Symptom diagnosis: a comparison of mathematical models related to upper abdominal pain.

Abstract On the basis of 11 dichotomously valued attributes of upper abdominal pain, two different mathematical techniques, i.e., Bayes's Theorem and Discriminant Analysis, were used to diagnose 300 patients having one of six gastroenterological diseases. As was done in a previous study for Bayes's Theorem, Discriminant Analysis was used in an attempt to choose objectively an optimal subset of attributes from the entire set. Diagnostically, no subset was found to be superior to the entire set, though many yielded equal diagnostic accuracy. Both mathematical models were used to deduce the “superior” profiles for each disease, i.e., those profiles of attributes whose mathematical value was maximal for that disease. These “superior” profiles were compared for each mathematical model separately, using sex as a distinguishing characteristic. Diagnostic comparisons for the two mathematical models were also made over the entire 2048 possible profiles, and agreement was noted for 1417 of these. Finally the accuracy of diagnosis on the 300 patients was evaluated by comparing the number of correct and incorrect diagnoses with the numerical differences between the maximal values and the competing values of the probabilities and discriminant functions. Results showed that diagnostic accuracy increased dramatically with increases in such numerical differences.