Simultaneous comparison of sensitivity and specificity of two tests in the paired design: a straightforward graphical approach.

Often the performances of two binary diagnostic or screening tests are compared by applying them to the same set of subjects, some of whom are affected, some unaffected. The McNemar test, and corresponding interval estimation methods, may be used to compare the sensitivity of the two tests, but this disregards both any observed difference in specificity and its imprecision due to sampling variation. The suggested approach is to display point and interval estimates for a weighted mean f of the differences in sensitivity and specificity between the two tests. The mixing parameter lambda, which is allowed to range from 0 to 1, represents the prevalence in the population to which application is envisaged, together with the relative seriousness of false positives and false negatives. The confidence interval for f is obtained by a simple extension of a closed-form method for the paired difference of proportions, which has favourable coverage properties and is based on the Wilson single proportion score method. A plot of f against lambda is readily obtained using a Minitab macro.