Efficient block designs for comparing dual with single treatments.

Experiments in blocks having two treatment factors are considered in which a particular treatment must be excluded. The work is motivated by medical trials of two drugs in which a double placebo cannot be administered on ethical grounds. The contrasts of interest compare the effects of having both treatment factor at non-zero labelled levels with the effects of having only one treatment factor at a non-zero labelled level. For nx2 experiments, a class of designs containing highly efficient members is identified and a lower bound on the efficiencies of designs in this class is derived. Tables of efficient designs are provided