Sensitivity and specificity are used to characterize the accuracy of a diagnostic test. Receiver operating characteristic (ROC) analysis can be used more generally to plot the sensitivity versus (1-specificity) over all possible cutoff points. We develop an ROC analysis that can be applied to diagnostic tests with and without a gold standard. Moreover, the method can be applied to multiple correlated diagnostic tests that are used on the same individual. Simulation studies were performed to assess the discrimination ability of the no-gold-standard method compared with the situation where a gold standard exists. We used the area under the ROC curve (AUC) to quantify the diagnostic accuracy of tests and the difference between AUCs to compare their accuracies. In particular, we can estimate the prevalence of disease/infection under the no-gold-standard method. The method we proposed works well in the absence of a gold standard for correlated test data. Correlation affected the width of posterior probability intervals for these differences. The proposed method was used to analyze ELISA test scores for Johne’s disease in dairy cattle.