Estimating the difference between differences: measurement of additive scale interaction for proportions

A simple, effective closed-form method to calculate a confidence interval for the difference between two differences of proportions is proposed. The method is based on the Wilson score interval for the single proportion, and may be used to compare either unpaired or paired differences. It is equally applicable whether cell frequencies are large or small; and coverage properties are favourable. It is easily adapted to give a confidence interval for the treatment effect for a binary outcome in a two-period cross-over trial.