Hughes Gareth, Kopetzky Jennifer, McRoberts Neil
SRUC (Scotland's Rural College), The King's Buildings, Edinburgh EH9 3JG, UK.
Department of Plant Pathology, University of California, Davis, CA 95616, USA.
Entropy (Basel). 2020 Aug 26;22(9):938. doi: 10.3390/e22090938.
The predictive receiver operating characteristic (PROC) curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for the evaluation of binary diagnostic tests using metrics defined conditionally on the outcome of the test rather than metrics defined conditionally on the actual disease status. Application of PROC curve analysis may be hindered by the complex graphical patterns that are sometimes generated. Here we present an information theoretic analysis that allows concurrent evaluation of PROC curves and ROC curves together in a simple graphical format. The analysis is based on the observation that mutual information may be viewed both as a function of ROC curve summary statistics (sensitivity and specificity) and prevalence, and as a function of predictive values and prevalence. Mutual information calculated from a 2 × 2 prediction-realization table for a specified risk score threshold on an ROC curve is the same as the mutual information calculated at the same risk score threshold on a corresponding PROC curve. Thus, for a given value of prevalence, the risk score threshold that maximizes mutual information is the same on both the ROC curve and the corresponding PROC curve. Phytopathologists and clinicians who have previously relied solely on ROC curve summary statistics when formulating risk thresholds for application in practical agricultural or clinical decision-making contexts are thus presented with a methodology that brings predictive values within the scope of that formulation.
预测性受试者工作特征（PROC）曲线与更为知名的受试者工作特征（ROC）曲线不同，在于它为使用基于测试结果有条件定义的指标而非基于实际疾病状态有条件定义的指标来评估二元诊断测试提供了基础。PROC曲线分析的应用可能会受到有时产生的复杂图形模式的阻碍。在此，我们提出一种信息理论分析方法，该方法允许以简单的图形格式同时评估PROC曲线和ROC曲线。该分析基于这样的观察结果：互信息既可以看作是ROC曲线汇总统计量（敏感性和特异性）及患病率的函数，也可以看作是预测值及患病率的函数。在ROC曲线上针对指定风险评分阈值从2×2预测 - 实现表计算出的互信息与在相应PROC曲线上相同风险评分阈值处计算出的互信息相同。因此，对于给定的患病率值，使互信息最大化的风险评分阈值在ROC曲线和相应的PROC曲线上是相同的。以前在为实际农业或临床决策制定背景下制定应用风险阈值时仅依赖ROC曲线汇总统计量的植物病理学家和临床医生，因此有了一种将预测值纳入该制定范围的方法。
