  Accurate diagnosis of disease is of great importance in clinical practice and
medical research. The receiver operating characteristic (ROC) surface is a
popular tool for evaluating the discriminatory ability of continuous diagnostic
test outcomes when there exist three ordered disease classes (e.g., no disease,
mild disease, advanced disease). We propose the Bayesian bootstrap, a fully
nonparametric method, for conducting inference about the ROC surface and its
functionals, such as the volume under the surface. The proposed method is based
on a simple, yet interesting, representation of the ROC surface in terms of
placement variables. Results from a simulation study demonstrate the ability of
our method to successfully recover the true ROC surface and to produce valid
inferences in a variety of complex scenarios. An application to data from the
Trail Making Test to assess cognitive impairment in Parkinson's disease
patients is provided.
