Optimal and efficient crossover designs for comparing test treatments to a control treatment under various models

We study the optimality, efficiency, and robustness of crossover designs for comparing several test treatments to a control treatment. Since A-optimality is a natural criterion in this context, we establish lower bounds for the trace of the inverse of the information matrix for the test treatments versus control comparisons under various models. These bounds are then used to obtain lower bounds for efficiencies of a design under these models. Two algorithms, both guided by these efficiencies and results from optimal design theory, are proposed for obtaining efficient designs under the various models.