Locally Optimal Binary Crossover Designs

Optimal two-treatment, p period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of n subjects to 2p possible treatment sequences. An appropriate logistic regression model is postulated and the within subject covariances are modeled through a working correlation matrix. The marginal mean of the binary responses are fitted using generalized estimating equations. The efficiencies of some crossover designs for p = 2, 3, 4 periods are calculated. An equivalence theorem is provided to verify optimality of numerically obtained locally optimal designs.