Estimation of the area under the ROC curve for non-normal data

Abstract The Receiver Operating Characteristic curve is one of the widely used classification tools that helps in assessing the performance of the diagnostic test as well as accommodates for comparing two diagnostic tests/statistical procedures using its intrinsic and accuracy measures, such as, sensitivity; specificity, and the Area under the Curve. The conventional and standard ROC model is the Bi-normal ROC model which is based on the assumption that the test scores/marker values underlie Normal distributions. Over the years, several researchers have developed various bi-distributional ROC models where the data possess the pattern of Exponential, Gamma, the combination of Half Normal and Rayleigh, etc. However, there are many practical situations, particularly in the field of medicine, where these available distributions may not be of fit for the data at hand. In this article, we attempted to propose two new ROC models and showed that these models have a better fit and explain better accuracy than that of the existing ROC models. The work is supported by a real dataset and simulated datasets.