AGENT BASED MODELING AND SYSTEM DYNAMICS
IN HEALTHCARE
Modeling Two Stage Preventive Medical Checkup Systems
Andreas Martischnig, Siegfried Voessner
Department of Engineering and Business Informatics, Graz University of Technology
Kopernikusgasse 24, 8010 Graz, Austria
Gerhard Stark
Department of Internal Medicine, LKH Deutschlandsberg, 8530 Deutschlandsberg, Austria
Keywords: Agent based modeling, System dynamics, Healthcare, Preventive medical checkup, Preventive cancer
checkup.
Abstract: Modeling preventive medical checkup systems (PMCS) is an important part of predicting future healthcare
coverage. In this paper we show how to model a two stage interdependent System as it applies to basic
cancer prevention. Starting with a short introduction of the two used modeling techniques we show the basic
principle of the preventive cancer checkup process (PCCP) and how it was modeled with these opposing
approaches. We then extract the key benefits from each technique and also their shortcomings when
applying it onto the PCCP. Furthermore we show at what level of detail which method should be used to
gain the most valuable insight into those complex checkup systems.
1 INTRODUCTION
In medical science, especially health care, computer
simulation is still a relatively young field. In contrast
to that social sciences use computer simulation as a
well-established domain of research, to gain insight
to a system and make predictions for the future.
Troitzsch (1997) divided prediction into two parts:
(1) qualitative prediction, which is prediction of
behavior modes, and (2) quantitative prediction,
which is to predict a certain system state in timeline.
Currently there are two major schools, System
Dynamics and Agent Based Modeling, which use
computer simulation to gain insight into non-linear
social and socio-economic systems (Milling and
Schieritz, 2003). Both approaches have a broad
overlap in research topics, but have been quite
unnoticed by each other. (Phelan, 1999)
There are only a few publications about health
care systems concerning prevention frameworks.
The health care system itself is complex and large
and it is quite hard to understand all the
dependencies and influences in this system. Because
of the constantly growing demand for preventive
cancer checkups the main purpose of this paper is to
show how to model those systems with both
approaches.
Western industrial countries are facing an over
aging of their population. This makes it necessary to
model future health care scenarios to get valid
answers to problems arising from these systems
because media seems to continuously bombard us
with one horror scenario of health care issues after
the other. For example the amount of people in
Austria above the age of 60 will grow till 2030 by
54% although the whole population will just grow
by 8% (Statistik Austria, 2007). Is this significant
increase in older people an indication requiring 50%
more medical specialists to cope the demand of
preventive medical checkup in this age group? This
is just one pressing question concerning preventive
medical checkups for the future. In this paper we
will discuss the main modeling differences of the
two approaches based on the preventive cancer
checkup process (PCCP) and give a first short
answer to the question above.
416
Martischnig A., Voessner S. and Stark G. (2009).
AGENT BASED MODELING AND SYSTEM DYNAMICS IN HEALTHCARE - Modeling Two Stage Preventive Medical Checkup Systems .
In Proceedings of the International Conference on Agents and Artificial Intelligence, pages 416-421
DOI: 10.5220/0001659404160421
Copyright
c
SciTePress
1.1 The System Dynamics Approach
System Dynamics is an approach that has been
developed by Jay W. Forrester, an electrical
engineer, in the mid 1950s and was originally called
Industrial Dynamics since the initial applications,
which he described in the book of the same title,
were all in private industry (Forrester, 1961). Later
works focused on urban dynamics (Forrester, 1969)
and on social systems, with the probably most
popular publication “Limits to growth”. (Meadows
et al). In 1983 the International System Dynamics
Society (SDS) has been established, and within it a
special interest group on health issues was organized
in 2003 (Homer and Hirsch, 2006). Although many
papers dealing with health care systems have been
published, in a variety of journals worldwide, since
then very few of them focused on prevention
frameworks. (Koelling and Schwandt, 2005)
The basic concept behind System Dynamics is
that the complex behaviors of organizational and
social systems are the result of both reinforcing and
balancing feedback mechanisms. The central
observation point when modeling a system in SD is
to describe its feedback loops, which consist of the
real-world processes, called stocks, and the flows
between these stocks. These generated computerized
models can then be used to test alternative scenarios
and policies in a systematic way to answer both
“what if” and “why” questions. (Borshchev and
Filippov, 2004), (Sterman, 2001).
1.2 The Agent Based Modeling
Approach
Agent Based Modeling (ABM) is a relatively new
computational modeling paradigm. Although it had
been developed in the late 1940s, it did not become
widespread until the 1990s, because compared to SD
significantly more computational power is required.
