An Estimator for the Hypervolume Under the ROC Manifold

Accepted - February 2025

Abstract

Measuring the diagnostic accuracy of biomedical tests is crucial in clinical research for both diagnosis
and prognosis. For binary classification, ROC analysis and the area under the curve (AUC) are widely used. However, many real-world problems involve multiple classes, requiring extensions like the ROC manifold and the hypervolume under the manifold (HUM). This study develops a new estimator for assessing a continuous diagnostic marker’s accuracy in multi-class settings, deriving its analytical form and variance. Simulation studies compare its performance with existing methods, and an empirical application is presented.