Comparing dual with single treat ments in block design

Experiments having two treatment factors and one blocking factor are considered in which a particular combination of treatment factor levels must be excluded. The motivation for the work is a medical trial 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 factors at non-zero labelled levels with the effects of having only one treatment factor at a non-zero labeled level. A lower bound is derived on the average variance of the contrast estimators n x m experiments. For n×2 experiments a balance property is defined which is possessed by many efficient designs. Designs having the property are characterized through the structure of the intra-block information matrix. Efficient reinforced group divisible designs are constructed and assessed against the lower bound.

Keywords:

A-criterion , Dual Versus Single Treatment Contrasts , Factorial Experiment , Group Divisible Designs , Part. Balance