Optimal Approximate Designs for Comparison with Control in Dose-Escalation Studies

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.