Comparison of the likelihood ratios of two binary diagnostic tests in paired designs

The performance of two binary diagnostic tests is traditionally compared by their respective sensitivities and specificities. Other measures to describe the performance of a binary diagnostic test are likelihood ratios, defined as the ratio between the likelihood of a diagnostic test result in a group of diseased patients and the likelihood of a diagnostic test result in a group of non-diseased patients. In this study, we propose a method, based on the log-transformation of the ratio of the likelihood ratios, to compare the likelihood ratios of two binary diagnostic tests in paired designs. We have deduced hypothesis tests to compare the likelihood ratios and we have carried out simulation experiments to study the power and the type I error of the hypothesis tests deduced. We have also deduced a joint hypothesis test to simultaneously compare the likelihood ratios. The procedure used has been extended to the situation in which more than two binary diagnostic tests are applied to the same sample, and the situation in which two diagnostic tests with multilevel results are compared.