Consider an experiment, in which a new drug is tested for the first time on
human subjects, namely healthy volunteers. Such experiments are often performed
as dose-escalation studies: a set of increasing doses is preselected; individuals are
grouped into cohorts; and in each cohort, dose number i can be administered only if
dose number i − 1 has already been tested in the previous cohort. If an adverse effect
of a dose is observed, the experiment is stopped, and thus, no subjects are exposed to
higher doses. In this paper, we assume that the response is affected both by the dose
or placebo effects and by the cohort effects. We provide optimal approximate designs
for estimating the effects of the drug doses compared with the placebo with respect to
selected optimality criteria (E-, M V - and L V -optimality). In particular, we prove the
optimality of the so-called Senn designs with respect to all of the studied optimality
criteria, and we provide optimal extensions of these designs for selected criteria.

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• Optimal approximate designs for comparison with control in dose-escalation studies