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Archimedes
"Archimedes" is the name of a very
detailed, comprehensive, continuous simulation model of health
care developed by the Biomathematics Unit of the Kaiser Permanente's
Care Management Institute. It can be used to explore the effects
of a wide variety of health care interventions on health,
logistic and economic outcomes of major diseases in a complex
health care system. The simulation is at the level of biological,
clinical and administrative detail at which interventions
have their effects and clinical decisions are made. Potential
applications include the design of guidelines, analysis of
best practices, estimation of return on investment of care
management programs, setting of clinical targets, priority
setting, strategic goals, forecasting, design of performance
measures, and research design.
Archimedes is a powerful new tool that
can be used to answer clinical, administrative or healthcare
organization questions that cannot be addressed by clinical
trials (they would be to costly and take too much time) or
expert opinion (the human mind can't accurately sort, weigh
and integrate many variables) or other models.
Q: What is Archimedes?
A: Archimedes is a simulation model that
creates a "virtual reality" in which all the important
objects and events in the real world have corresponding objects
and events in the model's world. When a simulation model is
run, the objects interact and events occur as they would in
the real world.
Archimedes can simulate a health care
system of virtually any size.
Q: How does Archimedes differ from other models?
A: Archimedes differs from other models
in that it includes virtually all aspects of care, including
member/patients, diseases, providers, interventions, facilities,
equipment and supplies, policies and protocols, and finances.
Each of these features is included in a high level of detail,
attempting to reproduce the biological and clinical events
at the level of detail at which physicians think and clinical
management decisions are made. Archimedes is also unique in
health care in that it is a true continuous time model; any
event can occur at any time.
Archimedes has unmatched:
- Depth - for example, it approaches "blood pressure"
from the Starling curve, end diastolic volume, right atrial
pressure, mean arterial filling pressure…, etc.
- Breadth - demographics, epidemiology, biology, behavior
outcomes, logistics, costs
- Validation - reproduces clinical trials through the biology
of the disease
- Power - analyzes problems at the level of detail and flexibility
at which clinical and administrative decisions are actually
made
Q: How does Archimedes work?
A: The most innovative and powerful feature
of Archimedes is the use of differential equations to describe
the progress of disease. For each disease there are one or
more features that describe its progression. For example,
the feature that describes coronary artery disease is the
occlusion of coronary arteries. The differential equations
calculate the progression of each feature; the occurrence
of signs, symptoms and health outcomes as a function of the
feature; and the effects of interventions on the disease's
progression. The parameters of the differential equations
are calibrated with actual data so that the outcomes of the
diseases in the model match what is seen in reality. This
includes not only matching the basic epidemiology of the disease
(e.g., incidence, prevalence, morbidity and mortality rates)
but also the effects of treatments on the occurrence of symptoms
and health outcomes. To accomplish this, many of the parameters
of the equations are themselves functions of other parameters,
including not only patient characteristics (e.g., risk factors),
but also features, treatments and outcomes of other diseases.
This enables the model to address such things as co-morbidities.
Q: What are the model's advantages?
A: Archimedes creates a virtual world
in which you can "experiment" with different interventions
and/or different assumptions, either individually or in combination,
and explore the effects on all the important health, logistic,
or economic outcomes. You can specify the speed and degree
with which any intervention is implemented. For example, if
you want to estimate the maximum potential of a proposed program,
you can have practitioners and patients change their behavior
instantaneously and completely. Or if you want to simulate
more realistic scenarios, you can have their behavior change
gradually or imperfectly. Because time is sped up in this
virtual world, you can try out many different combinations
of interventions, and compare them to current practice or
to each other. You can also look into the system as deeply
as you desire, to understand not only what happens (e.g.,
"The net savings will be about $1.2 million."),
but also why it happens (e.g., the breakdown of each budget
center and which specific interventions produced which effects).
Q: What types of questions can Archimedes help answer?
A: The following are examples of the
types of questions Archimedes can help answer:
- A prominent clinic publishes a new protocol to evaluate
patients with chest pain and decides whom to admit. At the
Mayo clinic it reduced costs 30% without harming quality.
However, the protocol that was previously used at the Mayo
clinic, and against which their comparison was made, was
quite different than the way chest pain patients are currently
managed. If this new protocol were to be used in our system,
what effect would it have on our quality and cost?
- What actual difference does it make - in morbidity, mortality
and costs - if we increase by 10 percentage points the proportion
of patients who get an annual lipid profile?
- Physicians are complaining that they do not have enough
time in their brief visits to do all the things they are
asked to do. What are the five most important things for
them to concentrate on?
- A specialty society has just revised its guidelines for
a disease. What difference does it make?
- How many heart attacks in years 1, 3 and 5 will be prevented
if we lower the average HbA1C from 8.5% to 8.0%? What is
the impact on drug, office visits and hospitalization costs?
- Which of the key process measures related to diabetes
(e.g., HbA1C test, eye exam, lipid profile) will have the
greatest impact on outcomes?
- We can hire 10 new case managers next year. Should they
be put on CAD, CHF, diabetes, asthma, cancer…?
Q: Are differential equations the only type of mathematics
used in Archimedes?
A: Other formulas describe the clinical,
logistical and economic events that are set in motion by the
symptoms and outcomes of each person's disease. These formulas
are typical of regression models, decision trees, flow charts,
and accounting models. All the formulas can include person-to-person
differences, random variations, and uncertainty. Because Archimedes
is a simulation model that follows thousands of patients,
its results are subject to random variations and sampling
like those of a real clinical trial.
Q: Where does Archimedes get its data?
A: Information about the demographics
of the simulated members comes from large, existing administrative
data sets. Information about risk factors for diseases is
obtained from epidemiological studies, such as the Framingham
heart study. Models of the biology of the diseases are based
on known physiology. Information about the effects of different
treatments is obtained from clinical research. Information
about personnel, facilities and logistics is drawn from the
experience of existing medical centers. Protocols are either
copied from existing protocols or obtained from interviews
with practitioners and staff. Cost information is taken from
accounting departments.
Q: What if there are no good data on a variable?
A: Any method for making a decision
- whether it is expert judgment, a clinical consensus, administrative
intuition, or a mathematical model - is limited by the quality
of the available information. The value of a mathematical
model like Archimedes does not lie in any ability to generate
new empirical data. A model like Archimedes is valuable because
it can squeeze much more understanding from the data that
do exist.
When data are sparse, Archimedes can perform
"What if…" calculations, to determine what
would happen if certain assumptions were true. It can also
determine if the range of uncertainty about a variable makes
any difference or determine where variations in practices
make the most difference, among other valuable uses.
For long term planning, the appropriate roles
of Archimedes are:
- To estimate what would happen if all other factors remain
constant
- To estimate the effect of the intervention on outcomes
- the difference in outcomes caused by the intervention
- rather than the absolute value.
- To suggest what variables should be monitored to determine
if the model's predictions are on track
- To use that information to make the best choice possible
today, and use the results of tracking to continually improve
the choices, as new information becomes available.
- This is the best that can be done by any method for making
decisions because no method can foresee unforeseeable events.
The value of Archimedes is that it can do these four things
far better (faster and more accurately) than other methods,
such as expert judgment, or even other mathematical models.
Q: How has Archimedes been validated?
A: The core equations of the model
- those that describe the progression of diseases and how
they respond to treatments - are validated by simulating actual
clinical trials. This is a very deep validation that tests
the entire chain of events from the fundamental biology and
pathology of the disease; to the development of symptoms,
patient behavior in seeking care, performance of tests, and
delivery of treatments; to the changes in biological and health
outcomes.
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