Diagnosis with dependent symptoms: Bayes theorem and the analytic hierarchy process

Judgments are needed in medical diagnosis to determine what tests to perfor m given certain symptoms. For many diseases, what information to gather on symptoms and what combination of symptoms lead to a given disease are not w ell known. Even when the number of symptoms is small, the required number o f experiments to generate adequate statistical data can be unmanageably lar ge. There is need in diagnosis for an integrative model that incorporates b oth 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 co mbine judgment with statistical data to identify the disease that best desc ribes the observed symptoms. Here we are interested in the Analytic Hierarc hy Process (AHP) framework that deals with dependence among the elements or clusters of a decision structure to combine statistical and judgmental inf ormation. It is shown that the posterior probabilities derived from Bayes t heorem are part of this framework, and hence that Bayes theorem is a suffic ient condition of a solution in the sense of the AHP. An illustration is gi ven as to how a purely judgment-based model in the AHP can be used in medic al diagnosis. The application of the model to a case study demonstrates tha t both statistics and judgment can be combined to provide diagnostic suppor t to medical practitioner colleagues with whom we have interacted in doing this work.