Confidence Intervals for Differences Between Volumes Under ROC Surfaces and Generalized Youden Indices

Receiver Operating Characteristic (ROC) surfaces are used in three-class diagnostic testing especially in settings were an ordering between classes exists. The ROC surface is a 3D plot of the true-class fractions for the classes under study over all possible threshold values (c1 and c2, with c1 less than c2) of a diagnostic marker. To evaluate the discriminatory ability of a marker we summarize the information of an ROC surface into a single global index. The Volume Under the ROC surface (VUS) and the Generalized Youden Index (GYI) are two such indices. For the comparison of diagnostic markers the difference between VUSs or the difference between GYIs can be considered. We describe and compare parametric and nonparametric methods for inference based on the difference between VUSs and GYIs in a paired setting where all subjects under study undergo two diagnostic tests and interest lies in comparing these diagnostic tests. Parametric methods include the use of the asymptotic delta method under normality or after applying the Box-Cox transformation for data normalization, and the use of Generalized Pivotal Quantities. Different variants of these methods are studied. Nonparametric methods involve empirical estimation and kernel smoothing. We compare methods through extensive simulations and discuss an application