The construction of multi-factor crossover designs in animal husbandry studies

For ethical reasons it is important to try to obtain as much useful information as possible from an animal experiment whilst minimizing the number of animals used. Crossover designs, where applicable, provide an ideal framework for achieving this. If two or more treatment factors are included in the crossover design then the reduction in total animal usage can be considerable. In this paper we consider such designs, defined as multi-factor crossover designs. The designs are applicable when there are several different treatment factors, each at t levels, to be applied to the experimental units. The motivation for investigating these designs was a study conducted at GlaxoSmithKline to determine the preference of male and female dogs for t=5 different types of bed and t=5 different bedding conditions. A construction method is given for forming universally optimal designs for t not too large. Also given is an example for the special case where the number of treatment levels t=6.