Bayesian bootstrap inference for the receiver operating characteristic surface

Abstract

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, and 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 ROC surface (VUS). The proposed method is based on a simple, yet interesting, representation of the ROC surface in terms of placement variables and has the appealing feature of producing point and interval estimates for the ROC surface and its corresponding VUS in a single integrated framework. 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.