  We consider the optimal design problem for a comparison of two regression
curves, which is used to establish the similarity between the dose response
relationships of two groups. An optimal pair of designs minimizes the width of
the confidence band for the difference between the two regression functions.
Optimal design theory (equivalence theorems, efficiency bounds) is developed
for this non standard design problem and for some commonly used dose response
models optimal designs are found explicitly. The results are illustrated in
several examples modeling dose response relationships. It is demonstrated that
the optimal pair of designs for the comparison of the regression curves is not
the pair of the optimal designs for the individual models. In particular it is
shown that the use of the optimal designs proposed in this paper instead of
commonly used "non-optimal" designs yields a reduction of the width of the
confidence band by more than 50%.