The increase of available and powerful
computational resources in the last years and the
inherent parallel nature of ABM approaches
contributed to their popularity. There are three
different fields of research for ABM: (1) artificial
intelligence, (2) object oriented programming and
concurrent object-based systems, and (3) human-
computer interface design (Jennings and
Wooldridge, 1998). The concept of agents can be
tracked through many different disciplines, but using
agents on designing simulation models is mainly
applied in complexity science and game theory
(Milling and Schieritz, 2003). In contrast to SD there
is no universally accepted definition of ABM and
this makes it much more difficult to identify the
basic concept and assumptions underlying this
paradigm. An Agent is basically an independent
component that has individual rules and is able to
interact with its environment or not. The behavior
can range from primitive reactive decision rules to
complex adaptive intelligence (Macal and North,
2005). The global System behavior emerges as a
result of the agents following their rules and doesn’t
need to be known at the beginning of the modeling
session.
That’s why ABM is often called bottom-up
modeling (Borshchev and Filippov, 2004). Agent
Based Modeling is used in a wide range in medical
health care but mostly to simulate patient scheduling
and workflow management (Nealon and Moreno,
2004). Estimating the medical demand of equipment
and specialists for the future is quite a new area for
ABM.
1.3 Short Comparison of the
Approaches
To characterize both approaches, the major
differences are summarized in Table 1 and described
below (Milling and Schieritz, 2003) (Stotz and
Größler, 2004).
Table 1: System Dynamics versus Agent Based Modeling.
System
Dynamics
Agent Based
Modeling
Basic building
Block
Feedback loop Agents
Level of
modeling
Macro Micro
Mathematical
formulation
Differential
equations
Logic,
Differential
equations
Perspective Top-down Bottom-up
Unit of analysis Structure Rules
The core building blocks:
The main behavior of a System Dynamics model is
generated by its interacting feedback loops that
consist of Stocks and Flows. In Agent Based Models
the behavior emerges from the interaction rules of
the Agents. These elements can therefore be
considered as the basic building blocks of their
approaches.
Level of modeling:
In macro simulations, individuals are viewed as a
structure that can be characterized by a number of
variables, whereas in micro simulations the structure
AGENT BASED MODELING AND SYSTEM DYNAMICS IN HEALTHCARE - Modeling Two Stage Preventive
Medical Checkup Systems
417
is viewed as emergent from the rules and the
interacting individuals. (Davidson, 2002)
Mathematical formulation:
The basic principle behind SD is to couple non-
linear first-order differential equations. This is done
by Levels that accumulate the difference between
the Flows (in- and outflows). In ABM there are
many diverse methodologies from logic-based to
emergent equations and that’s why no universally
accepted formalism for the mathematical description
of a model exists. (Milling and Schieritz, 2003)
Perspective:
In SD the structure of the basic system phenomenon
is modeled and in ABM this evolves in the
simulation.
Unit of analysis:
SD models behavior is determined by the structure
that is fix and has to be defined before simulation. In
ABM the focus lies on the rules an agent obeys to, to
interact with other ones.
2 THE BASIC PREVENTIVE
CANCER CHECKUP PROCESS
(PCCP)
Modern preventive cancer checkups can diagnose
cancer risks at a very early stage making necessary
treatment easier, more effective, and more efficient.
Most of the common malignant diseases, if detected
in an early stage, can successfully be cured, due to
tremendous progress in treatment possibilities.
That’s why regular checkups can prolong a healthy
life.
The basic preventive cancer checkup process that
is shown in Figure 1 can be applied to all of the
malignant diseases for example (colon cancer,
prostate cancer, gynecological tumors, skin tumors,
etc.). There is always a risk group in a population,
normally being addressed by age and gender. This
group can then be divided into two parts (percentage
R1 and R2): the ones that will never go to a
preventive medical checkup and the other ones that
go to a preventive medical checkup at least once in
their lifetime after entering the specific risk group.
Once entering the prevention path there will be a
medical checkup. If an indication for the specific
cancer is found during the checkup an intervention
will be performed and the patient will be send back
to regular preventive medical checkup after some
years (indicated by X2). If no indication is detected
the patient will also be sent back to regular
preventive medical checkup after some years
(indicated by X1). Once being in the prevention
cycle the normal mortality for the specific cancer
will decreases with a given percentage (indicated by
PI). The basic PCCP will now be applied onto the
colon carcinoma one of the most common cancer
type of men and women.
