A parametric comparison of diagnostic accuracy with three ordinal diagnostic groups

Many medical diagnostic studies involve three ordinal diagnostic groups in which the diagnostic accuracy can be summarized by the volume or partial volume under a Receiver Operating Characteristic (ROC) surface. We study in this paper the statistical comparison of diagnostic accuracy from multiple diagnostic tests when three ordinal diagnostic groups are involved. Under the assumption that the multiple diagnostic tests follow a multivariate normal distribution within each diagnostic group, we provide the asymptotic variance and covariance for the maximum likelihood estimates of the volumes under the ROC surfaces from multiple diagnostic tests and propose statistical tests to test whether the diagnostic accuracy as measured by the volume under the ROC surface is the same for multiple diagnostic tests. We also propose a confidence interval estimate to the difference of two volumes under two ROC surfaces. Our approach depends crucially on the assumptions of normal distributions on diagnostic tests, which might not be robust when such assumptions are violated. Finally, we apply our proposed methodology to a real data set of 118 subjects to compare the diagnostic accuracy of early stage Alzheimer's disease (AD) from multiple neuropsychological tests.