Mutual Information as an Index of Diagnostic Test Performance

Abstract

This paper demonstrates that diagnostic test performance can be quantified as the average amount of information the test result (R) provides about the disease state (D). A fundamental concept of information theory, mutual information, is directly applicable to this problem. This statistic quantifies the amount of information that one random variable contains about another random variable. Prior to performing a diagnostic test, R and D are random variables. Hence, their mutual information, I(D;R), is the amount of information that R provides about D. I(D;R) is a function of both 1). the pretest probabilities of the disease state and 2). the set of conditional probabilities relating each possible test result to each possible disease state. The area under the receiver operating characteristic curve (AUC) is a popular measure of diagnostic test performance which, in contrast to I(D;R), is independent of the pretest probabilities; it is a function of only the set of conditional probabilities. The AUC is not a measure of diagnostic information. Because I(D;R) is dependent upon pretest probabilities, knowledge of the setting in which a diagnostic test is employed is a necessary condition for quantifying the amount of information it provides. Advantages of I(D;R) over the AUC are that it can be calculated without invoking an arbitrary curve fitting routine, it is applicable to situations in which multiple diagnoses are under consideration, and it quantifies test performance in meaningful units (bits of information).