Comparing the likelihood ratios of two binary diagnostic tests in the presence of partial verification

The comparison of the efficiency of two binary diagnostic tests requires one to know the disease status for all patients in the sample, by applying a gold standard. In two-phase studies the gold standard is not applied to all patients in a sample, and the problem of partial verification of the disease arises. At present, one of the approaches most used for comparing two binary diagnostic tests are the likelihood ratios. In this study, the maximum likelihood estimators of likelihood ratios are obtained. The tests of hypothesis to compare the likelihood ratios of two binary diagnostic tests when both are applied to the same random sample in the presence of verification bias are deduced, and simulation experiments are performed in order to investigate the asymptotic behaviour of the tests of hypothesis. The results obtained have been applied to the study of Alzheimer's disease.