Exact Probability Distribution for the ROC Area under Curve

SIMPLE SUMMARY: This contribution allows for the computation of exact p-values and for conducting accurate statistical hypothesis tests of ROC AUC-values. As a result, the development of diagnostic tests is facilitated. This work is illustrated via simulated data and through the development of proteomic blood biomarkers for the early detection of cancer. ABSTRACT: The Receiver Operating Characteristic (ROC) is a de facto standard for determining the accuracy of in vitro diagnostic (IVD) medical devices, and thus the exactness in its probability distribution is crucial toward accurate statistical inference. We show the exact probability distribution of the ROC AUC-value, hence exact critical values and p-values are readily obtained. Because the exact calculations are computationally intense, we demonstrate a method of geometric interpolation, which is exact in a special case but generally an approximation, vastly increasing computational speeds. The method is illustrated through open access data, demonstrating superiority of 26 composite biomarkers relative to a predicate device. Especially under correction for testing of multiple hypotheses, traditional asymptotic approximations are encumbered by considerable imprecision, adversely affecting IVD device development. The ability to obtain exact p-values will allow more efficient IVD device development.