Identifying effective and/or safe doses by stepwise confidence intervals for ratios

Typical randomized clinical dose-finding studies consist of the comparison of several doses of a drug versus a placebo. Interest lies in estimating relevant doses among those under investigation for efficacy and safety variables, such as the minimum effective dose or the maximum safe dose (or estimating both doses simultaneously). Step-down procedures have been proposed for comparing the standardized differences of the dose groups against placebo. In this paper we consider the ratio of population means and propose stepwise confidence intervals for these ratios. These confidence intervals do not require multiplicity adjustments and yield the same decisions as the associated test procedures. In addition, several power concepts are investigated within the present framework. The results allow sample size determination in the design phase of a study for the probability of estimating correctly the dose of interest. Auxiliary results of a numerical study show the range of application of these methods.