One-sided simultaneous confidence intervals for effective dose steps in unbalanced designs

An important issue in dose finding is whether a further dose increment leads to a relevant increase in efficacy. Clinical efficacy should not be considered by point zero null hypotheses. instead. shifted hypotheses for the difference or the ratio can be used. Because the a priori definition of a relevance threshold is frequently difficult, confidence intervals should be used for a posteriori interpretation. Sample size estimation - a-priori or by adaptive interim analysis- is inherent, because the effective dose steps are arbitrary in un-designed studies. For simultaneous confidence intervals without order restriction the exact distributions under the null and the alternative hypothesis is proposed for the general unbalanced one-way design.