Comparing diagnostic tests: a simple graphic using likelihood ratios

The diagnostic abilities of two or more diagnostic tests are traditionally compared by their respective sensitivities and specificities, either separately or using a summary of them such as Youden's index. Several authors have argued that the likelihood ratios provide a more appropriate, if in practice a less intuitive, comparison. We present a simple graphic which incorporates all these measures and admits easily interpreted comparison of two or more diagnostic tests. We show, using likelihood ratios and this graphic, that a test can be superior to a competitor in terms of predictive values while having either sensitivity or specificity smaller. A decision theoretic basis for the interpretation of the graph is given by relating it to the tent graph of Hilden and Glasziou (Statistics in Medicine, 1996). Finally, a brief example comparing two serodiagnostic tests for Lyme disease is presented. Published in 2000 by John Wiley & Sons, Ltd.