negotiate the payment
model in a more flexible way. ACO could be paid under a combination of previous
payment models or their variants. For example, the payer could pay the outpatient
services using Risk-adjusted Capitation while pay the inpatient services by FFS or
Bundled Payment. The payer could also reward the ACO extra bonuses for achieving
certain criteria such as improvements on certain quality or efficiency measures.

2.2.3. Measurement System
The third category of an ACO design is its Measurement System. As the saying “You
cannot improve the things you cannot measure”, a comprehensive, meaningful and
practical Measure System is necessary for the success of an ACO. The Measure System
can continuously check the progress of the ACO to its design goals, determine and adjust
the payment model, provide evaluation and feedback to the providers’ performance and
inform the decision makers. ACO could take advantage of current existing measures sets
16

and customize them into their measure system or it can also develop its own measures
based on its special needs. Examples of current measures sets include Core Measures, a
set of hospital process measures developed by Joint Commission and Centers for
Medicare and Medicaid Services (CMS); the Healthcare Effectiveness Data and
Information Set (HEDIS), a broad performance measure set on important dimensions
such as effectiveness of Care, Access/Availability of Care, Utilization, etc..

Generally, an ACO needs at least two categories of measures: the quality measures and
efficiency (cost) measures associated with its goals of improving quality and controlling
costs. The quality measures can include the process of care measures like the CMS Core
Measures, outcomes measures such as hospital-acquired infection rate, and Preventive
care measures. Examples of Efficiency measures include the number of avoidable ER
visits, percentage of genetic drug use, total health care costs for the patient population,
etc.. Measure system itself is not enough. An ACO also needs the capability of collecting,
distributing and reporting the data which can be facilitated by good collaboration between
ACO and insures and the infrastructure such as Health Information Technology (HIT).
Furthermore, different ACOs could vary the way they manage and report these measures
depends on their goals.

17

In sum, ACO is a provider organization designated to take the accountability of
performance risks to controlled the growth of healthcare costs and improve the quality of
care. To design an ACO demonstration, one needs to define its model parameters:
organizational structure, payment model, measure system and management methods.
Now we will give an introduction to our Agent-based model approach that is used to
model the ACO demonstration.

2.3. Agent-based Model
The ACO and its environment can been seen as a complex system which is composed of
a large number of interacting agents (e.g. providers, patients). The aggregated behaviors
of these agents are not intuitive from the individual agent behaviors and the relationships
between the model input and output are usually nonlinear. Hence, it requires the
nonlinear and out-of equilibrium approach. Computer simulation emerges as such kind of
mathematical model that can estimate the performance of a system that is too complex to
have analytical solutions.

Computer simulation has been increasingly used in healthcare from the process redesign
of Emergency Department to the public health problems. It abstracts the real healthcare
events and procedures including decision making, care delivery, health condition changes
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into mathematical model, and can systematically synthesize discrete evidences such as
clinic trials, cost-effectiveness analyses, and public health statistics to gain insights that
sometimes are not intuitive.

2.3.1. Modeling Technique Comparison
Generally, there are three system modeling approaches that are mainly used to model and
analyze a complex system: Agent-based model (ABM), System Dynamic (SD) and
Discrete Event Simulation (DES).

System Dynamic, developed in 1950s, models the complex system in term of stock and
flows between them. The stocks represent the entity which can accumulate or deplete
over time such as the diabetes patients in a community or the mortality rate of a hospital.
The flow is the change rate of stocks. The connecting stocks and flows form a number of
feedback loops to capture the interaction of different components and factors in the
system. The System Dynamic model can also be represented in a set of differentiated
equations. Compared with ABM, the entity in the stock is indistinguishable and passive,
following the same globe rules defined by the differentiated equations.

19

The Discrete Event Simulation, developed in 1960s, is a powerful tool to model the
stochastic real-world processes which can be represented in the flowchart format. The
entity representing a patient or document etc. goes through the blocks in the flowchart
incurring the discrete ‘events’ such as decision making, queuing, and delay. Although
each entity could have its own attributes, they are still passive objects following the globe
rules defined in each block.

Agent-based model (ABM) is a relatively new modeling technique and there is no
universally accepted definition yet. It is basically composed of a number of autonomous
decision-making components called agents, which have their own behavior pattern,
learning capability, and can interact with other agents and the environment. In our case,
the agent can be any entity in a health system, such as a patient, a primary care physician,
a hospital, and an ACO. Unlike SD and DES, in ABM the behavioral and interaction rules
are defined at individual agent level not at globe system level. Instead, the globe behavior
or trend that we are interested in emerges through the thousands and millions of agents
act following their own behavior rules and interact with each other, which are comparable
with what happened in the real world.

Compared the passive entity in the two other modeling approaches, the agent in ABM has
20

two distinguishing features: the heterogeneity and autonomy. It is more accordant with
the providers in an ACO as they have different characteristics and can make decision
based on their own interests.

Although some special problems can be modeled in any of these three modeling
approaches, they do have their own strength depends on the nature of the problem.
System Dynamic suits the problem that the relationship between aggregated variables can
be defined by differentiated equations, and the individual differences are negligible or
only aggregated data is available, while the Discrete Event Simulation is very
straightforward to model the process that can be represented by flowchart. ABM, on the
other hand, has its unique advantage of modeling the interactions between agents. The
improved coordination and collaboration between provides is an essential part and a goal
of the ACO which can be modeled by provider agent interactions. It therefore makes
ABM a more suitable tool for our modeling purpose.

Another favorable feather of ABM is its flexibility and compatibility with the other
modeling techniques. For example, a hospital can be modeled as an individual agent; the
relationships between its financial parameters (e.g. operating costs, marginal profits) and
its investment behaviors (e.g. investing on process improvement initiative, HIT) can be
21

represented by System Dynamics. Another example is a patient can be modeled as an
individual agent; but he/her health status and seeking care pattern can be modeled by the
Discrete Event Simulation or the more general traditional stochastic process model.

Furthermore, as a bottom-up modeling approach is more comparable with the real world,
AMB has the advantages such that it can capture more real world phenomena and easier
to explain to and receive valuable feedbacks from experts who may not be familiar with
modeling and computer simulation (e.g. health care professions or policy maker).
Therefore, ABM is chose as the main modeling framework while System Dynamics and
other modeling techniques could be used within the framework where appropriate.

2.3.2. ABM Application
ABM has been used to model a variety of complex systems in the recent decade. Bing et
al. [21] built an ABM based policy analysis framework to model the emission trade
market and examine the market efficiency under different policy design scenarios. In
their model, the agents (power plants) are free to trade their emission rights and they also
can learn from the experience of previous orders to update their trading strategy.
Anderson et al. [22] constructed an ABM model to study humanitarian assistance policies
22

to aid the refugee communities. They built intelligent agents representing different
government institutions, organizations, individuals, etc. and analyzed the interactions and
behaviors between the agents using Design of Experiment.

Lee et al. [23] used ABM to study the impacts of public health mitigation strategy such as
school closure during an influenza pandemic. Each agent represents an individual
school-aged child or adult. Interactions between infected and healthy agents could cause
influenza transmission with certain possibility. Therefore, the effects of different school
closure strategies (solely isolating the sick student or closing the entire school) could be
tested based on the ABM model. ABM has also been increasingly used to study the
trading strategies, consolidation effects and policy design of the electricity market in
Germany [24-26]. To the author’s best knowledge, ABM has not been applied to study
the development of ACO which is complex given its numerous components and
sophisticated interactions between them.

2.4. CHF Care
Although ideally an ACO should be designed to cover all the diseases conditions for
patients from all the payers, practically it is difficult to achieve this goal in current ACO
demonstrations, because current ACO demonstrations are usually initiated by a single
23

payer (such as Aetna or Blue Cross Blue Shield of Illinois) with a group of providers.
Also, it is reasonable to experiment with some procedures when testing a new payment
model, and then expend to other procedures just like how Geisinger Health System
implemented their bundled payment experiment. For the practical concern of the
modeling, we would model an ACO demonstration specific to one condition as one
purpose of the analytical simulation framework is to demonstrate that it is applicable to
simulate the development of health system and in particular the ACO. So once the model
framework for one condition has been built, it can be applied and extended to other
conditions and even for comprehensive care. As the chronic disease care usually needs
more coordination between providers and care management for the patients than acute
condition, we chose a chronic care condition for our model demonstration specifically the
Congestive Heart Failure (CHF).

CHF affects more than 5.8 million Americans and is one of the leading causes of
hospitalization and readmission, causing an estimated direct and indirect cost of $39.2B
in 2009 [27]. CHF is a leading cause of hospitalization in the United States and study has
shown that, among Medicare beneficiaries, one-fifth of patients were readmitted within
one month and had a longer length of stay at rehospitalization [28]. Multiple
meta-analyses have examined the effect of comprehensive discharge planning plus
24

post-discharge support interventions in randomized trials and showed a combination of
these care elements and procedures could significantly reduce CHF readmissions and
may improve other health outcomes, such as survival rate and quality of life [11, 12].
However, current healthcare system and payment model create many barriers to
implement these evidence-based cares. For example, if providers are paid on FFS model,
reducing readmission will only reduce their revenue. In addition, these interventions need
coordination and collaboration between hospitals, primary care physicians, or homecare
facilities over the care delivery continuum while current fragmented system has little
mechanism and incentives for the providers to collaborate. In other words, the providers
involved in the care processes do not share accountability for the costs and quality
outcomes of patient’s care.

Therefore, ACO aims to eliminate these barriers and create shared accountability between
provides by creating the mechanism and incentives to facilitate the implementation of the
evidence-based care for CHF. However, to accomplish these goals, an ACO needs to be
appropriately designed to create right incentives for provider behavior changes. Our
Agent-based model is used to study the impacts of the design of an ACO and its
associated payment model on provider’s behavior pattern for the evidence-based care,
and the effects on the outcomes of CHF care.
25

3. Analytic Framework
3.1. Framework Overview
In this chapter, we will describe the analytical framework we developed to build our
Agent-based model. This framework can be applied to guide the modeling and analysis of
an ACO model, and even other healthcare policy initiatives. As shown in Figure 1, the
framework defines three input elements for an ACO model: stakeholders, ACO model
design and implementation.

