The Hybrid ROC (HROC) Curve and its Divergence Measures for Binary Classification

In assessing the performance of a diagnostic test, the widely used classification technique is the Receiver Operating Characteristic (ROC) Curve. The Binormal model is commonly used when the test scores in the diseased and healthy populations follow Normal Distribution. It is possible that in real applications the two distributions are different but having a continuous density function. In this paper we considered a model in which healthy and diseased populations follow half normal and exponential distributions respectively, hence named it as the Hybrid ROC (HROC) Curve. The properties and Area under the curve (AUC) expressions were derived. Further, to measure the distance between the defined distributions, a popular divergence measure namely Kullback Leibler Divergence (KLD) has been used. Simulation studies were conducted to study the functional behavior of Hybrid ROC curve and to show the importance of KLD in classification

On the binormal predictive receiver operating characteristic curve for the joint assessment of positive and negative predictive values

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

Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves are Described by Kullback-Leibler Divergences

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Generalization of Kullback-Leibler Divergence for Multi-Stage Diseases: Application to Diagnostic Test Accuracy and Optimal Cut-Points Selection Criterion

The Kullback-Leibler divergence (KL), which captures the disparity between two distributions, has been considered as a measure for determining the diagnostic performance of an ordinal diagnostic test. This study applies KL and further generalizes it to comprehensively measure the diagnostic accuracy test for multi-stage (K \u3e 2) diseases, named generalized total Kullback-Leibler divergence (GTKL). Also, GTKL is proposed as an optimal cut-points selection criterion for discriminating subjects among different disease stages. Moreover, the study investigates a variety of applications of GTKL on measuring the rule-in/out potentials in the single-stage and multi-stage levels. Intensive simulation studies are conducted to compare the performance of GTKL and other diagnostic accuracy measures, such as generalized Youden index (GYI), hypervolume under the manifold (HUM), and maximum absolute determinant (MADET). Furthermore, a comprehensive analysis of a real dataset is performed to illustrate the application of the proposed measure