Bayesian analysis versus discriminant function analysis: their relative utility in the diagnosis of coronary disease
Both Bayesian analysis assuming independence and discriminant function analysis have been used to estimate probabilities of corodary disease. To compare their relative accuracy, we submitted 303 subjects referred for coronary angiography to stress electrocardiography, thallium scintigraphy, and cine fluoroscopy. Severe angiographic disease was defined as at least one greater than 50% occlusion of a major vessel. Four calculations were done: (1) Bayesian analysis using literature estimates of
... ure estimates of pretest probabilities, sensitivities, and specificities was applied to the clinical and test data of a randomly selected subgroup (group I, 151 patients) to calculate posttest probabilities. (2) Bayesian analysis using literature estimates of pretest probabilities (but with sensitivities and specificities derived from the remaining 152 subjects [group II]) was applied to group I data to estimate posttest probabilities. (3) A discriminant function with logistic regression coefflcients derived from the clinical and test variables of group II was used to calculate posttest probabilities of group I. (4) A discriminant function derived with the use of test results from group II and pretest probabilities from the literature was used to calculate posttest probabilities of group I. Receiver operating characteristic curve analysis showed that all four calculations could equivalently rank the disease probabilities for our patients. A goodness-of-fit analysis suggested the following relationship between the accuracies of the four calculations: (1) < (2)-(4) < (3). Our results suggest that data-based discriminant functions are more accurate than literature-based Bayesian analysis assuming independence in predicting severe coronary disease based on clinical and noninvasive test results. The accuracy of the Bayesian method is degraded by the assumption of independence and perhaps more importantly by the use of sensitivities and specificities derived from other patient populations with different testing protocols. Circulation 73, No. 5, 970-977, 1986. BAYES' THEOREM with conditional independ-ence1-7 and discriminant function analysis'-3 have From the Cleveland Clinic Foundation, Cleveland.