Figure 1 Analytic Framework
The stakeholders are the key participants of an ACO including payers, providers and
patients. Identifying the stakeholders and understanding their objectives and
Time period
Comprehensive
or condition
specific
Other supports
Goals
Improvement
opportunities
Organizational
Structure
Payment Model
Measurement
System
Payers
Providers
Patients
Stakeholder
ACO Model
Design
Implementation
ACO
26

characteristics are the first step to design an ACO. The ACO model design element
includes five components: goals, improvement opportunities, organizational structure,
payment model, and measurement system. The goals component defines the specific
objectives that an ACO intends to accomplish. The improvement opportunities element
defines the best practices such as evidence-based care and other improvement
opportunities discussed in section 2.1 that an ACO intends to implement in order to
achieve its goals.

The organizational structure component defines what type of providers can participate in
the ACO and how they are organized. For example, a Chronic Care Model initiative
usually only involves primary care physicians [13] while a payment reform initiative
usually includes a broader group of providers. The payment model component determines
how providers are paid in an ACO. The payment model should be designed to align the
incentives with desirable providers behaviors. The measurement system component
defines the set of key performance measures for an ACO and the mechanism of data
collection, analysis and reporting. It monitors the progress of an ACO implementation
and provides timely feedbacks to the stakeholders.

The Implementation element defines the implementation configurations such as the time
27

period of an ACO initiative, whether it addresses a specific condition or a full continuum
of care, and what extra supports are available. Examples of extra supports include outside
consultative services, enhanced decision supports, and HIT.

These three input elements are correlated with each other and together define an ACO
model. Now we have introduced the analytic framework we developed. In next section,
we will show how we applied this analytic framework to build and configure our CHF
Agent-based model.

3.2. CHF ACO Model
In this section, we will introduce how we defined our stakeholders, ACO model design
and implementation elements in our CHF Agent-based model by applying the analytic
framework.

First, we should identify the stakeholders in our model. As stated in chapter 2 , We aim to
study the effects of the ACO and its associated payment model on provider behavior
changes, and the impacts on the outcomes of CHF care. As majority of the CHF patients
are the elderly and Medicare eligible, we set Medicare patients with age over 65 as our
target patient population. Hence, we assume that the payer in our model is a single payer,
28

the CMS. For the provider, CHF is a chronic disease and can be managed by a patient’s
PCP. On the other hand, CHF is also the leading cause for hospitalization. Hence, the
hospital and PCP are the two main types of provider for CHF care, and are included as
the stakeholders in our model.

Next, we will discuss our ACO model design. We defined the goals from the payer, the
CMS’s, perspective, which are controlling the costs as well as improving the quality of
care. Sometimes these objectives can be conflicting and the payer may need to choose a
balance point. The improvement opportunities for CHF care have been discussed in
section 2.4. For the rest of the ACO model design parameters, we will discuss the main
design options and what are used in our model.

3.2.1. Organizational Structure
The organizational structure parameter defines what kind of provider should be included
in an ACO and how they are organized. There are diverse types of provider
organizational structures in current health system. We will first introduce the three
representative organizational structures: Independent Providers, Independent Practice
Association (IPA), and Integrated Health System and how they can be modeled using
29

Agent-based modeling. We then will discuss the ACO organizational structure used in our
CHF model.

An ACO with independent provider structure is comprised of multiple independent
providers such as hospital and PCP. Although the PCPs and hospitals may have virtual
connections such as the consistent patient referral pattern identified in Fisher et al.’s study
[4], they don’t have either contractual or ownership relationships. Hence, each provider
entity can be modeled as an independent decision making agent.

An IPA is usually referred to an organization that contracts with independent physicians
to provide healthcare services to managed care or other health plans [29]. With the
capacity and experience of providing full outpatient services to patient population, some
IPAs have the potential to hold more accountability and become an ACO. From the
modeling’s perspective, an IPA can be modeled as an agent network consisting of one IPA
agent and a number of PCP agents who have contractual relationship with the IPA agent.
The IPA agent is the decision maker to decide organizational level strategies and to
negotiate with the payer agent about the payment model. However, as the IPA agent
doesn’t own the PCP agents, a PCP agent can keep its operational autonomy and may
decide to stay or leave the IPA in each contract cycle depending on its own interests.
30

Hospitals are usually not included in an IPA based ACO. A patient will be referred to get
hospital care outside the ACO if inpatient services are needed.

An integrated health system includes both outpatient care and inpatient care facilities and
the providers within it are usually the employees of the integrated health system. An
integrated health system based ACO can be modeled as a provider network with one
integrated system agent and a number of hospital agents and PCP agents which are
owned by the integrated system agent. The integrated system agent is the only decision
maker in the network which will make decisions to maximize the interests of the overall
system. Beyond these three organizational structures discussed above, an ACO could
have mixed organizational structures composed of different types of provider
organizations.

In our Agent-based model, we will model the individual providers based ACO. Because
even there were a couple waves of mergers and consolidations in the healthcare industry,
a large portion of the providers in the US are still practicing independently. In addition, in
an individual providers based ACO, all the agents can make decision to change behaviors
in order to maximize their own interests, which allows us to understand more about the
dynamics of the ACO model design.
31

3.2.2. Payment Model
As discussed in chapter 2, an ACO payment model should be risk-sharing so that
providers take the performance risks and payers take the insurance risks. We have
discussed three risk-sharing models: the Shared Saving, Bundled payment and
Risked-adjust capitation. These three payment models represent three general payment
ideas and there are many variants in implementation.

In our Agent-based model, we will analyze the Shared Saving payment model. It is
important to study the shared saving model because first it is a choice of many current
ACO demonstrations. Secondly, as it builds on the FFS, it can serve as a bridge for the
transition from the traditional FFS model to more fundamental risk-sharing model such as
the bundled payment. Under the shared saving model we defined, the ACO providers will
be paid under the FFS. But if the ACO can manage the cost per CHF patient lower than
that from a comparable provider group serving similar patient population. A portion of
the difference, the saving from the payer’s perspective, will be awarded to provide agents.
The specifics of the shared saving model will be described in chapter 4.

32

3.2.3. Measurement System
The measurement system includes three categories of performance measures: cost
measures, utilization measures and quality measures. The measure system is used to
continuously monitor the performances of ACO, determine the payment and provide
feedbacks for the providers. The providers can have access to these measures on a timely
basis to see their own performances as well as comparing with the performances of other
providers. Examples of the key performance measures tracked in our model include
payment per CHF patient, hospitalization rate, mortality rate, the shared saving, etc..
More details of these measures and how they are used for decision making will be
discussed in chapter 4.

3.3. Model Structure and Agent Overview
As shown in Figure 2, the structure of our Agent-based model is outlined by three layers
of agents based on the stakeholders identified: the payer agent, provider agent, and
patient agent. We also defined two types of provider agent: the hospital agent and primary
care physician (PCP) agent as they are the main providers involved in CHF care. Under
each agent, there are modules each of which represents a set of related functions for the
agent. In the rest of section 3.3, we will discuss the three layers agent model structure and
give an overview of the agents and its modules. The details of the agent specifics will be
33

introduced in chapter 4.

Figure 2 Agent-based Model Structure

As mentioned earlier, the payer agent in our model represents the CMS. In the ACO
Model Design Module, we can set the ACO design parameters as the input for the model.
The operations module of the payer agent includes the functions that support the
implantation of the ACO from the payer side such as collecting and reporting the
performance measures, calculating and distributing shared savings. The payer agent can
interact with the provider agents through the payment model and measurement system.

Payer Agent
ACO Model Design
Module
Provider
Agent
Patient Agent
Decision and Learning
Module
Operations Module
Health Stage Transition
Module
PCP
Hospital
34

The provider agent has two modules: the decision making module and operations module.
Using Artificial Intelligence (AI) techniques and decision making theory, the Decision
Making module can model and simulate the real world decision making and learning
processes, through which an agent can not only makes the decision based on its best
interests given its current knowledge, but also can learn or update its knowledge from its
interactions with the environment and other agents. The operations module of the
provider agent includes the functions that support provider’s daily operations such as
collecting performance data, providing services to patients, and interaction with other
provider agents.

Each individual patient is modeled as a patient agent that can transit between different
health stages and demand for healthcare services. In our model for CHF care, a patient
agent can develop CHF and other conditions, be in different health states, seek care and
receive treatment from different kinds of provider agent. These processes will result in
different health outcomes, the use of health care resources and generate costs, which are
modeled and simulated in the health stage transition module.

35

4. CHF Model and Agents Specification
In the previous chapter, we have described the analytical framework and how we can
apply this framework to analyze and model the ACO with Shared Saving payment model
for CHF care. In this chapter, we will describe our Agent-based simulation model and the
specifications of each agent in more details. Shown in Figure 2, the Agent-based
simulation model includes three types of agents: the payer agent, the provider agent
(including the hospital agent and PCP agent), and the patient agent.

4.1. Patient Agent
4.1.1. Generation of Simulated Patient Agent Population
A patient agent represents one Medicare patient, whose age is 65 or older. Each patient
agent is characterized by seven variables: four demographic variables (age, race, gender,
and income) and three health condition variables (diabetes, hypertension and CHF). We
selected these variables because they are the key factors that have impact on CHF disease
progression and healthcare utilization, providing enough level of detail for the purpose of
this model.

