Bayesian ROC surface estimation under verification bias

Abstract: The Receiver Operating Characteristic (ROC) surface is a generalization of ROC curve and is widely used for assessment of the accuracy of diagnostic tests on three categories. A complication called the verification bias, meaning that not all subjects have their true disease status verified often occur in real application of ROC analysis. This is a common problem since the gold standard test, which is used to generate true disease status, can be invasive and expensive. In this paper, we will propose a Bayesian approach for estimating the ROC surface based on continuous data under a semi-parametric trinormality assumption. Our proposed method often adopted in ROC analysis can also be extended to situation in the presence of verification bias. We compute the posterior distribution of the parameters under trinormality assumption by using a rank-based likelihood. Consistency of the posterior under mild conditions is also established. We compare our method with the existing methods for estimating ROC surface and conclude that our method performs well in terms of accuracy.