On optimal crossover designs when carryover effects are proportional to direct effects

There are a number of different models for crossover designs which take account of carryover effects. Since it seems plausible that a treatment with a large direct effect should generally have a larger carryover effect, Kempton et al. (2001) considered a model where the carryover effects are proportional to the direct effects. The advantage of this model lies in the fact that there are fewer parameters to be estimated. Its problem lies in the nonlinearity of the estimators. Kempton et al. (2001) considered the least squares estimator. They point out that this estimator is asymptotically equivalent to the estimator in a linear model which assumes the true parameters to be known. For this estimator they determine optimal designs numerically for some cases. The present paper generalises some of their results. Our results are derived with the help of a generalisation of the methods used in Kunert and Martin (2000).