Assessing multiple-group diagnostic problems with multi-dimensional receiver operating characteristic surfaces:...

We present the multi-dimensional Receiver Operating Characteristic (ROC) surface, a plot of the true classification rates of tests based on levels of biological markers, for multi-group discrimination, as an extension of the ROC curve, commonly used in two-group diagnostic testing. The volume under this surface (VUS) is a global accuracy measure of a test to classify subjects in multiple groups and useful to detect trends in marker measurements. We used three-dimensional ROC surfaces, and associated VUS, to discriminate between HIV-negative (NEG), HIV-positive neurologically asymptomatic (NAS) subjects and patients with AIDS demential complex (ADC), using brain metabolites measured by proton MRS. These were ratios of markers of inflammation, Choline (Cho) and myoinositol (MI), and brain injury, N-acetyl aspartate (NAA), divided by Creatine (Cr), measured in the basal ganglia and the frontal white matter. Statistically significant trends were observed in the three groups with respect to MI/Cr (VUS=0.43; 95% confidence interval (CI) 0.33-0.53), Cho/Cr (0.36; 0.27-0.45) in the basal ganglia and NAA/Cr in the frontal white matter (FWM) (0.29; 0.20-0.38), suggesting a continuum of injury during the neurologically asymptomatic stage of HIV infection, particularly with respect to brain inflammation. Adjusting for age increased the combined classification accuracy of age and NAA/Cr (p=0.053). Pairwise comparisons suggested that neuronal damage associated with NAA/Cr decreases was mainly observed in individuals with ADC, raising issues of synergism between HIV infection and age and possible acceleration of neurological deterioration in an aging HIV-positive population. The three-dimensional ROC surface and its associated VUS are useful for assessing marker accuracy, detecting data trends and offering insight in disease processes affecting multiple groups.