36

We created our patient agent population from the National Health and Nutrition
Examination Survey (NHANES) 1999 to 2010 and we only included patient samples
whose age is 65 or older. Because the variables of a patient agent are correlated, we need
to estimate the joint distribution of these variables. Due to the complexity of the joint
distribution, we estimated it based on a conditional probability model::
P(CHF , Hypertension, Diabetes, Demographics) = P(CHF | Hypertension, Diabetes,
Demographics) *P(Hypertension | Diabetes, Demographics)* P(Diabetes | Demographic)
* P(Demographics)

The reason we used the conditional probability model is that we can examine and utilize
independence relationships between these variables to simplify the calculation. We will
describe in more details by walking through the process of generating a patient agent.
First, we used another variable agegroup to code the age variable by 5-year interval in
accordance with CHF literature. The definition and coding of other variables are the same
as that in NHANES. Correlation test showed that agegroup, gender, and race are not
significantly correlated and income significantly depends on race. So the joint probability
of demographics variables can be simplified as:
P(Demographics) = P(Income| Race) * P(Agegroup) * P(Gender) * P(Race)

37

As for the demographics variables, we conducted ANOVA analysis for each health
condition variable to identify its independency with other variables. Identified
independency was used to simplify the conditional probability model. The results are
shown below:
P(Diabetes | Demographics) = P(Diabetes | Agegroup, Race, Income)
P(Hypertension | Diabetes, Demographics) = P(Hypertension | Diabetes, Race)
P(CHF | Hypertension, Diabetes, Demographics) = P(CHF | Agegroup, Diabetes,
Hypertension)

Then we used the estimated joint distribution to generate our patient agent population.
The distribution of these variables of the generated patient agent population and that of
the NHANES sample are shown in Table 1. We can see that although we made some
simplification during the estimation of the joint distribution, the characteristics of the
generated patient agent population closely match that of the real NHANES population.
More importantly, the correlations between these patient agent variables are preserved by
the conditional probability model, which allows users to create user-defined patient agent
population. For example, if users want to generate a patient agent population with higher
average age than the NHANES population, the other variables correlated to age such as
CHF will also change accordingly.
38

Table 1 Patient Agent Characteristics
Variable Definition Distribution in our
estimation
Distribution in
NHANES
Age group 65-69 .2544 .2544
70-74 .2424 .2424
75-79 .1853 .1853
80-84 .1818 .1801
85+ .1360 .1378
Gender Male .4889 .4889
Female .5111 .5111
Race None Hispanic White .6237 .6237
None Hispanic Black .1557 .1557
Mexican American .1445 .1445
Other .0761 .0761
Income Poor: .1472 .1462
Near Poor: .3005 .3011
Non Poor: .5524 .5527
Diabetes Have diabetes .2065 .2067
No diabetes .7935 .7933
Hypertension Have hypertension .5874 .5847
No hypertension .4126 .4153
CHF Have CHF .0892 .0884
No CHF .9108 .9116

4.1.2. Patient Agent State Transition Module
The patient agent’s CHF disease progression and healthcare resources utilization are
modeled in the patient agent state transition module. The key components of the patient
agent state transition module is shown in Figure 3.
39

Figure 3 Patient Agent Transition Model

A patient agent starts in either the CHF free state or CHF onsite state depending on if it
has CHF when it was generated. In the CHF free state, a patient agent is exposed to the
risk of developing CHF in either outpatient setting (move to the CHF onsite state) or
inpatient setting (move to the CHF related hospitalization state). A patient agent in the
CHF onsite state is at risk of CHF related hospitalization (move to the CHF related
hospitalization state). Patient agents in any of the above states also have possibility of
death (move to the mortality state and will be deleted from the simulation). We defined
the CHF-related hospitalization as the hospitalization that CHF is listed in any of its first
to seventh diagnosis. As this model targets on CHF care, we do not include
CHF onsite
CHF related
hospitalization
CHF Free
Mortality
40

non-CHF-related hospitalizations. In addition, for patient agents who haven’t been
diagnosed with diabetes or hypertension, they are exposed to the risks of developing
diabetes or hypertension. Because CHF, diabetes and hypertension are incurable chronic
diseases, once a patient agent developed any of these diseases, it will have it during the
rest of the simulation.

An overview of the patient agent model is shown in Figure 4. The cycle time for the
patient state transition module is 15 simulation days which allows us to model CHF
hospitalization and disease progression in enough level of details. At each cycle, a patient
agent will move to other states or remain at current state according to state transition
probabilities, which are determined by a patient agent’s own characteristics variables and
are adjusted by if the patient agent receives care from the CHF intervention. The impacts
of these risk factors on the state transition probabilities are derived from literature and
public health surveys and statistics.

41

Figure 4 Patient Agent Model Overview

The current literature of public health study and clinical trial usually reports a relative
risk (RR) for each individual risk factor of a health event (e.g. disease incidence).
Because risk factors are usually correlated, it is difficult to derive the absolute risk of an
health event from the RR of multiple risk factors. To address this problem, we examined
and compared a variety of literature to study the correlative effects of multiple risk
factors. For example, race is a significant indicator for CHF incidence without
considering diabetes and hypertension. But for patients who have developed diabetes or
Patient Characteristics
Age Gender Race
Income Diabetes Hypertension
Influence Transition Probabilities
Patient Health Transition
Healthcare
Utilization
Health
Outcomes
Healthcare
Cost
Provider
Behaviors
Quality
Improvement
Intervention
Determine
42

hypertension, race becomes an insignificant risk factor to predict CHF incidence [30-32].

Based on the examination of literature, we carefully selected a subset of the patient agent
variables as significant risk factors for each state transition. To consider the effects of
other unobservable variables, transition probabilities are further calibrated with published
statistics. The outputs of the patient state transition module are the patient population’s
health outcomes and healthcare utilization. Healthcare utilization will determine
healthcare costs depending on the payment model. Next, we will introduce how we
calculate the state transition probabilities.

CHF Incidence Rate
CHF incidence rate is risk adjusted by patient’s agegroup, diabetes, and hypertension.
Agegroup is the main indicator for CHF incidence. In our model, the incidence rate for
each age group was derived from Curtis et al.[33] and was listed in Table 2. Furthermore,
Patient with diabetes has much higher CHF incidence rate than non-diabetic patient [32].
We therefore model the effect of diabetes by multiplying the overall incidence rate with a
diabetes coefficient
d
c or
nd
c for diabetic and non-diabetes patient respectively.
d
c and
nd
c
can be calculated by the following way:
43

(1 ) 1
d d nd d
d
nd
c p c p
c
RR
c
  


Where RR is the relative risk of diabetes for CHF incidence set as 1.85 [34, 35] and
d
p is
the prevalence of diabetes, which is 20.5% derived from NHANES data. By solving the
equations above, we get 1.58
d
c  0.85
nd
c  . In addition, as the NHANES data shows
the diabetes prevalence is similar among different age groups, we assume that
d
p is
consistent among the agegroups and therefore the values of
d
c ,
nd
c are applicable for all
agegroups.
Table 2 CHF incidence rate by age
Age Agegroup CHF incidence before
calibration
CHF incidence after
calibration
65-69 1 19.3 15.9
70-74 2 22.0 18.1
75-79 3 32.8 27.0
80-84 4 48.4 39.8
85+ 5 80.8 66.5
Overall 29.1
Rate is case per 1000 patient-year

For the effect of hypertension, we used the similar method to calculate the hypertension
coefficients for patient with hypertension and without hypertension. Because diabetes and
hypertension is highly correlated, we calculate the hypertension coefficients for diabetic
and non diabetic patient separately. The RR of hypertension is set as 1.1 [31, 35] for
44

diabetic patient and 1.4 for non diabetic patient [32]. The hypertension prevalence in
diabetic and non diabetic patients are derived from NHANES data. Multiplying the
diabetes and hypertension coefficients, we can get the risk coefficients for CHF incidence
listed in Table 3. In the end, a patient agent’s CHF incidence rate is calculated by
multiplying the incidence rate of its agegroup with a risk coefficient determined by its
diabetes and hypertension status.
Table 3 Risk coefficient for CHF incidence rate
Risk coefficients Patient with hypertension Patient without hypertension
Patient with diabetes 1.61 1.47
Patient without diabetes 0.98 0.70

CHF Mortality Rate
If a CHF patient is dead, it moves from the CHF diagnosed state to the CHF related
mortality state. The risk-adjusted transition probability is based on published literature on
CHF mortality rate. Based on the data from Curtis et al.[33], there is a significant
difference in mortality rate between CHF patients who were first identified from inpatient
diagnosis and those from outpatient diagnosis. So we added the diagnosis source as a risk
factor for CHF mortality and constructed two separate survival curves from the 30 day, 1
year, and 5 year CHF patient mortality rate reported by Curtis et al.[33] (shown in Table 4)
i for each diagnosis source. Linear interpolation was used to construct the survival curve
45

which can be seen as a function () St , where t is the time since CHF onsite and () St is the
survival proportions.
Table 4 Data input for CHF survival curve
Time since onsite of CHF
Survival proportions
Outpatient diagnosis Inpatient diagnosis
0 1 1
30 days 0.98 0.84
1 years 0.87 0.66
5 years 0.49% 0.32.5

Therefore the probability the a patient will die during time i and 1 i  since CHF onsite
can be calculated by ( ) ( 1) S i S i  . However, what we need in our patient health
transition model is the conditional probability of mortality, which is the probability that a
patient will die during time i and 1 i  since CHF onsite given the patient has survived
until time t . We demonstrate how we calculate conditional probability below:

We denoted the event that a patient has survived by time i as S, and the event that it
dies during time i and 1 i  as D. Then we have
( | ) ( )
( | )
()
P D S P D
P D S
PS

 . If a
patient agent dies during time i and 1 i  , it must survives by time i . Hence,
( | ) 1 P S D  and we have ( ) ( ) P S S i  and ( ) ( ) ( 1) P D S i S i    . Therefore, we can
calculate the conditional probability by
{ ( ) ( 1)}
( | )
()
S i S i
P D S
Si

 .

