Bayesian Semiparametric ROC surface estimation under verification bias

Abstract

The Receiver Operating Characteristic (ROC) surface is a generalization of the ROC curve and is widely used for assessment of the accuracy of diagnostic tests on three categories. Verification bias occurs when not all subjects have their labels observed. This is a common problem in disease diagnosis since the gold standard test to get labels, i.e., the true disease status, can be invasive and expensive. The same situation happens in the evaluation of semi-supervised learning, where the unlabeled data are incorporated. A Bayesian approach for estimating the ROC surface is proposed based on continuous data under a semi-parametric trinormality assumption. The proposed method is then extended to situations in the presence of verification bias. The posterior distribution is computed under the trinormality assumption using a rank-based likelihood. The consistency of the posterior under a mild condition is also established. The proposed method is compared with existing methods for estimating an ROC surface. Simulation results show that it performs well in terms of accuracy. The method is applied to evaluate the performance of CA125 and HE4 in the diagnosis of epithelial ovarian cancer (EOC) as a demonstration.