Crossover designs have been used in practice for a long period of time and remain an indispensable tool for a number of applications, including drug development studies in the pharmaceutical industry. For the last 30 years attention has also been given to the determination of optimal and efficient crossover designs under a variety of different models. One of the issues that has been controversial is how to deal with possible carryover effects. In this talk, which assumes no prior knowledge of crossover designs, we will present some recent results on optimal and efficient crossover designs for a model that allows two types of carryover effects from each treatment. The results are also compared to those for more traditional models used with crossover designs.

New results in this talk are based on joint work with Joachim Kunert, some of which will be reported in an article scheduled to appear in the Journal of the American Statistical Association.