Power and sample size evaluation for the mcnemar test with application to matched case‐control studies

Various expressions have appeared for sample size calculation based on the power function of McNemar's test for paired or matched proportions, especially with reference to a matched case‐control study. These differ principally with respect to the expression for the variance of the statistic under the alternative hypothesis. In addition to the conditional power function, I identify and compare four distinct unconditional expressions. I show that the unconditional calculation of Schlesselman for the matched case‐control study can be expressed as a first‐order unconditional calculation as described by Miettinen. Corrections to Schlesselman's unconditional expression presented by Fleiss and Levin and by Dupont, which use different models to describe exposure association among matched cases and controls, are also equivalent to a first‐order unconditional calculation. I present a simplification of these corrections that directly provides the underlying table of cell probabilities, from which one can perform any of the alternative sample size calculations. Also, I compare the four unconditional sample size expressions relative to the exact power function. The conclusion is that Miettinen's first‐order expression tends to underestimate sample size, while his second‐order expression is usually fairly accurate, though possibly slightly anti‐conservative. A multinomial‐based expression presented by Connor, among others, is also fairly accurate and is usually slightly conservative. Finally, a local unconditional expression of Mitra, among others, tends to be excessively conservative.