Defining optimal cut-off points for multiple class ROC analysis: generalization of the Index of Union method

A variety of well-developed methodologies exist for the purpose of binary classification. Some of these methodologies have been extended to accommodate multi-class settings with three or even more classes. In this study, we generalize the Index of Union (IU) method, which we previously demonstrated to be more effective than other methods in binary classification. We evaluate the Generalized Index of Union (GIU) method and compare it with existing methods using both simulated and real data. The results of the comparisons demonstrated that the GIU method is an effective approach in a multitude of scenarios, including those involving high volume under the surface (VUS) values and all distributions. It is therefore recommended that the GIU method can be used to determine the optimal cut-off points in all the ROC analyses due to its structure, which does not require complex calculations and thus provides fast results.