Interval Estimation and Inferential Procedures for the Measures of Hybrid Roc (HROC) Curve

The Receiver Operating Characteristic (ROC) Curve originated during Second World War to analyse radar signals by observing the relationship between signal and noise [1]. The framework of ROC Curve has a wide spread of interdisciplinary applications such as human perception, decision making [2], industrial quality control [3], military monitoring [4] etc. In later years, the applications of ROC Curve branched to many other fields such as experimental psychology, engineering, machine learning, biosciences etcetera [5]. Leo Lusted [6] introduced the concept of ROC Curve analysis into medicine for analysing radiographic images. Smoothed ROC Curves were fitted when the populations have certain probability distribution, such as Binormal and BiLogistic models [2]. Further, Maximum Likelihood Estimation of ROC Curve from categorical confidence rating data was first used by Dorfman & Alf [7] based on the conventional Binormal model. In particular, the conventional Binormal ROC Curve and its extension to continuously distributed data have been applied successfully to a wide variety of problems in Radiology [8,9]. The Binormal model assumes independent Normal distributions with different population means and variances, other models considered in the literature include Bi-Logistic [10], BiExponential model [11]. Campbell & Ratnaparkhi [12] derived an ROC model by considering that the rating data follows Lomax Distribution. Further, Dorfman et. al. [13] proposed a model which assumes Gamma Distributions.