A Study on the Bi-Rayleigh ROC Curve Model

Receiver Operating Characteristic (ROC) curves are used to describe and compare the accuracy of diagnostic test or the ability of a continuous biomarker in discriminating between the subjects into healthy or diseased cases in medical field. The most familiar form of ROC curve is Bi-normal (Gaussian) ROC curve model, which assumes that the test scores or a monotone transformation of the test scores are from two normal populations (i.e. healthy and diseased). It may not be true all the time, it may violate the assumptions of normal distribution in some situations and also we cannot adopt the model as it is when the sample size is small. In this paper, we have proposed ROC curve model for Rayleigh distribution which can be used even when sample size is small. The properties of Bi-Rayleigh ROC model are studied and Area Under the ROC Curve (AUC) are derived. The proposed model is supported by real life example as well as simulation studies. The confidence interval for the population parameter is studied with simulation studies of varying sample sizes. It is found that Bi-Rayleigh ROC model provides better accuracy of classification than the conventional bi-normal ROC model.