| Summary: | The predictive receiver operating characteristic (PROC) curve differs from the more<br />well-known receiver operating characteristic (ROC) curve in that it provides a basis for the<br />evaluation of binary diagnostic tests using metrics defined conditionally on the outcome of the test<br />rather than metrics defined conditionally on the actual disease status. Application of PROC curve<br />analysis may be hindered by the complex graphical patterns that are sometimes generated. Here<br />we present an information theoretic analysis that allows concurrent evaluation of PROC curves and<br />ROC curves together in a simple graphical format. The analysis is based on the observation that<br />mutual information may be viewed both as a function of ROC curve summary statistics (sensitivity<br />and specificity) and prevalence, and as a function of predictive values and prevalence. Mutual<br />information calculated from a 2 × 2 prediction-realization table for a specified risk score threshold<br />on an ROC curve is the same as the mutual information calculated at the same risk score threshold<br />on a corresponding PROC curve. Thus, for a given value of prevalence, the risk score threshold that<br />maximizes mutual information is the same on both the ROC curve and the corresponding PROC<br />curve. Phytopathologists and clinicians who have previously relied solely on ROC curve summary<br />statistics when formulating risk thresholds for application in practical agricultural or clinical<br />decision-making contexts are thus presented with a methodology that brings predictive values<br />within the scope of that formulation.
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