Optimal crossover designs when carryover effects are proportional to direct effects

Crossover designs are used for a variety of different applications. While these designs have a number of attractive features, they also induce a number of special problems and concerns. One of these is the possible presence of carryover effects. Even with the use of washout periods, which are for many applications widely accepted as an indispensable component, the effect of a treatment from a previous period may not be completely eliminated. A model that has recently received renewed attention in the literature is the model in which first-order carryover effects are assumed to be proportional to direct treatment effects. Under this model, assuming that the constant of proportionality is known, we identify optimal and efficient designs for the direct effects for different values of the constant of proportionality. We also consider the implication of these results for the case that the constant of proportionality is not known.