46

Now we consider the effect of age on CHF mortality rate. Chen et al. [36] examined the
one year mortality rate after CHF related hospitalization by agegroups, based on which
we calculated an age adjusted coefficient for each agegroup (shown in Table 5). Finally,
we calculated a patient agent’s transition probability from CHF diagnosed state to CHF
related mortality state by multiplying its conditional probability of CHF mortality by the
age adjusted coefficient specified to its agegroup.
Table 5 Age adjusted coefficients for CHF mortality
Age One year mortality rate
after hospitalization
Age adjusted coefficients
65-74 (age group 1-2) 22% 0.74
75-84 (age group 3-4) 30.3% 1.02
>=85 (age group 5) 42.7% 1.44
Overall 29.6% 1

Non CHF Mortality Rate
If a patient agent is dead before it is diagnosed with CHF, it moves from the CHF free
state to the Non CHF mortality state and we defined the transition probability as non
CHF mortality rate. First, the overall mortality includes the mortality from CHF patients
(CHF related mortality) and the mortality from non CHF patients (non CHF mortality).
The overall mortality rate was retrieved from US life table 2006 by agegroup, race and
gender. We applied the same method used in the CHF mortality rate to calculate the
conditional probability of mortality.
47

We then estimated the non-CHF mortality rate by multiplying the overall mortality rate
by an agegroup specific coefficient. We estimated the coefficients by the following
formula:
_
(1 )
chf non chf
M p M p M     

Where
chf
M
is the CHF one year mortality rate,
_ non chf
M
is the non CHF one year
mortality rate, M is the overall mortality rate, and p is the CHF prevalence rate
estimated from NHANES. The agegroup specific coefficients were then calculated by
_ non chf
M
M
and were shown in Table 6.
Table 6 Age adjusted coefficients for Non CHF mortality
Age Age adjusted coefficients
65-74 (age group 1-2) 0.55
75-84 (age group 3-4) 0.66
>=85 (age group 5) 0.89

CHF related Hospitalization Rate
When a CHF patient agent is hospitalized, it moves from the CHF diagnosed state to the
CHF related hospitalization state, and moves back to the CHF diagnosed state after
discharge. CHF related hospitalization rate was adjusted by agegroup based on the
estimations from Fang et al.[37] and Chen et al.[36], where we consider the
hospitalization that CHF is listed as one of the 1
st
to 7
th
diagnosis. One thing needs to be
noted is we modeled the inpatient CHF diagnosis by moving a patient agent from the
48

CHF free state to the CHF related hospitalization state. Therefore, the transition
probability from the CHF diagnosed state to the CHF related hospitalization state should
be calculated by excluding the hospitalizations where the patients were first diagnosed
with CHF from the overall CHF related hospitalization. The agegroup adjusted transition
probabilities from the CHF diagnosed state to the CHF related hospitalization state are
shown in Table 7.
Table 7 Transition probability from the CHF diagnosed state to the CHF related
hospitalization
Age Transition probability
65-74 (age group 1-2) 0.01663
75-84 (age group 3-4) 0.02360
>=85 (age group 5) 0.03489

Diabetes and Hypertension Incidence Rate
Because diabetes and hypertension are two key risk conditions for CHF disease
progression, we also modeled the incidence of diabetes and hypertension. For each risk
condition, there are two states: the condition free state and the condition onsite state. For
diabetes, a patient agent starts in either the diabetes free state or the diabetes onsite state
depending on if it had diabetes when it was generated. If a diabetes free patient agent is
diagnosed with diabetes, it moves from the diabetes free state to the diabetes onsite state.

49

Table 8 Diabetes incidence rate by race
Race Diabetes incidence rate
None Hispanic White 34.3
None Hispanic Black 52.3
Mexican American 76.9
Other 49.4
Rate is case per 1000 patient-year

Because diabetes is an incurable chronic disease, once a patient agent is in the diabetes
diagnosed state, it cannot go back to the diabetes free state. According to Mcbean et al.
[38], for patients older than 65, race is a significant risk factor for diabetes incidence,
while agegroup is insignificant. Hence, we developed diabetes incidence rates based on
Mcbean et al. [38] conditioning on race (shown in
Table 8).

As for the diabetes, a patient agent starts in either the hypertension free state or the
hypertension onsite state depending on if it had hypertension when it was generated. If a
hypertension free patient agent was diagnosed with hypertension, it moves from the
hypertension free state to the hypertension onsite state and it cannot go back to the
hypertension free state. The literature [39, 40] shows that hypertension incidence rate
increases with age and is higher in black population. Hence, based on Dannenberg et al.
50

[39] and Dischinger et al.[40], we built our hypertension incidence rates conditional on a
patient agent’s age and race (shown in Table 9).
Table 9 Hypertension incidence rate by age and race
Age
Race
Other None Hispanic Black
65-69 31.35
61.76
70+ 36.95 72.79
Rate is case per 1000 patient-year

Clinic Visit Rate
In our model, a patient agent generates inpatient care utilization by moving into the
CHF-related hospitalization state. For outpatient care utilization, we modeled a patient
agent’s regular outpatient visit as a Poisson Process with the parameter  . NHANES
data shows that the average number of outpatient visit per year for CHF patients is 8.6.
The estimations from published studies [41-43] range from 7 to 9.5 outpatient visits per
year. Hence, we set 9   . In addition to regular visits, a follow up visit after hospital
discharge will be scheduled if a patient agent receives the intervention.

4.2. Provider Agent
Our model includes two types of provider agents: the hospital agent and PCP agent, each
represents a hospital or a PCP clinic, respectively. Each provider agent has its defined
51

goals and behaviors. The key element of a provider agent is its decision making module,
by which a provider agent can perceive the environment and make decisions to change its
behaviors aiming to maximize it interests.

The ACO and the associated payment model is intended to create incentives and
mechanisms for providers to conduct evidence-based care, hence to control healthcare
costs and improve quality of care. The evidence-based care of CHF in our model refers to
the intervention of comprehensive discharge planning with post discharge follow up
(intervention thereafter). To implement the intervention, hospitals usually need to assign a
dedicated staff member, usually a care manager or CHF nurse, to manage the intervention
with the support of a multidisciplinary team. The care manager or CHF nurse will also
communicate with patients’ PCP to update patients’ condition, arrange a follow up
outpatient visit, and develop collaborative care plans. For the PCP side of the intervention,
a PCP needs to spend time on communicating and collaborating with the care manager
and to set up a follow up visit.

In our model, the behavior choice for provider agents is whether to implement the
intervention. In particular, for the hospital agent, it is whether to conduct the
comprehensive discharge planning with post discharge follow up. For the PCP agent, it is
52

whether to spend time on communicating and collaborating with the hospital agent.
Implementation of the intervention can influence the quality of care and healthcare
utilization, and there are also intervention costs for provider agents. The healthcare and
intervention cost will be discussed in section 4.4. Next, we will first discuss the effects of
the intervention, and then introduce the provider agent decision making module.

4.2.1. The effects of the intervention
As described in the literature review chapter, the intervention has been demonstrated by a
number of clinic trials and meta-analysis studies that it can reduce hospital readmission
and mortality rate for CHF patients. In our model, the effects of the intervention are
modeled by its influence on patient agent’s state transition probabilities. In particular, if a
patient agent has received the intervention from its providers, its transition probability to
the CHF hospitalization state will be multiplied with an Intervention Effect Factor which
is less than 1, hence reducing the probability. Meanwhile, the transition probability to the
CHF mortality state will be multiplied with another Intervention Effect Factor.

The Intervention Effect Factors hence are the relative risk reduction of the intervention
reported in CHF intervention literature. Every time when the Intervention Effect Factors
53

are needed to calculate transition probability, its value will be drawn from a normal
distribution whose parameters are derived from a meta-analysis of CHF interventions [11]
(shown in Table 10).
Table 10 Intervention Effect Factor
Intervention Effect Factor
Mean (95% CI ） Normal Distribution (Mean, sd)
CHF Hospitalization rate 0.80 (0.66-0.97) Normal (0.80, 0.080)
CHF mortality rate 0.87 (0.73-1.03) Normal (0.87, 0.076)

Because the majority of published CHF interventions involve collaboration of hospitals
and PCPs, we assumed that the full effects of the intervention can only be achieved when
both the hospital where a patient was admitted and the patient’s PCP are conducting the
intervention. If only one party is conducting the intervention without the collaboration of
the other, the intervention can only achieve partial effect which is modeled by
multiplying a Partial Effect Parameter with the Intervention Effect Factor. Unfortunately,
current literature didn’t identify the partial effects of the intervention. Therefore, we set
the Partial Effect Parameter as an adjustable parameter for users and its value can be
assigned according to expert judgment or future studies. In our model run, the value of
the Partial Effect Parameter is set at 1.1.

54

4.2.2. Provider Agent Decision Making Module
In this section, we will introduce how we model a provider agent’s decision making
process to determine whether it will conduct the intervention. The decision making
process includes three main steps. The first step is the perceiving step when a provider
agent perceives information to update its knowledge about the environment and itself.
There are two types of information a provider agent can perceive. The first type is the
information that is directly observable by a provider agent, for example, the
reimbursement amount received from the payer or its performance on quality measures
last year. The second type is the information that is not directly available to a provider
agent (imperfect information) such as other provider agent’s attitude toward the
intervention and expected reimbursement next year. For the second type of information,
provider agents needs to reason and learn from current available information and make
related estimations and predications.

In the second step of the decision making process, a provider agent will combine the
information and estimations it perceived in the first step with its memory to update its
intention toward the intervention. In the third step, the provider agent will choose
whether it will implement the intervention based on its updated intention. Next, we will
discuss the details of these three steps.
55

We applied the well-established psychological theory, the Theory of Planned
Behavior(TPB) [44] as the framework to model the provider agent decision making. The
TPB has been demonstrated well performed for explanation of health related intention
and behaviors [45]. The TPB has also been used by some researchers to model their agent
behaviors [46, 47]. As shown in Figure 5, the TPB model suggests a person’s actual
behavior is determined by his/her intention to perform the behavior, and the intention is
influenced by three predicting factors: the attitude, subjective norm and perceived
behavior controlled (PBC).

At the end of each simulation year j, a provider agent will perceive and form its intention
of performing the intervention as the weighted average of the three predicting factors
using the formula:

Where
k
p
I is the perceived intention and the subscript p represents perceived.
1
k
j
A

,
1
k
j
SN

, and
1
k
j
PBC

are the attitude, subjective norm, and PBC of behavior k for year j+1.
i
 is a weight parameter between 0 and 1 for predicting factor i and we have 1
i
i
 

.
The weight parameters define the characteristics of a provider agent and can be
configured by users. Behavior 0 k  denotes not conducting the intervention and 1 k 
1 1 2 1 3 1
k k k k
p j j j
I A SN PBC   
  
     
56

denotes conducting the intervention. A provider agent will update its intention for both
behaviors and use them to choose a behavior to perform in the third step.

