Basic principles of ROC analysis

The limitations of diagnostic "accuracy" as a measure of decision performance require introduction of the concepts of the "sensitivity" and "specificity" of a diagnostic test. These measures and the related indices, "true positive fraction" and "false positive fraction," are more meaningful than "accuracy," yet do not provide a unique description of diagnostic performance because they depend on the arbitrary selection of a decision threshold. The receiver operating characteristic (ROC) curve is shown to be a simple yet complete empirical description of this decision threshold effect, indicating all possible combinations of the relative frequencies of the various kinds of correct and incorrect decisions. Practical experimental techniques for measuring ROC curves are described, and the issues of case selection and curve-fitting are discussed briefly. Possible generalizations of conventional ROC analysis to account for decision performance in complex diagnostic tasks are indicated. ROC analysis is shown to be related in a direct and natural way to cost/benefit analysis of diagnostic decision making. The concepts of "average diagnostic cost" and "average net benefit" are developed and used to identify the optimal compromise among various kinds of diagnostic error. Finally, the way in which ROC analysis can be employed to optimize diagnostic strategies is suggested.