The meaning and use of the area under a receiver operating characteristic (ROC) curve.

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Abstract
A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the rating method, or by mathematical predictions based on patient characteristics, is presented. In such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen nondiseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These 2 relationships are exploited to provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve; to guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area; and to determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.

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