Figure 1: Basic principle of a preventive cancer checkup
process (PCCP).
To demonstrate both principles we assumed the
following standard values, taken from literature
(Citarda et al. 2000) (Barclay et al. 1993) (Barclay et
al. 2006) for the colon carcinoma prevention:
Table 2: System parameters for simulating a preventive
cancer checkup process (PCCP).
R1 R2 F1 F2 X1 X2 PI X
60
%
40% 10% 90% 7 3 80% 0,45
* 10
-3
With this given values the average year a patient
comes to the preventive medical checkup is 6.6
according to equation (1).
average year = X1 * F2 + X2 * F1 (1)
2.1 Modeling PCCP with System
Dynamics
Based on the basic PCCP process we designed a first
Causal Loop Diagram (CLD) of the system and
simulated it in Powersim Studio 2005. We split up
populations age groups into those within the risk
group and those outside. Because of the intuitive
user Interface of Powersim the model was quickly
built but the output did not quite match real systems
data because SD averaged all the Stocks
representing the age groups. Population distributions
in Western industrial countries are more like bulbs
or apples than rectangles and because of the two
ICAART 2009 - International Conference on Agents and Artificial Intelligence
418
world wars and the baby boom generation Austria’s
population distribution has two abnormal spikes.
And these two spikes are completely filtered in the
standard SD model.
So we split up the age groups into one year
groups and added both prevention cycles to the
simulation to get a more detailed output. A
simplified version of the extended basic Causal
Loop Diagram (CLD) is shown in Figure 2.
The implemented model now was an “Array
Model” with all the different probabilities for each
group and the output was qualitatively quite near to
real data.
To look at the consequences of another cancer
prevention model, for example prostate cancer, we
added a second cycle for this disease. This was
really a challenging problem because of the arrays
and global death rates and at the end we weren’t able
to complete it because of cyclic references. Both
prevention models affect the death rate of the
population and are also affected by this rate. When
you think in stock and flows you get cyclic
references between these rates. Our basic SD model
can only capture the qualitative behavior well but
lacks realistic quantitative output. The extended
model is able to produce a realistic quantitative
output but is due to the specialization not able to
handle more than one prevention model.
Figure 2: Extended basic Causal Loop Diagram (CLD).
2.2 Modeling PCCP with Agent based
Modeling
In the ABM solution we first had to decide what
defines an agent to produce an output like the real
data. So we decided to model an agent with the
basic attributes like number, age and gender and
some medical attributes we needed for the
preventive checkup process as shown in Figure 3. In
this first solution we modeled non interacting agents,
because it was not necessary for the concerning
question.
Figure 3: Population of agents with migration effects.
Before implementing the PCCP into our agent
framework we had to calibrate our agents to build up
a population that was quite similar to the real one in
each age group. That’s why we had to add
immigration, migration and fertility data to each
agent. In this case we took statistical data rates from
the past decades and added them to the framework.
This data can now be loaded from several input files
into the framework. Furthermore this attributes can
be changed in time to get a similar characteristic as
data from the past. Mortality is divided into the main
parts of the ICD-10 (International Classification of
Diseases endorsed by the WHO in 1990) code and
can also be changed in time. Due to this
classification the framework is able to handle all
different types of classified diseases. To add a
specific prevention model one first has to define the
ICD-10 category it belongs to and then add the
needed attributes to an agent. In our case this new
“disease data sheet” that is connected to an agent
contains the number of performed interventions, the
waiting period till next check is performed, the new
death probability, and so forth. Depending on the
input data that is linked to the agents they act on
probabilities each simulation period. Because this
paper is about how to model a PCCP and not about
the whole ABM framework we will not go into deep
detail this time.
Since we are looking for population effects the
number of agents that make up this population has to
be sufficiently high. There is obviously a tradeoff
between accuracy and computational effort. Agent
Based simulation can be seen as a numerical solver
to Dynamic System’s system of differential
equations. The more agents the smoother is the
integration.
In the following we will show the first results
from the ABM model to illustrate the great level of
detail our framework is able to handle. We used 1.5
AGENT BASED MODELING AND SYSTEM DYNAMICS IN HEALTHCARE - Modeling Two Stage Preventive
Medical Checkup Systems
419
million agents and 50 simulation runs to get a robust
estimate of mean and standard deviation.
