Multi-Class Classification using Mixtures of Univariate and Multivariate ROC Curves

Receiver Operating Characteristic (ROC) curve is one of the widely used supervised classification techniques to allocate/classify the individuals and also instrumental in comparing diagnostic tests. Generally to deal with classification problems we need to have knowledge of class labels. In most of the scenarios, data exhibit multi-model patterns in class labels which leads to multi-class classification problems.

The main aim of this study is to address the issue of constructing ROC models when there exist multi-models patterns in the class labels further, to classify the individuals for better diagnosis, and also to reduce the complexity of graphical representation of ROC curves in such classification problems.

A new version of univariate and multivariate ROC models are proposed in the framework of Finite Mixtures, due to the flexibility of identifying and modeling the subcomponents in the heterogeneous populations.

Oral Glucose Tolerance Test and Disk Hernia datasets are used and simulation studies are also performed. Results show that the proposed models possess better accuracy when compared with Bi-Normal and MROC models with reasonable low 1-Specificity and higher Sensitivity. The ROC curves are depicted in a 2D space rather than a higher dimension for multi-class classification problems.

It is suggested that before one proceeds to model ROC curves, it is better to take a look at the density patterns of the study variable(s), which in turn help in explaining the true information between the classes and also provides a good amount of “true” accuracy.