Abstract

The first step when evaluating a diagnostic test is to determine the variation in its values across different disease groups. In the three-class disease setting, the volume under the receiver characteristic surface (VUS) and the three-class Youden index (YI) are the commonly used summary measures of a test’s discriminatory ability. However, these measures are only appropriate under a stochastic ordering assumption for the distributions of test outcomes in the three groups. This assumption is stringent, not always plausible, particularly when covariates are involved. Violating this assumption can lead to incorrect conclusions about a test’s performance to distinguish between the three classes. To address this, we propose the underlap coefficient, study its properties, as well as its relationship with the VUS and YI when a stochastic order is enforced. We further propose Bayesian nonparametric estimators for both the unconditional underlap coefficient and for its covariate-specific version. A simulation study reveals a good performance of the proposed estimators across a range of conceivable scenarios. We also illustrate the proposed approach with an application to an Alzheimer’s disease (AD) dataset to assess how different potential AD biomarkers distinguish between individuals with normal cognition, mild impairment, and dementia, and how age and gender impact this discriminatory ability.