With three ordinal diagnostic categories, the most commonly used measures for the overall diagnostic accuracy are the volume under the ROC surface (VUS) and partial volume under the ROC surface (PVUS), which are the extensions of the area under the ROC curve (AUC) and partial area under the ROC curve (PAUC), respectively. A gold standard (GS) test on the true disease status is required to estimate the VUS and PVUS. However, oftentimes it may be difficult, inappropriate, or impossible to have a GS because of misclassification error, risk to the subjects or ethical concerns. Therefore, in many medical research studies, the true disease status may remain unobservable. Under the normality assumption, a maximum likelihood (ML) based approach using the expectation-maximization (EM) algorithm for parameter estimation is proposed. Three methods using the concepts of generalized pivot and parametric/nonparametric bootstrap for confidence interval estimation of the difference in paired VUSs and PVUSs without a GS are compared. The coverage probabilities of the investigated approaches are numerically studied. The proposed approaches are then applied to a real data set of 118 subjects from a cohort study in early stage Alzheimer's disease (AD) from the Washington University Knight Alzheimer's Disease Research Center to compare the overall diagnostic accuracy of early stage AD between two different pairs of neuropsychological tests.
Keywords: EM algorithm; Generalized pivot; Gold standard; Parametric bootstrap; Volume under the ROC surface.