  The issue of determining not only an adequate dose but also a dosing
frequency of a drug arises frequently in Phase II clinical trials. This results
in the comparison of models which have some parameters in common. Planning such
studies based on Bayesian optimal designs offers robustness to our conclusions
since these designs, unlike locally optimal designs, are efficient even if the
parameters are misspecified. In this paper we develop approximate design theory
for Bayesian $D$-optimality for nonlinear regression models with common
parameters and investigate the cases of common location or common location and
scale parameters separately. Analytical characterisations of saturated Bayesian
$D$-optimal designs are derived for frequently used dose-response models and
the advantages of our results are illustrated via a numerical investigation.
