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.