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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  can be administered only if dose number  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 (-, - and -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.

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