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The partial effectiveness of drugs is of importance to the pharmaceuticalindustry. Randomized controlled trials (RCTs) assuming the existence of asubgroup sensitive to the treatment are already used. These designs, however,are available only if there is a known marker for identifying subjects in thesubgroup. In this paper we investigate a model in which the response in thetreatment group $Z^T$ has a two-component mixture density $(1-p)\mathcalN(\mu^C, \sigma^2)+p\mathcal N(\mu^T, \sigma^2)$ representing the treatmentresponses of \emph{placebo responders} and \emph{drug responders}. Thetreatment-specific effect is $\mu = \frac{\mu^T-\mu^C}{\sigma}$ and $p$ is theprevalence of the drug responders in the population. Other patients in thetreatment group react as if they had received a placebo.  We develop one- and two-stage RCT designs that are able to detect a sensitivesubgroup based solely on the responses. We also extend them to a multicenterRCTs using Hochberg's step-up procedure. We avoid extensive simulations and usesimple and quick numerical optimization methods.

Adaptive multicenter designs for continuous response clinical trials in the presence of an unknown sensitive subgroup