Figure 5 the Theory of Planned Behavior

The attitude in TPB is a person’s belief about the consequences of a particular behavior.
Usually, a decision maker could have multiple objectives that could be influenced by
performing a behavior. In our model, we assume the provider agent care about its
financial return as well as patient health outcomes measured by the CHF hospitalization
rate and mortality rate. Hence the attitude of a provider agent is defined as:

1 1 1 2 1
( ) ( )
k k k
j p j q j
A U EP U EQ 
  
   
Where
1
k
j
EP

and
1
k
j
EQ

are the expected profit and expected quality performance if
behavior k will be performed in year j+1. U is a function that transforms the expected
Provider
Organization
Agent
Attitude
Subjective Norm
Perceived
Behavior
Control
Intention Behavior
Financial
outcomes
Patient health
outcomes
Peer pressure
Perceived
difficulty level
57

profit or the expected quality performance into a utility value from 0 to 1.  is a weight
parameter that can be configured by users too.
1
k
j
EP

and
1
k
j
EQ

can be expressed by:
   
1 1 1 1
1 1 1
( ) ( )
( ) )
k k k k
p j p j j j
k k k
q j ar ar j mr mr j
U EP U ER EOC EIC
U EQ w U EAR w U EMR
   
  
  
   

Where
1
k
j
ER

,
1
k
j
EOC

, and
1
k
j
EIC

are expected revenue, expected operation costs, and
expected intervention cost. The utility of expected quality measure
1
()
k
qj
U EQ

is
formulized as a weighted average of the utility of expected admission rate
1
k
j
EAR

and
the utility of expected mortality rate
1
k
j
EMR

. Under the shared saving payment model,
the expected revenue is:

1 1 1
k k k
j j j
ER PR ENS ESS
  
  
Where PR is the payment rate. For the hospital agent, it is the Perspective Payment Rate
for CHF related admission under the Medicare Perspective payment model. For the PCP
agent, it is the rate defined in the Medicare Physician Fee Schedule. The rate we used in
our model will be introduced in the healthcare cost section later.
1
k
j
ENS

is the expected
number of service that will be provided in year j+1. For the hospital agent, it is the
expected total number of CHF related admission. For the PCP agent, it is the expected
total number of clinic visit.
1
k
j
ESS

is the expected shared saving to the provider by the
payer agent. These variables can be formulized as:
58

11
11
/
kk
jj
k k k k
j j j m
EOC OCR ENS
EIC IC ENS NS





Where OCR is the operating cost rate.
k
j
IC is the intervention cost in year j.
k
j
IC is 0 if
the provider agent didn’t conduct the intervention in year j.
k
m
NS is the number of
service provided in year m where m is the most recent year when the behavior k was
performed. For hospital agent, the expected number of services can expressed as:
11
kk
j j j
ENS EAR NP


Where
j
NP
is the number of CHF patient population the provider agent serves in year j.
For PCP agent, it is:
11
kk
j j j
ENS ECR NP


Where
1
k
j
ECR

is the expected clinic visit rate.

The subjective norm is a person’s perception of his/her significant others' beliefs that if
he/she should perform a behavior. In our model, we define the provider agent’s subjective
norm in the form of peer pressure, which is an provider agent’s perception of other
provider agent’s beliefs that whether it should conduct the intervention. We model this
process through agent communication. Based on its current attitude towards the
intervention, a provider agent will send a positive or negative message about the
intervention to a random agent within its network. An agent then can have a sense about
59

other provider agents’ attitude based on the number of negative and positive messages
received. The subjective norm of an agent therefore is expressed by:

1
()
kk
j sn j
SN U nm


where
0
j
nm and
1
j
nm are the respective number of negative and positive messages
received during year j and
sn
U is also an utility function that transfers the number of
messages into utility value ranging from 0 to 1.

The third predicting factor PBC is a person’s perceived ease or difficulty of performing
the particular behavior. As discussed before, the effects of the interventions are
influenced by if both the hospital and PCP agent are conducting the intervention. Hence,
for a hospital agent, if more PCP agents are conducting the intervention, the overall
effects of the intervention would be better than the situation that only few PCP agents are
conducting the intervention. It is the same from the PCP agent’s perspective to perceive
how many hospital agents are conducting the intervention. Therefore in our model, the
PBC of a provider agent is defined as its perception of the percentage of collaborating
agents conducting the intervention.

In our model, an agent perceives the percentage of collaborators through agent
interactions. As described before, one component of the intervention is that before a
60

patient is discharged from the hospital, the care manager or CHF nurse will contact the
patient’s PCP to arrange a follow up visit and update patient’s condition. This is the time
when a hospital agent interacts with a PCP agent. If a PCP agent is conducting the
intervention, there is a high chance that it will respond actively to a hospital agent’s
contact; on the contrary, if the PCP agent is not conducting the intervention, it will
respond negatively in most of the cases. In other words, there is a smaller probability that
a PCP agent’s response is not consistent with its actual behavior. For example, a PCP
agent could pretend to respond actively just to keep a good relationship with the hospital
but it actually isn’t conducting the intervention. On the other hand, a PCP agent who is
conducting the intervention may not respond actively due to time schedule or
communication issues. We set the probability of inconsistency as 0.2 which can be
adjusted by the users and is unknown to all the agents.

Hence, for a hospital agent who is conducting the intervention and is dealing with
multiple PCP agents who may or may not conduct the intervention, it would perceive
both active responses and negative responses. As a hospital agent is usually dealing with
a number of PCP agents, it is hard to track the responses of each individual PCP agent.
Therefore, a hospital agent is defined to use the percentage of active responses to
estimate how many PCP agents are conducting the intervention.
61

In particular, for a hospital agent, the PBC for the behavior of conducting the intervention
(k=1) is formalized as:
1
1
j
j
j
nar
PBC
tr


Where
j
nar
is the number of active responses and
j
tr
is the total number of responses. If a
hospital agent didn’t conduct the intervention in year j (it didn’t contact the physician and
therefore no response is received),
1
1 j
PBC

will equal to
1
k
PBC where k is the latest year
when the hospital agent conducted the intervention. Because an agent doesn’t need any
collaboration from other agents to not conduct the intervention (k=0), we set
0
1
1
j
PBC

 .

For a PCP agent, if a hospital agent contacted it, it will know for sure that the hospital
agent is conducting the intervention. Therefore, PBC is defined as:
1
1
j
j
j
nh
PBC
th


Where
j
nh
is the number of hospitals who ever contacted the PCP agent for the
intervention purpose in year j, and
j
th
is the total number of hospitals to which the PCP
agent has referred its patients. Same with the hospital agent,
0
1
1
j
PBC

 also holds for
the PCP agent.

So far, a provider agent has perceived from the environment and formed its perceived
62

intention
k
p
I . In the next step, the provider agent will combine the current perceived
intention with its memory
k
j
I which is its intention for behavior k in year j, to update its
intention toward the intervention using the formula:

1
(1 )
k k k
j j p
I I I 

    
Where
1
k
j
I

is the final intention to choose behavior in year j+1, and  is a parameter
to adjust the weights for its memory and current perceived intention. The default value of
 is set at 0.7 in our model.

In the third and final step, the provider agent will choose whether it will implement the
intervention based on its updated intention. The probability of choosing the intervention
is calculated by a Softmax function:

0
1 0
1 01
11
exp( / )
=
exp( / ) exp( / )
j
j
jj
I
P
II







The parameter  is used to model the randomness and irrationality of the decision making
process. When  is set at a large positive number, all behaviors will have the same
probability to be performed. When the value of  closes to zero, the behavior with higher
intention will have higher probability to be performed. In our model,  is assigned a value
of 0.15 to have a reasonable randomness level to model the provider agent decision
making process.
63

At last, to test how different provider agents respond to environment changes, we have
defined three types of provider agent by assigned different weight
12
[ , ]     to the
predicting factors of the attitude. The three types of provider agents are: profit-oriented
with  =[0.8,0.2], quality-oriented with  =[0.2,0.8], and neutral with  =[0.5,0.5]. We
will compare the outputs of the model with different mixes of these three types of
provider agents.

4.3. Payer agent
In this section, we will describe how the Shared Saving payment model is defined and
implemented in our model.

We assumed that there are two groups of providers: the ACO group and controlled group
(CG group), each of which serves a patient population with the same patient
characteristics distribution. At the end of each year or decision cycle, the total CHF
related healthcare costs per CHF patient will be calculated for each group, which includes
inpatient costs of CHF-related hospitalization and outpatient cost of PCP clinic visit. The
cost difference between these two groups is the saving per CHF patient from the payer’s
perspective. For example, if the cost per CHF patient in the ACO group is $16,000 and
64

the cost per CHF patient in the CG group is $18,000, the saving will be $2,000 per CHF
patient.

One key parameter of the Shared Saving payment is shared saving rate (SSR), which
defines the percentage of the total saving that will be rewarded to providers. The shaved
saving per CHF patient is calculated by multiplying the saving per CHF patient with SSR,
and the total shared saving is determined by multiplying the shaved saving per CHF
patient with the number of CHF patients that the ACO group serves. The total shared
saving then will be distributed among hospital agents and PCP agents in the ACO group.
The distribution of the shared saving is defined by another key parameter, sharing rate to
hospital, which is the percentage of the total shared saving distributed to hospital agents.
Within each type of provider agents, we assume the shared saving will be distributed
equally. If the cost per CHF patient of the ACO group is higher than that of the CG group,
there will be no shared saving.

Following the last example, if the shared saving rate is set at 50%, the shared saving will
be $1,000 per CHF patient. Assume that the number of CHF patients is 1,000 in the ACO
group, which achieves a total $1,000,000 shared saving. If the sharing rate to hospitals is
set at 0.9, the total shared saving to hospital agents and PCP agents will be $900,000 and
65

$100,000 respectively. Assuming there are 3 hospital agents and 10 PCP agents in the
ACO group, each hospital agent will be rewarded with $300,000 shared saving and each
PCP agent will be rewarded with $10,000 shared saving.

Because we aim to compare the effects of different payment model parameters on the
ACO outcomes, we did not introduce the variation of payment model during each
simulation run. In other words, we did not assign a decision making module to the payer
agent which can make it capable of adjusting the payment model during a simulation.
Instead, we will conduct scenario analysis to examine the relations between the design of
a payment model and the overall financial and quality outcomes.

4.4. Healthcare cost
So far, we have described how each type of agent is modeled. In this section, we will
describe the healthcare cost parameters used in our model. Because the cost for one agent
could be the income or revenue for another agent, we will discuss the cost parameters
from different agents’ perspective. All dollar amounts were converted into USD 2011
dollars value by US Consumer Price Index (CPI). The impacts of uncertainty in these
cost parameters will be tested in the sensitivity analysis.