The output for the PCCP with the given values
for the colon carcinoma was really astonishing for us
and is shown in the Figures 3 and 4. Although more
people are entering than leaving the risk group the
demand for preventive checkup will not grow when
we assume that the same percentage of people as
today will go to checkup in the future. This is
because most of the demand is already generated by
the people in this two stage cycle. The demand will
not grow until the prevention percentage is set up to
more than 60% and this is in fact a relatively
unrealistic scenario for the future. In Figure 4 we see
the absolute difference of people dieing from colon
cancer per year. The absolute amount of people that
could be saved due to more preventive checkups will
not dramatically fall just by doing 55% more of
these checkups. This output is really crucial when
we think about investing more money in these
preventive checkups or advertisement to increase the
amount of people going to cancer prevention.
Figure 4: ABM-Framework output for the PCCP, showing
medical checkups as a consequence of different policies.
Figure 5: ABM-Framework output for the PCCP, showing
PCCP death rates as a consequence of different policies.
3 DISCUSSION
During our modeling sessions we were able to
produce the needed output data with both modeling
techniques. Building a SD model with realistic real
life behavior was really a hard challenge, because of
the averaging effect within stocks. Despite all
difficulties we found a solution by transferring the
initial model into an "Array Model". Due to the
specialization of this model it is not possible to
simulate more than one PCCP as mentioned above.
That’s why we had to switch the modeling approach
to implement the given PCCP with ABM. After
defining the attributes and rules of an agent we
implemented our own arbitrary extendable
framework. Because of the astonishing answers for
the future demand in specialists for colon carcinoma
the framework will now be object of further
research. Integrating more cancer prevention
models, interactions between the agents like
transmissibility of diseases, word of mouth
advertising for preventive medical checkup, are just
a few work packages for the future.
In general both techniques can not be
differentiated just by modeling size because both are
capable to model small and large-scale systems.
They can rather be classified by the problem or
perspective and the required output information. One
fact that should be considered when deciding for one
technique is that with today’s modeling tools it is
much more complicated to implement a solution in
an ABM Framework, when you are not experienced
in programming, than implementing a model in one
of the intuitive graphic oriented SD tools.
Quantifying the parameters of a model is the main
difficulty both approaches have in common. In
ABM it is tough defining the rules for the agent’s
behavior and their attributes and in SD it is
sometimes quite hard to quantify or find the
correlation function between the connections of
variables. In contrast to SD ABM allows increasing
the level of detail as long as relevant data is
available but will not work when this required data
does not exist at that level of detail. The next factors
to be concerned with are computational effort,
memory management, and simulation time. SD
provides the output within a few runs lasting only
seconds depending on the method that is used to
solve the differential equations. When trying to
solve the same problem with agents one first has to
define the width of the confidence interval and then
calculate the needed runs to hit that spread. The
simulation time with our model in SD is just a few
seconds on an ordinary office computer and there is
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420
no need to worry about memory management
contrary to our ABM solution.
In general picking one or the other modeling
approach depends on the system to be simulated.
There are lots of applications where it is much easier
and efficient to solve given problems with SD but if
you want to capture more realistic real-life
phenomena you have to choose the ABM approach.
A general decision for one of the two techniques
always deals with a trade-off between efficiency and
significance.
4 CONCLUSIONS
As we could see from our simulation System
Dynamics is useful to model the basic system’s
behavior. With the causal loop diagram SD provides
a powerful tool for modeling, to describe a model
and its interactions. Combined with Vesters
sensitivity analysis
(Vester, 2005) one can easily
extract the different kinds of elements in the system
(active, reactive, buffering, critical, and neutral) to
make steering actions more efficient. A substantial
advantage of SD is the big number of available
Simulation Software and their intuitive and easy use,
when needing quick answers about a systems
behavior. Generating realistic quantitative output
data was quite a challenging problem with SD and
we could just manage it by transferring the original
model into an “Array Model” but due to the
specialization of this model it is not able to cope
with more details or other preventive checkups and
therefore we had to switch the modeling approach to
ABM.
The ABM approach took much more time to
implement, but now agents, the primary building
block, can easily be extended with more and more
details. That is why the ABM approach and our
framework can get beyond the limits of SD,
especially when the system contains active objects.
However it is difficult to decide on attributes and
rules of agents in order to get a behavior that is
sufficiently similar to the real system and it is much
more difficult to get all the data at the needed level
of detail for the simulation than just modeling the
structure of the system which is where SD ends.
Memory management restrictions still become a big
issue for the future of our framework when
simulating with millions of agents as we experienced
it in our simulation.
With the existing framework we are now able to
answer questions for the future demand of several
preventive checkup systems and we will extend the
model as mentioned above to address more crucial
questions concerning futures healthcare
management.
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