W A Benish1. 1. Department of Internal Medicine, Case Western Reserve University, Cleveland, OH, USA. wab4@po.cwru.edu
Abstract
OBJECTIVES: The purpose of this communication is to demonstrate the use of "information graphs" as a means of characterizing diagnostic test performance. METHODS: Basic concepts in information theory allow us to quantify diagnostic uncertainty and diagnostic information. Given the probabilities of the diagnoses that can explain a patient's condition, the entropy of that distribution is a measure of our uncertainty about the diagnosis. The relative entropy of the posttest probabilities with respect to the pretest probabilities quantifies the amount of information gained by diagnostic testing. Mutual information is the expected value of relative entropy and, hence, provides a measure of expected diagnostic information. These concepts are used to derive formulas for calculating diagnostic information as a function of pretest probability for a given pair of test operating characteristics. RESULTS: Plots of diagnostic information as a function of pretest probability are constructed to evaluate and compare the performance of three tests commonly used in the diagnosis of coronary artery disease. The graphs illustrate the critical role that the pretest probability plays in determining diagnostic test information. CONCLUSIONS: Information graphs summarize diagnostic test performance and offer a way to evaluate and compare diagnostic tests.
OBJECTIVES: The purpose of this communication is to demonstrate the use of "information graphs" as a means of characterizing diagnostic test performance. METHODS: Basic concepts in information theory allow us to quantify diagnostic uncertainty and diagnostic information. Given the probabilities of the diagnoses that can explain a patient's condition, the entropy of that distribution is a measure of our uncertainty about the diagnosis. The relative entropy of the posttest probabilities with respect to the pretest probabilities quantifies the amount of information gained by diagnostic testing. Mutual information is the expected value of relative entropy and, hence, provides a measure of expected diagnostic information. These concepts are used to derive formulas for calculating diagnostic information as a function of pretest probability for a given pair of test operating characteristics. RESULTS: Plots of diagnostic information as a function of pretest probability are constructed to evaluate and compare the performance of three tests commonly used in the diagnosis of coronary artery disease. The graphs illustrate the critical role that the pretest probability plays in determining diagnostic test information. CONCLUSIONS: Information graphs summarize diagnostic test performance and offer a way to evaluate and compare diagnostic tests.