Estimation of Volume under ROC surface and Asymptotic Variance for diagnostic classifier following Rayleigh distribution

Abstract

Clinical diagnosis emphasizes the importance of assessing biomarker performance for disease screening and diagnosis. The Receiver Operating Characteristic (ROC) Curve is a crucial tool for evaluating and interpreting biomarker performance. Various models and methods have been developed to evaluate biomarkers in binary classification (i.e., Non-Diseased and Diseased). This research article aims to extend the binary classification problem to a three-class scenario, including Diseased, Suspicious, and Non-Diseased classes for Rayleigh distribution. It introduces a three-class Rayleigh ROC model based on a Parametric approach, deriving metrics such as Volume Under the ROC Surface (VUS) and Asymptotic Variance, as well as an alternative Non-Parametric approach. The model was validated using simulated data generated for the underlying distribution, and the real-life dataset was used to fit the VUS and ROC curves.