An empirical likelihood confidence interval for the volume under ROC surface

ROC surface analysis was recently developed as an extension of ROC curve analysis to accommodate tests with three outcomes. The volume under ROC surface (VUS) is the most commonly used summary measure of the diagnostic accuracy of a test. In this paper, we develop an empirical likelihood approach for the inference on VUS. First we define an empirical likelihood ratio for VUS and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood confidence interval for VUS. A small simulation study as well as analysis of a real example is also presented in this paper.