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

The meaning and use of the area under a receiver operating characteristic (ROC) curve. 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. It is shown that 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 non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) 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, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Radiology Radiological Society of North America, Inc.

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

Radiology, Volume 143 (1): 29 – Apr 1, 1982

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Publisher
Radiological Society of North America, Inc.
Copyright
Copyright © 1982 by Radiological Society of North America
ISSN
1527-1315
eISSN
0033-8419
Publisher site
See Article on Publisher Site

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. It is shown that 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 non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) 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, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.

Journal

RadiologyRadiological Society of North America, Inc.

Published: Apr 1, 1982

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