66

Payer Agent
The cost from the payer’s perspective, or CMS’s perspective in particular, is the
reimbursement paid to providers for CHF-related care services provided to Medicare
patients. The reimbursement amount is determined by the payment model. We first
examine the reimbursement under current Medicare Fee-for-service payment model,
which is the basis to calculate the shared saving.

CMS currently pays hospital inpatient services through the Hospital Inpatient Prospective
Payment Systems (IPPS), under which hospitals receive a fixed amount of payment based
on geographic factors, patient’s Medicare Severity Diagnosis Related Groups (MS-DRG),
and discharge status [48]. CMS reported a $7,418 national average reimbursement per
hospitalization where CHF is the first diagnosis (MS-DRG 291, 292, 293) [48]. In our
model, we consider CHF-related hospitalization (CHF is any of the first to seventh
diagnosis), whose cost is substantially higher than that of the hospitalization where CHF
is listed in the first diagnosis [2]. In our model, we used AHRQ’s estimation [2] for the
reimbursement of CHF-related hospital services, which is $14822 per hospitalization.

In the literature, the physician inpatient cost was mainly estimated from the Medicare
Physician Fee Schedule. Cowper et al. [41] estimated that the average inpatient physician
67

charge is 18% of the mean hospital cost. Angus et al. [49] also estimated that the inpatient
physician fee equals to 17% of the reimbursement for hospital. Hence, we used 18% of
the reimbursement for hospital service, that is $2,668, for the physician inpatient cost.

The reimbursement for outpatient visit is determined by the Medicare Physician Fee
Schedule. The reimbursement amount per outpatient visit is calculated by multiplying the
Relative Value Unit (RVU) assigned to each service with a conversion factor (CF) and a
geographical adjustment. In FY 2011, the reimbursement amount per visit ranged from
$69 to $102 [50] depending on the time and effort spent on the visit. In our model, we set
the reimbursement per outpatient visit at the average value $85.

There are some costs that we didn’t include in our model. We didn’t include the CHF
outpatient medication cost in our model, because the majority of CHF disease
management intervention literature either didn’t include it in their reported outcomes or
there is no significant difference between the intervention group and controlled group for
outpatient medication costs. We also didn’t include the cost of hospitalization where CHF
is not listed as any of the first to seventh diagnosis, because this model only focuses on
CHF care.

68

Hospital Agent
The profit (or cost if negative) from a hospital agent’s perspective is defined by the
payment received from the payer minus its own operating cost and any intervention cost.
A report from the Medicare Payment Advisory Commission [51] estimated that the
margin for Medicare inpatient services was 1.7%  in 2010. Titler et al. [52] estimated a
$1000 lost per CHF admission for hospitals in 2000. American Heart Association [53]
also reported that in 2010 the payment received from Medicare only covered 92% of the
costs of caring Medicare patients and 53% of hospitals received less Medicare payments
than their cost, which is calculated by multiplying their charges with hospital specific
cost-to-charge ratio. Based on Medicare’s reported reimbursement [48] and hospital
operating cost [54, 55] for CHF hospitalization, we estimated a 8.4%  margin for CHF
inpatient services which is used to calculate hospital profit in our model.

For CHF intervention cost, a meta-analysis of CHF disease management interventions
[11] showed that the pooled intervention cost was $108 per patient per month for a
usually six-month long intervention. We assumed the intervention effects would last for
the whole year which gives us an average cost of $54 per patient per month. The reported
intervention cost was mainly contributed by the labor cost of hiring a care manager or a
CHF nurse, which was usually paid by the hospital in the literature and hence is assigned
69

to hospital agents in our model. The intervention cost from a PCP’s perspective will be
discussed next.

PCP Agent
A PCP’s income is defined as revenue (reimbursement) minus operating (overhead) cost.
The revenue per outpatient visit has been discussed in the payer’s perspective part and
was set at $85. PCP’s operating cost was estimated as 60 % of its revenue for a typical
primary care practice [56] which was used in our model. We defined the intervention cost
from a PCP’s perspective as the time spend on communicating with care managers. After
a patient is discharged, his/her care manager will update the patient’s condition and care
management plan to his/her PCP. We assumed that this communication costs the PCP 15
minutes on average. The same amount of time could be used for a standard outpatient
visit (CPT 99213) which is reimbursed at $69 [50]. Hence, the intervention cost from a
PCP’s perspective is the opportunity cost of losing potential reimbursement. Note that in
CHF intervention literature, a follow-up outpatient visit after discharge is usually planned.
Because the follow-up visit will be reimbursed by Medicare, we don’t consider it as a
cost for PCPs. The revenue and cost from different agents’ perspectives are summarized
in Table 11.

70

Table 11 Healthcare Cost
Variable Cost for
payer
Profit for hospital Income for primary
care physician
CHF hospitalization -$14,822 $-1186
Inpatient physician fee -$2668
Outpatient visit -$85 $34
Intervention cost $-54 -$69
Intervention cost for hospital is per patient per month; Intervention cost for primary care
physician is per patient per year
All numbers are shown in USD 2011 dollars value

4.5. Model Implementation and Simulation Setting
The Agent-based model was implemented using Anylogic version 6.6 (XJ Technologies).
The software was chosen because of its flexible modeling language and powerful
experimental framework for simulation of complex systems. The agents were
implemented according to the settings in previous sections.

In this section, we will describe the setting of the simulation environment. The simulation
time is customizable and should be set based on research questions of users and the
nature of the disease. In our model, we set the simulation time at 5 simulation years,
which is reasonable to test the effects of an ACO implementation on CHF care.

There is one single payer agent representing CMS and two networks of provider agents
71

(one ACO network and one controlled network) generated in the model. Both of the
provider networks are composed of 3 hospital agents and 15 PCP agents. The ACO
network is reimbursed under the Shared Saving model and the controlled network is
reimbursed under the traditional Medicare Fee-for-service model.

We have generated 10,000 patients agents. For each patient agent, the values of its
characteristics variables were assigned based on our constructed joint distribution.
According to the NHANES sample, most of the patients (95%) have a unique place to
seek outpatient care. Therefore, we randomly assigned each patient agent to a PCP agent
from whom the patient agent will seek outpatient care. A patient agent was assigned to
the ACO network if its PCP agent is in the ACO network and was assigned to the
controlled network if its PCP agent is in the controlled network. A patient agent will seek
inpatient care randomly from one of the three hospital agents within its network. During
the simulation, new patient agent will be generated to represent the patient who just
turned to 65 years old and became Medicare eligible. The number of new patients
generated each simulation year is a user defined parameter. For example, it can be set as a
increasing number to reflect the trend of increasing Medicare beneficiaries. In our model,
the number of new patients generated each simulation year is set to keep the total number
of patient agents alive relatively constant during the simulation.
72

In the simulation year 1, all the provider agents in the ACO network start with conducting
the CHF intervention. At the end of each simulation year, the payer agent will collect the
performance measures for both provider networks including the payment per CHF patient,
the hospital admission rate, and the CHF patient mortality rate. Then the payer agent will
calculate and distribute the shared saving to the ACO providers as described in the payer
agent section. ACO provider agents have access to their own financial and quality
performance as well as the amount of shared saving they received. They also have access
to the average quality performance of the controlled network, provided by the payer agent.
With all the information, an ACO provider agent will go through the decision making
process, described in the provider agent section, and choose if it will implement the
intervention next simulation year.

The outputs of each simulation run are the average shared saving to the payer agent per
CHF patient per year, average annual CHF related admission rate and CHF patient
mortality rate of both the ACO and controlled network over 5 simulation years. For each
setting of the model input parameters, 100 simulation runs are performed to calculate the
mean and 95% level confidence interval of all the simulation outputs.
73

5. Simulation Result
In this chapter, we will first describe the configurations and simulation results of a
baseline model. Then, we will describe the results of our scenario analysis to determine
the method to be used to design the shared saving model that will maximize the utility of
the payer. The scenario analysis will also show how provider agents with different
individual preferences respond to the payment model. Finally, the sensitivity analysis will
be presented to show how the uncertainty in the model input influences the model output.
A screen shot of the model runtime dashboard is shown in Figure 6.

Figure 6 Model Runtime Dashboard Screen Shot

74

5.1. Baseline Model
In the baseline model, the three hospital agents in the ACO network are a profit-oriented
agent, a quality-oriented agent, and a neutral agent with a PCP agent in the ACO network
having equal probability of being assigned as one of the three types. The key payment
model parameters, shared sharing rate (SSR) and sharing rate to hospital (SRH), are set at
0.5 and 0.7 respectively, which means half of the saving will be shared to provider agents
and 70% of the shared saving to providers will be distributed to hospital agents.

The results are calculated from 500 runs of the baseline model. The ACO network
performed better in the CHF-related hospitalization rate and annual mortality rate of CHF
patients due to the implementation of evidence-based care. The annual CHF related
hospitalization rate is 63.89% (95% CI: 63.69%–64.09%) for the ACO network and 72.72%
(95% CI: 72.56%–72.88%) for the controlled network. The annual mortality rate of CHF
patients is 18.44% (95% CI: 18.37%–18.52%) for the ACO network and 19.69% (95% CI:
19.61%–19.77%) for the controlled network. From the payer’s or the CMS’s perspective,
the average saving after distribution of the shared saving is $760 (95% CI: $735–$785)
per CHF patient per year or a 5.64% saving compared with the $13,469 (95% CI:
$13,440–$13,499) payment per CHF patient in the controlled network. The saving in the
ACO network is mainly caused by the reduction of the hospitalization rate.
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5.2. Model Verification and Validation
For the model verification, we first verified each transition in the patient agent state
transition module with the input data. Then we further verified the two aggregate
transition outputs: the overall mortality rate (CHF-related mortality plus non-CHF-related
mortality) and the CHF-related hospitalization rate (hospitalizations from the first CHF
diagnosis plus hospitalization for patients who have already been diagnosed with CHF).
The overall mortality rate has been verified with the 2006 US life table and the
CHF-related hospitalization rate has been verified with the data report by Chen et al. [34].

For model validation, we first validated the CHF-related hospitalization rate and
mortality rate of the controlled network (without intervention) with both CHF clinical
trial literature and CHF simulation studies. The CHF-related hospitalization rate and
mortality rate of the controlled network in our model are 74% and 20%, respectively.

