An Integrated Bayesian Nonparametric Approach for Stochastic and Variability Orders in ROC Curve Estimation: An Application to Endometriosis Diagnosis

In this article, we proposed an integrated modeling approach for ROC curves that jointly accounts for stochastic and variability orders. The stochastic order constrains the distributional centers of the diseased and healthy populations within a test, while the variability order constrains the distributional spreads of the tests within each of the populations.

Under a Bayesian nonparametric framework, we used features of the Dirichlet process mixture to incorporate these order constraints in a natural way. We applied the proposed approach to data from the Physician Reliability Study that investigated the accuracy of diagnosing endometriosis using different clinical information. To address the issue of no gold standard in the real data, we used a sensitivity analysis approach that exploited diagnosis from a panel of experts.