Nonparametric Bayesian estimation of the three-way receiver operating characteristic surface

We describe a nonparametric Bayesian approach for estimating the three-way ROC surface based on mixtures of finite Polya trees (MFPT) priors. Mixtures of finite Polya trees are robust models that can handle nonstandard features in the data. We address the difficulties in modeling continuous diagnostic data with skewness, multimodality, or other nonstandard features, and how parametric approaches can lead to misleading results in such cases. Robust, data-driven inference for the ROC surface and for the volume under the ROC surface is obtained. A simulation study is performed to assess the performance of the proposed method. Methods are applied to data from a magnetic resonance spectroscopy study on human immunodeficiency virus patients.