Curtis et al. [31] reported the one-year and five-year mortality rate which were around 27%
and 62%, respectively. That indicates that the annual probability of mortality for a CHF
patient is highest in the first year since the diagnosis of CHF and it decreases
significantly if the patient survives that period of time. Hence, in our model, where we
have a mix of patients varied years following their diagnosis of CHF, the overall annual
76

mortality rate should be lower than 27%, as reported by Curtis et al.

The mortality rate for CHF patients reported in the clinical trials ranges from 15% to 28%
[55-58]. Their sample sizes are usually small and that could cause larger variation in their
estimations. In the CHF simulation literature, Nichol et al. [59] reported an annual
mortality rate of 24.7%. Other CHF simulation studies usually directly utilized the
mortality rates reported in these clinical trials. Therefore, the mortality rate in our model
is comparable to and within the range of the mortality rates reported by the literature.

For the hospitalization rate, Chen et al. [34] reported the hospitalization rate with CHF
listed as the first diagnosis is 20.8%. Fang et al [35] reported that hospitalizations with
CHF listed as the first diagnosis account for 30.3% of all the hospitalizations in which
CHF is listed as the first to the seventh diagnosis. Hence, the CHF related hospitalization
rate is around 68.6%. The average annual hospitalization rate is 72.9%, calculated from
the SOLVD trial [58], which was a large trial whose estimates have been used by many
CHF simulation studies. Hence, the CHF-related hospitalization rate in our model is
comparable to that within the literature.

Next, we tried to validate our saving per CHF patient with that reported from the CHF
77

intervention literature. However, direct comparison is difficult because the reported
saving from the CHF intervention literature is extremely variable and mainly depends on
the ways the intervention costs and effectiveness were calculated. The short period of
time studied (usually 3 to 6 months) and small patient samples (50 to 200 CHF patients)
also contributed to the variation in reported saving. To compare with the intervention
literature, we rerun our model with all the provider agents forced to conduct the
intervention throughout the simulation and no shared saving distributed. The results show
a $177 saving per CHF patient per month from the payer’s perspective. Note that our
estimation of saving is conservative because we used the cost data of Medicare payment
(which is less than the payment by private insurers or that calculated by hospitals’ cost
schedule) and included only the costs of CHF-related hospitalization (compared with
costs of all-cause hospitalization used in some literature) and outpatient clinic visits.

For example, Riegel et al. [60] reported a $208 cost saving per CHF patient per month
based on the calculation of hospital cost. Applying the –8.5% average margin of
hospitalization for Medicare patients used in our model, the saving reported by Riegel et
al. can be converted to a $191 saving from the payer’s perspective and is comparable to
our result. On the other hand, Krumholz et al. [61] reported a $1,037 saving per patient
per month. However, they reported a 0.69 relative risk reduction on the admission rate,
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which is lower than the value of 0.8, that we used from the meta-analysis[11]. This will
generate much higher saving from the reduction of hospitalization. The variation could
also be caused by their small sample because they have only 44 CHF patients in their
intervention group. More importantly, Krumholz et al. calculated the cost of
hospitalization by summing the unit cost of each service provided during the
hospitalization, which could be much higher than the payment made by the Medicare
Perspective Payment System.

5.3. Scenario Analysis
To examine the influence of provider types on the model outputs, we created three
scenarios. The setting of the provider agent type in scenario one is the same with that in
the baseline model. In scenario two, all the provider agents are profit oriented, and in
scenario three, all the provider agents are quality oriented.

In each scenario, we systematically vary the two key parameters of the shared saving
payment model: shared sharing rate (SSR) (defines the percentage of saving that will be
shared with provider agents) and sharing rate to hospital (SRH) (defines the percentage of
the shared saving to providers that will be distributed to hospital agents). We run the
model with SSR ranging from 0 (no shared saving to the providers) to 1 (all the saving
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shared to the providers), incrementing by 0.1. Under each SSR, we run the model with
SRH ranging from 0.5 (half of the shared saving will be distributed to hospital agents) to
1 (all the shared saving will be distributed to hospital agents), incrementing by 0.1.
Because the hospital agents in our model setting bear the majority of the overall
intervention cost, a value of SRH lower than 0.5 is unreasonable and is not examined.

A payer agent (the CMS in our model) has multiple objectives to achieve both higher
financial return measured by the shared saving to payer agent (SSP) and better quality of
care (low CHF patient mortality rate). Figure 7 shows SSP decreases as the SSR increases
in all three scenarios. When the payer agent increases the SSR, the resulting additional
financial incentives motivate more provider agents to implement the intervention, causing
a reduction in CHF-related hospital admission rate (shown in Figure 8) and in the CHF
patient mortality rate (shown in Figure 9). The reduction in the CHF-related hospital
admission rate then generates more total saving in the system; however, the SSP actually
decreases because more saving is shared to the provider agents. In an extreme case, if the
SSR is set at 100%, all the saving is shared to the provider agents, leaving 0% to the
payer agent. Therefore, the payer agent is faced with a trade-off between financial return
and quality of care when determining the value of SSR.

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Figure 7 Shared saving to the payer by shared saving rate
This scenario analysis also shows how provider agents in different scenarios respond to
changes in SSR. As shown in Figure 7, given the same SSR, scenario three (all the
provider agents are quality oriented) always yields higher financial return to the payer
agent, followed in order by scenario one and scenario two. Because the quality oriented
agent is least sensitive to the financial incentive, the curve of scenario three in Figure 7 is
approximately linear, while the curve of scenarios one and two show a non-linear
relationship between the SSR and the payer’s financial return.

0
200
400
600
800
1000
1200
1400
1600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Saving per Patient after SS
Shared Saving Rate
scenario 1: mixed
providers
scenario 2:Profit-
oriented providers
scenario 3:quality-
oriented providers
81

Figure 8 CHF related hospitalization by shared saving rate
This observation is confirmed in Figure 8 and Figure 9, where the two measures have a
relatively flat trend with the SSR in scenario three. On the other hand, the profit-oriented
provider agents in scenario two are most sensitive to the changes in SSR.

Figure 9 Mortality rate by shared saving rate

0.62
0.63
0.64
0.65
0.66
0.67
0.68
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CHF related hospitalization
Shared Saving Rate
scenario 1: mixed
providers
scenario 2:Profit-
oriented providers
scenario 3:quality-
oriented providers
0.18
0.182
0.184
0.186
0.188
0.19
0.192
0.194
0.196
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mortality rate
Shared Saving Rate
scenario 1: mixed
providers
scenario 2:Profit-
oriented providers
scenario 3:quality-
oriented providers
82

We further examine the effects of varying SRH given a specific SSR. Analyzing the
payer’s financial return, SSP by SRH in scenario one, we observed different patterns
when the SSR is set at different values. When the SSR is low, there is no clear
relationship between SSP and SRH. Because even all of the saving is distributed to
hospital agents (when SRH is 1), it is not enough to cover the intervention cost for the
hospital agents and motivate their behavior changes.

Figure 10 SSP by SRH with the shared saving rate = 0.1
When SSR is set to 0.5 to 0.8, we can see a pattern with a concave shape whereby the
maximal financial return is achieved when the SRH is 0.7 (shown in
Figure 11). Because the effects of the intervention can be fully achieved only when both
the hospital agents and PCP agents are conducting it, the 0.7 value of SRH seems to be a
$200.00
$400.00
$600.00
$800.00
$1,000.00
$1,200.00
$1,400.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.1
83

good balance point that can motivate both the hospital and PCP agents to conduct the
intervention and thus achieve a maximal financial return for the payer agent.

When SSR is high (0.9), we see a relatively flat trend of SSR when SRH is around 0.5 to
0.7, and when the SRH is greater than 0.7, SSR decreases as SRH increases. Because the
hospital agent has enough financial incentives to conduct the intervention. a clear hospital
agent behavior switch is not observed as SRH increases from 0.5 to 0.7. When SRH is
greater than the balance point of 0.7, the PCP agents do not have enough financial
incentives to conduct the intervention, and therefore the SSP decreases. Similar patterns
have also been observed in the other two scenarios.

Figure 11 SSP by SRH with shared saving rate from 0.5-0.8
$200.00
$300.00
$400.00
$500.00
$600.00
$700.00
$800.00
$900.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.5
$200.00
$250.00
$300.00
$350.00
$400.00
$450.00
$500.00
$550.00
$600.00
$650.00
$700.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.6
$200.00
$250.00
$300.00
$350.00
$400.00
$450.00
$500.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.7
$200.00
$220.00
$240.00
$260.00
$280.00
$300.00
$320.00
$340.00
$360.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.8
84

Figure 12 SSP by SRH with the shared saving rate = 0.9

5.4. Sensitivity Analysis
After the scenario analysis on the Shared Saving payment model and provider types was
conducted, a sensitivity analysis was conducted to examine how the uncertainty in other
key model inputs influences the model outputs (using SSP). As is common practice, for
each testing parameter, we tested a high value (increased by 20%) and a low value
(decreased by 20%) and run the model using the same values as those in the baseline
model for all other parameters.

From the results (shown in Figure 13), we can see that SSP is most sensitive to the effects
of the intervention on hospital admission rates. This was expected because the saving is
$-
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
$180.00
0.5 0.6 0.7 0.8 0.9 1
Shared saving to payer
Distribution rate to hospital
Shared saving rate=0.9
85

mainly generated by the reduction of hospitalization. Next come the effects of the
intervention on CHF patient mortality rate. It is important because the quality outcomes
will also affect provider agents’ attitude toward the intervention. Hospital intervention
and operating costs, both affecting hospital agents’ profit, are the next two sensitive
parameters. Because we assume the hospital agent has the financial capability and covers
the main cost of the intervention such as hiring care managers, SSP is not sensitive to the
parameters on the PCP agent’s side.

Figure 13 Sensitivity analysis

-200 300 800 1300 1800
Risk reduction of the intervention on
admission rate
Risk reduction of the intervention on
mortality rate
Intervention cost for hospital
Hospital Operating Cost
Irrational adjust variable τ
Intervention cost for PCP
Payment per clinic visit
SSP
Low
High
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6. Discussion and Future Direction
In this chapter, first we will summarize and discuss our main findings from the CHF
model and then discuss the limitations and future research directions. How to provide
incentives to improve shared accountability is a difficult policy issue with a great deal of
uncertainties and trade-offs [16]. Our CHF Agent-based simulation model has
demonstrated and quantified how different implementations of the ACO and the Shared
Saving payment model can influence provider behavior regarding the evidence-based
intervention and therefore has generated different financial and quality outcomes. The
model can help decision makers better understand the complexity and risks of ACO
design and facilitate more informed decision-making.

