A non-inferiority test for diagnostic accuracy in the absence of the golden standard test based on the paired partial areas under receiver operating characteristic curves

Non-inferiority tests are often measured for the diagnostic accuracy in medical research. The area under the receiver operating characteristic (ROC) curve is a familiar diagnostic measure for the overall diagnostic accuracy. Nevertheless, since it may not differentiate the diverse shapes of the ROC curves with different diagnostic significance, the partial area under the ROC (PAUROC) curve, another summary measure emerges for such diagnostic processes that require the false-positive rate to be in the clinically interested range. Traditionally, to estimate the PAUROC, the golden standard (GS) test on the true disease status is required. Nevertheless, the GS test may sometimes be infeasible. Besides, in a lot of research fields such as the epidemiology field, the true disease status of the patients may not be known or available. Under the normality assumption on diagnostic test results, based on the expectation-maximization algorithm in combination with the bootstrap method, we propose the heuristic method to construct a non-inferiority test for the difference in the paired PAUROCs without the GS test. Through the simulation study, although the proposed method might provide a liberal test, as a whole, the empirical size of the proposed method sufficiently controls the size at the significance level, and the empirical power of the proposed method in the absence of the GS is as good as that of the non-inferiority in the presence of the GS. The proposed method is illustrated with the published data.