Alternative Summary Indices for the Receiver Operating Characteristic Curve

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The receiver operating characteristic curve (ROC) and its associated summary index, the area under the curve (AUC), have recently found an increasingly popular place in medical diagnosis and population screening surveys. Nevertheless, the index may erroneously rate a perfect or nearly perfect marker as having no diagnostic or screening value. In this paper, we propose two new summary indices, the projected length of the ROC curve (PLC) and the area swept out by the ROC curve (ASC), to summarize the ROC curve. Like the conventional AUC, these new indices both have clear probabilistic interpretations and are easily defined geometrically. In addition, they do not suffer from the shortcoming of the AUC. These properties render them good alternatives for evaluating the overall performance of a diagnostic or screening test.

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