Efficient cross-over designs allowing a check on the assumption that direct and carry-over effects do not interact

In cross-over experiments, each subject receives a sequence of treatments, one in each of a number of consecutive time periods, and a response is measured at the end of each period. Traditional models for these experiments assume that the direct effect of the treatment applied in the current period and the carry¬over effect of the treatment applied in the previous period act additively on the response. Recently, models involving directxcarry-over interaction have been considered and universally optimal designs for investigating such an interaction have been presented. However, these designs require large numbers of subjects and time periods, and such resources are not always available. This paper presents construction methods for designs that permit a test of the interaction, but which require a small number of subjects and periods. The best designs obtained by these methods are given. The designs are also optimal or near-optimal in the absence of directxcarry-over interaction