Interval estimation for the difference in paired areas under the ROC curves in the absence of a gold standard test

Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve (AUC). A gold standard (GS) test on the true disease status is required to estimate the AUC. However, a GS test may sometimes be too expensive or infeasible. Therefore, in many medical research studies, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, using the expectation-maximization (EM) algorithm in conjunction with a bootstrap method, we propose a maximum likelihood-based procedure for the construction of confidence intervals for the difference in paired AUCs in the absence of a GS test. Simulation results show that the proposed interval estimation procedure yields satisfactory coverage probabilities and interval lengths. The proposed method is illustrated with two examples.