Estimation of area under the ROC curve in the framework of gamma mixtures

Receiver operating characteristic (ROC) curve is one of the well-known classification tools. There are several bi-distributional ROC models in the literature, which can be applied only when there is a prior knowledge on the class/status of the subject. If the predefined status of the subject is not known, then we need to administer a statistical methodology to identify the homogeneous components within it. Once this is done, modeling of ROC can be made, and here it is assumed that the data underlie non-normal distribution. In this paper, the need for handling non-normal data in the framework of mixture model is discussed and demonstrated using a real data set and simulation studies. It is shown that, the proposed mixGamma ROC model replaces the existing ROC models when the data is of non-normal and multi-mode.