Role of Models
Mathematical models like the Archimedes Model can play an extremely important role in healthcare by helping decision makers sort through the huge amounts of information, the deep layers of complexity, and the unavoidable uncertainties, to see things that would otherwise be invisible. The information provided by models of this type enables users to make choices with a much better understanding of the potential consequences. To extract the full potential of healthcare models like the Archimedes Model in medical decision making it is necessary to understand how mathematical models work and the roles they play in scientific, engineering, economic, and social systems.
The power of mathematical models can be illustrated by considering one of the most common and simple examples, Distance = Rate * Time. Suppose you want to drive to visit a friend in a different city and you want to time your departure to arrive just before dinner. Pretend that you don’t know the equation D = R * T. How would you do it? Short of actually driving the route in advance, you couldn’t. However if you had a map, some information about speed limits, and the equation D = R * T the task would become trivial. Indeed you would be able to estimate the travel time from any location to any other location, anywhere. Navigation devices in rental cars do this millions of time a day.
Distance = Rate * Time is about as simple as a mathematical model can be, yet it has the power to melt an otherwise impossible task. How does it do that? The equation transforms the particular problem into an abstract form, manipulates it in its abstract form using the language of mathematics, and transforms the results back to the particular problem. In this way the equation answers not only the particular question - your trip to visit your friend - but all questions of that type.
This power that comes from abstracting and manipulating the essential features of a system using the language of mathematics is almost boundless. Mathematical models are used to calculate stresses in suspension bridges, predict the behaviors of buildings in earthquakes, design automobile engines, optimize delivery routes, transmit phone calls, create TV images, compute mortgages, launch satellites, calculate income taxes, fly airplanes, calculate the odds of poker hands, and millions of other things we take for granted every day. They have done for the human mind what jet engines have done for human speed and earth movers have done for human strength. Virtually every aspect of the modern world depends on mathematical models.
Clinical medicine should be no exception. It has all the attributes that have made mathematical models so helpful in other fields. Physiological pathways are extraordinarily complex. Diseases and their outcomes are probabilistic. Human behaviors and healthcare systems add additional layers of complexity and uncertainty. There are a virtually limitless number of options, choices, and decisions to be made. And the stakes are enormous. The preferred method of making decisions - clinical trials - can address only a tiny fraction of the questions decision makers face, and even when they can be used they are disruptive, are extremely expensive, take a long time, and are rapidly outdated. The other alternative -- the human mind --, for example is challenged to multiply 57.5 miles * 45 miles per hour, and can get confused by even the simplest conditional probability.
The unfortunate fact is that currently the great majority of decisions in healthcare are made with a very imperfect understanding of their consequences. At the individual level, physicians’ perceptions of their patients’ risks and the effects of treatments vary widely, with corresponding effects on practice patterns. At the population level, guidelines, performance measures, incentives, and disease management programs are launched with little if any knowledge of their potential effects.
Mathematical models can help provide the needed information for those decisions. In the same way that models can calculate how to land a probe on Mars without ever having gone there before, mathematical models can predict the effects of giving a patient a particular treatment, changing the treatment protocol in a national guideline, defining the indications for a drug, or paying physicians $50 to perform some test. Imagine the smartest possible physician, administrator or policymaker who can store and retrieve limitless amounts of information and process it at lightning speed with no errors. That’s what mathematical models can do.
In order for mathematical models to play this role in clinical medicine, they must have three main qualities.
- They need to include all of the variables that decision makers consider important. Otherwise they will fail to incorporate the experience and wisdom of those decision makers and will fail to gain their trust.
- They must represent the variables and their relationships in the same way and at the same level of realism as they are understood. This implies that the model should be structural, not statistical, and should represent things like physiological pathways as they have been discovered by the experts.
- They must demonstrate that they can reproduce what happens in reality to the extent that reality can be observed. This implies that they should be able to reproduce or predict the same clinical trials and epidemiological studies that currently provide the evidentiary anchors for clinical medicine.
These are the three qualities that drive the development and application of the Archimedes Model.
Schedule an in-depth discussion with Archimedes »