Abstract
Cross-over designs are widely used in many areas such as clinical trials or agricultural field experiments. In addition to the effect of the treatment applied to a given period, a residual effect of the previous treatment is often observed. In that case, the effect observed depends on both treatments. When the aim of the experiment is to select a single treatment, it is natural to consider the effect of a treatment preceded by itself, also called the total effect. We consider universally optimal or efficient circular cross-over designs for total effects under a model with interaction between treatment and carry-over effects. The optimal designs are obtained from the theory of approximate designs developed by Kushner (Ann Stat 25:2328–2344, 1997).
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