  Consider an experiment, where a new drug is tested for the first time on
human subjects - healthy volunteers. Such experiments are often performed as
dose-escalation studies: a set of increasing doses is pre-selected, individuals
are grouped into cohorts, and in each cohort, the dose number $i$ can be
administered only if the dose number $i-1$ has already been tested in the
previous cohort. If an adverse effect of a dose is observed, the experiment
stops 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 as
well as by the cohort effects. We provide optimal approximate designs for
selected optimality criteria ($E$-, $MV$- and $LV$-optimality) for estimating
the effects of the drug doses compared with the placebo. In particular, we
obtain the optimality of Senn designs and extended Senn designs with respect to
multiple criteria.
