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Peirce, Youden, and Receiver Operating Characteristic Curves

In 1884 Charles Sanders Peirce introduced two measures for evaluating predictions of a binary outcome, “the science of the method” and the “utility of the method.” In modern terminology, the former corresponds to the Youden index and the latter corresponds to the expected utility. The maximum of each measure is a commonly used criterion for the optimal point on a receiver operating characteristic curve that summarizes performance when predictions of a binary outcome are based on a continuous result.