Assessing the impact of carryover effects on the variances of estimators of treatment differences in crossover designs

Different models that include carryover effects have been studied in the optimal design literature. It has been suggested that the use of these models results in increased variances of estimated contrasts of the direct treatment effects, leading to inferior estimators in terms of precision. Under a number of models and selected designs, we present variance expressions for the pairwise differences of direct treatment effects and observe that adjusting for carryover effects need not affect the precision of estimators negatively. We investigate the existence of designs that produce estimators with relatively small variances under all models considered. We conclude that even if a model is not correct, it can still be useful in increasing the precision of estimators for treatment contrasts.