Determination of optimal designs using linear models in crossover trials

This study determines the optimal designs for crossover trials with fixed size of population, in order to estimate contrasts between two treatment effects, for various numbers of periods. The problem is approached in the framework of a linear model, taking into consideration the structure of a variance matrix constructed from two random sources: linked-to-subject random effect and linked-to-measurement random error. Different models, as well as different optimality criteria, are considered. For example, when two periods are planned, for the criterion of the minimization of the variance of the treatment-effect estimator, in the presence of residual effect, the optimal design corresponds to four groups of sequences, (T1, T2), (T2, T1), (T1, T1), (T2, T2); without residual effect it corresponds to two groups, (T1, T2), (T2, T1). Optimal designs are given for the comparison of two treatments when using three or four periods.