Accurate likelihood inference for the volume under the ROC surface

With three ordered diagnostic categories, the volume under the receiver operating characteristic (ROC) surface, which is the extension of the area under the ROC curve for binary diagnostic outcomes, is the most commonly used measure for the overall diagnostic accuracy. For a continuous-scale diagnostic test, classical likelihood-based inference about the area under the ROC curve can be inaccurate, in particular when the sample size is small, and higher order inferential procedures have been proposed.

The goal of this paper is to illustrate higher order likelihood procedures for parametric inference in small samples, which provide accurate point estimates and confidence intervals for the volume under the ROC surface.

Simulation studies are performed in order to illustrate the accuracy of the proposed methodology, and two applications to real data are discussed.

We show that likelihood modern inference provide refinements to classical inferential results. Furthermore, the freely available R package likelihoodAsy makes now their use almost automatic.

Modern likelihood inference based on higher-order asymptotic methods for the area under the ROC surface provide refinements to classical inferential results. A possible limitation of higher-order asymptotic methods for practical use is that their software implementation can be awkward. Nevertheless, use of the freely available R package likelihoodAsy makes such implementation straightforward.