Difference of two dependent sensitivities and specificities: Comparison of various approaches

Abstract

In diagnostic studies, a new diagnostic test is often compared with a standard test and both tests are applied on the same patients, called paired design. The true disease state is in general given by the so-called gold standard (most reliable method for classification), which has to be known for all patients. The benefit of the new diagnostic test can be evaluated by sensitivity and specificity, which are in fact proportions. This means, for the comparison of two diagnostic tests, confidence intervals for the difference of the dependent estimated sensitivities and specificities are calculated. In the literature, many comparisons of different approaches can be found, but none explicitly for diagnostic studies. For this reason we compare 13 approaches for a set of scenarios that represent data of diagnostic studies (e.g., with sensitivity and specificity ≥0.8). With simulation studies, we show that the nonparametric interval with normal approximation can be recommended for the difference of two dependent sensitivities or specificities without restriction, the Wald interval with the limitation of slightly anti-conservative results for small sample sizes, and the nonparametric intervals with t-approximation, and the Tango interval with the limitation of conservative results for high correlations.

Keywords: Comparison of two diagnostic tests; Confidence interval; Diagnostic studies; Paired difference of sensitivities; Paired proportions.