  A common problem in Phase II clinical trials is the comparison of dose
response curves corresponding to different treatment groups. If the effect of
the dose level is described by parametric regression models and the treatments
differ in the administration frequency (but not in the sort of drug) a
reasonable assumption is that the regression models for the different
treatments share common parameters. This paper develops optimal design theory
for the comparison of different regression models with common parameters. We
derive upper bounds on the number of support points of admissible designs, and
explicit expressions for $D$-optimal designs are derived for frequently used
dose response models with a common location parameter. If the location and
scale parameter in the different models coincide, minimally supported designs
are determined and sufficient conditions for their optimality in the class of
all designs derived. The results are illustrated in a dose-finding study
comparing monthly and weekly administration.
