Null Distribution of Volume Under Ordered Three-Class ROC Surface (VUS) With Continuous Measurements

Receiver operating characteristic (ROC) analysis has become an indispensable tool in medical care, with a major application to characterizing the performance of binary diagnostic tests in clinical practice. In many circumstances, however, the diagnostic test has three outcomes, that is, the abnormalities are two sided. To deal with this scenario, this letter develops a recursive algorithm for computing the exact null distribution of the volume under the ordered three-class ROC surface (VUS) for samples following continuous distributions. Based on the asymptotic normality, an approximately normal distribution with exact mean and variance is also proposed, which is hoped to be useful for large-sample scenarios. Moreover, an efficient rank-based formula, in linearithmic time, is established for nonparametric estimation of VUS. Monte Carlo simulations verify the usefulness of the theoretical and algorithmic findings in this letter.