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

Abstract

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.

Trial Design and Analysis with Incomplete Paired Data

“…In ROC literature, so far many models are proposed based upon bi-distributional assumptions, such as Bi-normal (Egan, 1975), Bilognoraml (Dorfman and Alf, 1968;1969), bi-gamma (Hussain, 2012) and many more. Recently, a new type of ROC Curve is developed based upon mixture of two distributions namely Half Normal and exponential distributions and referred as Hybrid ROC Curve (Balaswamy, et al, 2015).…”