Comparison of the accuracy of multiple binary tests in the presence of partial disease verification

In the presence of partial disease verification, the comparison of the accuracy of binary diagnostic tests cannot be carried out through the paired comparison of the diagnostic tests applying McNemar's test, since for a subsample of patients the disease status is unknown. In this study, we have deduced the maximum likelihood estimators for the sensitivities and specificities of multiple binary diagnostic tests and we have studied various joint hypothesis tests based on the chi-square distribution to compare simultaneously the accuracy of these binary diagnostic tests when for some patients in the sample the disease status is unknown. Simulation experiments were carried out to study the type I error and the power of each hypothesis test deduced. The results obtained were applied to the diagnosis of coronary stenosis.