Asymptotic hypothesis test to compare likelihood ratios of multiple diagnostic tests in unpaired designs

The accuracy of a binary diagnostic test is usually measured in terms of its sensitivity and its specificity. Other measures of the performance of a diagnostic test are the positive and negative likelihood ratios, which quantify the increase in knowledge about the presence of the disease through the application of a diagnostic test, and which depend on the sensitivity and specificity of the diagnostic test. In this article, we construct an asymptotic hypothesis test to simultaneously compare the positive and negative likelihood ratios of two or more diagnostic tests in unpaired designs. The hypothesis test is based on the logarithmic transformation of the likelihood ratios and on the chi-square distribution. Simulation experiments have been carried out to study the type I error and the power of the constructed hypothesis test when comparing two and three binary diagnostic tests. The method has been extended to the case of multiple multi-level diagnostic tests.