Diagnosis with Dependent Symptoms: Bayes Theorem and the Analytic Hierarchy Process

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Abstract
Judgments are needed in medical diagnosis to determine what tests to perform given certain symptoms. For many diseases, what information to gather on symptoms and what combination of symptoms lead to a given disease are not well known. Even when the number of symptoms is small, the required number of experiments to generate adequate statistical data can be unmanageably large. There is need in diagnosis for an integrative model that incorporates both statistical data and expert judgment. When statistical data are present but no expert judgment is available, one property of this model should be to reproduce results obtained through time honored procedures such as Bayes theorem. When expert judgment is also present, it should be possible to combine judgment with statistical data to identify the disease that best describes the observed symptoms. Here we are interested in the Analytic Hierarchy Process (AHP) framework that deals with dependence among the elements or clusters of a decision structure to combine statistical and judgmental information. It is shown that the posterior probabilities derived from Bayes theorem are part of this framework, and hence that Bayes theorem is a sufficient condition of a solution in the sense of the AHP. An illustration is given as to how a purely judgment-based model in the AHP can be used in medical diagnosis. The application of the model to a case study demonstrates that both statistics and judgment can be combined to provide diagnostic support to medical practitioner colleagues with whom we have interacted in doing this work.

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