  In a recent paper Dette et al. (2014) introduced optimal design problems for
dose fnding studies with an active control. These authors concentrated on
regression models with normal distributed errors (with known variance) and the
problem of determining optimal designs for estimating the smallest dose, which
achieves the same treatment effect as the active control. This paper discusses
the problem of designing active-controlled dose fnding studies from a broader
perspective. In particular, we consider a general class of optimality criteria
and models arising from an exponential family, which are frequently used
analyzing count data. We investigate under which circumstances optimal designs
for dose fnding studies including a placebo can be used to obtain optimal
designs for studies with an active control. Optimal designs are constructed for
several situations and the differences arising from different distributional
assumptions are investigated in detail. In particular, our results are
applicable for constructing optimal experimental designs to analyze
active-controlled dose fnding studies with discrete data, and we illustrate the
efficiency of the new optimal designs with two recent examples from our
consulting projects.
