**Gareth Hughes**

SRUC, Scotland's Rural College, The King's Buildings, Edinburgh EH9 3JG, UK; gareth.hughes@sruc.ac.uk

Received: 23 March 2020; Accepted: 5 May 2020; Published: 26 May 2020

**Abstract:** The predictive receiver operating characteristic (PROC) curve is a diagrammatic format with application in the statistical evaluation of probabilistic disease forecasts. The PROC curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for evaluation using metrics defined conditionally on the outcome of the forecast rather than metrics defined conditionally on the actual disease status. Starting from the binormal ROC curve formulation, an overview of some previously published binormal PROC curves is presented in order to place the PROC curve in the context of other methods used in statistical evaluation of probabilistic disease forecasts based on the analysis of predictive values; in particular, the index of separation (PSEP) and the leaf plot. An information theoretic perspective on evaluation is also outlined. Five straightforward recommendations are made with a view to aiding understanding and interpretation of the sometimes-complex patterns generated by PROC curve analysis. The PROC curve and related analyses augment the perspective provided by traditional ROC curve analysis. Here, the binormal ROC model provides the exemplar for investigation of the PROC curve, but potential application extends to analysis based on other distributional models as well as to empirical analysis.

**Keywords:** diagnostic test; evaluation; ROC curve; PROC curve; binormal; prevalence; positive predictive value; negative predictive value; Bayes' rule; leaf plot; expected mutual information
