A method of applying Bayes' theorem to diagnosis of patients who may have more than one diseases in various combinations is described. The underlying model (multiple disease model) assumes that symptom
S is a union of its subsets
Si—each caused solely by disease
Di—and that
D0 represents a base-line condition present in all people, healthy or ill, causing symptom
S0 which is unrelated to any disease. Further assumptions are that diseases, which are neither mutually exclusive nor inclusive, are independent, and that the conditional probability of
Si arising under
Di is independent of other coexisting diseases or symptoms. Thus, the likelihood ratios for any disease (whose posterior probability we would like to know), in the presence and absence of the symptoms, respectively, can be derived from the prior probabilities of all diseases, and relative frequencies of the symptom in healthy people as well as in patients each with single disease.
This method has been applied to detection of rectal cancer in an external sample of 59 patients with rectal cancer, 78 with hemorrhoid and 27 with both of these diseases, using 10 symptoms which are assumed to be independent. Of the 86 patients with rectal cancer, 74 have been correctly diagnosed as such by this method, as compared with 70 by the conventional method (single disease model). However, by the former and latter methods, 13 and 8 patients, respectively, with hemorrhoid alone have been incorrectly diagnosed as having rectal cancer. Of patients with rectal cancer, those with hemorrhoidal symptoms have shown lower probabilities of rectal cancer than those without the symptoms if the posterior probability is estimated by the conventional method.
Although this multiple disease model has been developed for automated interrogation and diagnosis system for coloproctological diseases, it may be applicable also to diagnosis of other diseases.
View full abstract