Assessing the gain in diagnostic performance when combining two diagnostic tests.

Combining dichotomous (or dichotomized) results of two diagnostic tests will result in a trade-off in sensitivity and specificity of the combined test relative to the component tests. Because of this inherent trade-off, likelihood ratios provide a clinically relevant means of comparing the combined test with one of its components. The likelihood ratios depend on both sensitivity and specificity and hence take into account the trade-off between them. A graphical approach is used to assess whether the combined test is superior to a component test, or vice versa. Asymptotic standard errors are derived for comparing likelihood ratios when a paired study design is used. The trade-off in the expected number of additional true positive and false positive results (or true negative and false negative results) is used as the basis for deciding whether to use tests in combination when neither the combined nor a component test shows superior test performance based on their likelihood ratios. These methods are illustrated with an example that considers the combined use of Pap and HPV testing.