The decision making process of designing the Shared Saving payment model includes the
configurations of SSR and SRH. From CMS’s perspective, objectives include both
controlling the cost and promoting the quality of care. The scenario analysis has shown
that there is a trade-off between the payer’s financial return and the quality outcomes
when setting SSR. Our model can help decision makers understand the constraints when
determining SSR. For example, if CMS wants to achieve a quality target to reduce the
CHF patient mortality rate to 18.8% when all the providers are quality-oriented, the
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model results indicate that CMS should set the shared saving rate at 45%, which would
generate an $850 saving per CHF patient per year (shown in Figure 14). The payer
therefore, would not achieve a financial objective, say $1,000 saving per patient, at the
same time. Hence, with the understanding of these constraints, CMS can determine a SSR
value that can balance its two objectives.

Once SSR is decided, the next step is to determine an SRH value that can motivate both
the hospital agents and PCP agents to work together on the CHF intervention. Creating a
mechanism to promote cooperation between hospitals and physicians is difficult, and an
immature payment model may incite tension and competition between hospitals and
physicians [57]. The simulation results have identified different patterns of outcomes by
SRH, which can help decision makers choose the optimal SRH value to maximize the
outcomes based on the configuration of SSR.

Our model also shows how different types of providers respond to the payment model. In
the previous example, when CMS wants to set a quality target of reducing the CHF
patient mortality rate to 18.8% (shown in Figure 14), if all the providers are profit
oriented instead, CMS then needs to set SSR at 85%. This will generate only a $200
saving per CHF patient per year instead of a saving of $850 when all the providers are
88

quality oriented. This result shows that the payer agent needs to provide different levels
of incentives for different types of providers to achieve the same level of quality
outcomes. This brings up the problem that the more profit oriented a provider agent is,
the more financial reward it will receive from the payer. This problem could be addressed
by expanding the payer’s strategies to develop mixed motives to stimulate all types of
providers [58], such as aligning the payment with quality requirements, public reporting
of quality performance, and initiating education programs to increase the awareness of
quality of care [59-61].
89

Figure 14 Effects of provider type
The sensitivity analysis shows the outcomes are most sensitive to the effects of the
intervention, followed by the intervention cost. Hence, selecting the cost-effective
intervention is critical for the success of an ACO. However, determining the
cost-effectiveness of an intervention is also a challenge. For example, the CHF
intervention cost can vary, largely depending on the services and components included.
Including specialty care in CHF care management could increase the cost substantially,
but its marginal effect is unclear. Current CHF intervention literature usually includes a
0
200
400
600
800
1000
1200
1400
1600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Saving per Patient after SS
Shared Saving Rate
scenario 1: mixed providers
scenario 2:Profit-oriented
providers
scenario 3:quality -oriented
providers
0.18
0.182
0.184
0.186
0.188
0.19
0.192
0.194
0.196
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Mortality rate
Shared Saving Rate
scenario 1: mixed
providers
scenario 2:Profit -oriented
providers
scenario 3:quality-
oriented providers
18.8%
$850
$200
90

set of care activities without identifying the effect of each individual activity and how
they correlate. Further studies could be done to examine the effects of care activities to
facilitate the design of cost-effective interventions.

For boarder applications beyond CHF, ACO stakeholders need to wisely choose
improvement opportunities to pursue based on their capability and current situations.
As discussed before, the improvement opportunities are the motives of creating the ACO,
and the ACO model design is focused on how to create good incentives and mechanisms
to better pursue these opportunities [5, 62].

There are some limitations to our Agent-based model for CHF care. First, our model
parameters are based on the best information we could obtain, including nationwide
health surveys, meta-analysis literature, analysis using Medicare claim data and
healthcare cost data published by CMS. Hence, the results reflect a national average trend
for Medicare patients. Adjustments should be made when referring to some specific
patient demographics, provider characteristics and geographic locations.

Second, some players in the system such as long-term care facilities and pharmacies not
included in our model, because they are not key participants of the CHF evidence-based
91

care intervention reported from the literature. However, for other applications, they could
be important elements and can be included in the model [63].

The third limitation is that the weight for each behavior predicting factor in the provider
decision module is not drawn from the survey from the physicians. Because first, to our
best knowledge, a national physician’s behavior survey with information to provide the
values of these weights is not available. Hence, in our model, we allow users to configure
the provider agent parameters based on the characteristics of the providers with whom
they are working.

There are additional limitations. We consider only the CHF-related hospitalization rate
and CHF patient mortality rate as our quality measures. We considered these two
measures because they are the most important outcomes reported in CHF intervention
literature and are the key measures tracked by CMS to determine the quality of care. The
CMS CHF core measures are not included because they are controversial and have been
considered ineffective in truly measuring quality of care [64]. However, to have a more
comprehensive evaluation of the ACO’s performance, more measures such as the patient
satisfaction and quality of life score can be added to future work [65, 66].

92

Our CHF model provides a platform and can be configured to study other ACO design
options and answer corresponding policy and research questions for future direction. For
example, to facilitate the design and implementation of other risk-sharing payment
models, the ACO model design module of the payer agent can be configured to
implement the bundled payment or risk-adjust capitation model by resetting the payment
calculation and distribution rules.

Our model also has the capability to construct a flexible provider agent relationship and
network for future studies about the effects of diverse provider organization structures.
For example, to model an integrated health system consisting of multiple PCPs and
hospitals, we can configure the model by assigning PCP agents and hospital agents into a
network, thus disabling their decision-making module, and adding a decision-making
module at the network level. Therefore, the network can represent an integrated health
system and make decisions to maximize its overall interests.

Moreover, as we preserve the correlation between a patient agents’ characteristics through
the conditional probability model, future studies can be done by constructing a different
patient population to study the influence of various patient population characteristics on
the ACO model.
93

Our model also has the capacity to be expanded to incorporate more dynamic functions.
For example, the provider agent can be equipped with diverse behaviors such as CHF
preventive care, disease management and prevention for CHF risk factors such as
diabetes and hypertension, health information technology (HIT) systems investment and
implementation, etc. The patient agent can be equipped with a provider choice module to
seek care based on previous experiences and thereby create competition among provider
agents. Different patient agents can also have variable behavior patterns that would
influence their adherence to a care plan or the effects of patient education.

94

7. Conclusion
To conclude, in this dissertation, we have developed an analytical framework that can be
used to guild the modeling and analysis of an ACO. We have also demonstrated our
framework by constructing an Agent-based model to study the ACO with the Shared
Saving payment model for CHF care. The Agent-based simulation model we developed is
not meant to be a substitute for an ACO pilot program but rather to facilitate the ACO
design and implementation process. It provides analytic support for decision makers to
make informed decisions on how to design an ACO and its corresponding Shared Saving
payment model given their current provider and patient population environment to
maximize the desired outcomes.

The Agent-based simulation model has identified critical determinants of an optimal
design for the payment model that can motive provider behavior changes to achieve
maximal financial and quality outcomes. The model has quantified the trade-off between
the payer’s financial return and the quality outcomes, helping decision makers configure
the Shared Saving model based on their objectives.

95

The Agent-based model has also shown that how different types of providers respond to a
payment model design. The payer may need to expand its strategies to motive all types of
providers. The sensitivity analysis shows the model outputs are most sensitive to the
effects of the intervention, followed by the intervention cost. Hence, implementing the
cost-effective intervention is critical for the success of an ACO.

Note that the ACO model is context dependent. For example, in our model, the PCP agent
is assumed to be independent and hence does not have enough financial and operational
capacity to initiate the CHF intervention. The hospital agent therefore needs to lead the
intervention and bears the majority of the intervention cost, such as hiring a care manager.
However, large physician groups, such as the Independent Practice Association (IPA),
may have enough capacity and incentives to lead the CHF intervention. Hence, the design
of an ACO with strong IPAs involved could be different from the design of an ACO
model with independent PCPs. Furthermore, the ACO model design would be different if
it targets another condition, procedure, or multiple conditions, which significantly
increases the complexity and risks of the ACO model design.

The complexity and risks of the ACO model design hence generate a strong need for
modeling and simulation tools that are flexible, capable, and user adjustable to facilitate
96

the design and implementation of an ACO model for different disease conditions,
payment models, and provider and patient agent characteristics. For the future use of our
model, users can, based on their situations and objectives, configure the ACO design
parameters, generate corresponding patient and provider agents, and then analyze
different scenarios and optimize their ACO models.

Different from the aggregated level modeling methods, such as System Dynamics, the
Agent-based model can capture individual agent characteristics and incorporate agent
decision making and behaviors. It is also capable of modeling agent communication and
interactions. The Agent-based model hence has demonstrated its capability of addressing
the system modeling challenges we discussed, making the model a closer approximation
of the real world. Therefore, the optimal solutions recommended by our Agent-based
model can have a higher chance of improving the real health system and generating more
influential impacts. In addition, because each agent represents a real entity in the health
system such as a physician or a patient, the Agent-based model can be more
understandable and acceptable by healthcare practitioners than traditional ISE system
models.

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Abstract (if available)

Abstract Creating Accountable Care Organizations (ACOs) has been widely discussed as a strategy to control rapidly rising healthcare costs and improve the quality of care

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Asset Metadata

Creator Liu, Pai (author)

Core Title An agent-based model to study accountable care organizations

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publication Date 04/30/2013

Defense Date 03/14/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag accountable care organization,agent-based model,health system,OAI-PMH Harvest,payment model

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wu, Shinyi (committee chair), Kesselman, Carl K. (committee member), Nichol, Michael B. (committee member)

Creator Email liup04@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-249058

Unique identifier UC11293576

Identifier etd-LiuPai-1639.pdf (filename),usctheses-c3-249058 (legacy record id)

Legacy Identifier etd-LiuPai-1639-1.pdf

Dmrecord 249058

Document Type Dissertation

Format application/pdf (imt)

Rights Liu, Pai

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA