ROC Analysis in Diagnostic Medicine

Abstract

The Receiver Operating Characteristic (ROC) curve and Area Under the ROC Curve (AUC) are effective statistical tools for evaluating the accuracy of diagnostic tests for binary-class medical data. However, many real-world biomedical problems involve more than two categories. The Volume Under the ROC Surface (VUS) and Hypervolume Under the ROC Manifold (HUM) measures are extensions for AUC under three-class and multiple-class models. Inference methods for such measures have been proposed recently. In this thesis, we propose rigorous and automated approaches to sort the multiple categories for HUM by using simple summary statistics such as means. We also supply a general discussion on the minimum acceptable HUM values in multiple-category classification problems. Furthermore, we explore statistical methods of combining multiple tests for multiple-category classification to optimize the accuracy of the combined markers under the criteria of ROC measures. Our works in this thesis provide insights on screening among large number of tests in health science studies.