Notes on testing equality in binary data under a three period crossover design

Under a random effects logistic regression model, asymptotic and exact test procedures in closed form for testing equality of binary responses are developed for comparing three treatments in a three-period crossover trial. Monte Carlo simulation is employed to evaluate the performance of these test procedures in a variety of situations. Interval estimators for the relative treatment effects are provided. The commonly-used procedures for testing the homogeneity of odds ratio (OR) is shown to be applicable for testing whether there is an interaction between treatments and periods. Finally, the data taken from a three-period crossover trial comparing two different doses of an analgesic with placebo for the relief of primary dysmenorrhea are used to illustrate the use the proposed test procedures and estimators.