McNemar's test is often used in practice to compare the sensitivities and specificities for the evaluation of two diagnostic tests. For correct evaluation of accuracy, an intuitive recommendation is to test the diseased and the non-diseased groups separately so that the sensitivities can be compared among the diseased, and specificities can be compared among the healthy group of people. This paper provides a rigorous theoretical framework for this argument and study the validity of McNemar's test regardless of the conditional independence assumption. We derive McNemar's test statistic under the null hypothesis considering both assumptions of conditional independence and conditional dependence. We then perform power analyses to show how the result is affected by the amount of the conditional dependence under alternative hypothesis.
Keywords: McNemar’s test; conditional dependence; diagnostic test; sensitivity; specificity.