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This chapter introduces medical professionals to basic stochastic models that combine economics with probability theory, and illustrates their use in medical decision making. The focus will be on the development and application of models that can be applied to mammography and other areas of medical imaging. In the interest of brevity, all models developed in this chapter will be referred to as probability models. Two specific applications of probability modeling are considered. The first concerns the determination of an optimal threshold value used to declare a patient to be positive or negative for a disease or condition. In this case, it is assumed that information contained on an image is converted to numerical output falling on a continuous scale. Signal detection theory will form the basis of the resulting modeling activity. In the second application, a medical testing system consisting of a combination of screening tests and diagnostic tests, each generating a categorical outcome, is considered. The medical tests may include human visual inspections, or computer-assisted visual inspections, or both. In this case, Bayes' theorem and principles of mathematical expectation are used to build models that allow for the determination of configurations that optimize system performance from a societal viewpoint. The intended audience includes clinical laboratory administrators as well as researchers involved in the development of computer software, algorithms, and enhancement methods to improve performance of medical imaging systems. While the specific examples will concern the use of CAD systems that test for breast cancer, the methods apply equally well to the analysis of other technological innovations in medical imaging. In medical testing for the detection of diseases and in the use of medical imaging to identify abnormalities, the decision maker must take into account a variety of costs and probabilities that influence the design of an optimal process management system. For example, Kaminsky et al. considered the design of a clinical laboratory for the detection of abnormal cells that could be associated with cervical cancer, with a focus on automated rescreening systems. Here, the decision maker would be evaluating a number of alternative system configurations that result from the choice of the number of multiple independent inspections by cytotechnologists, whether or not automated rescreening is performed (and under what conditions), and whether or not a pathologist inspects all slides or just those found to be positive by a cytotechnologist. In a related paper, Kaminsky et al. used probability models to show that the 10% rescreening rule mandated by the Federal Government's Clinical Laboratory Improvement Act of 1988 would add cost without improving system performance.
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