Guido Knapp, Joachim Hartung

We consider general adaptive group sequential designs for trials comparing three independent arms, say test group T, reference group R, and placebo group P. The goal of the trial is to establish noninferiority of T compared to R while T is also superior to P. Thus, we have a hierarchical testing procedure of a priori ordered hypotheses, that is, in the first testing problem, the superiority of T compared to P must be shown and the noninferiority of T compared to R using a predefined noninferiority margin should be then established in the second testing problem.

We derive nested confidence intervals on the trial parameters for normally distributed response variables with unknown variances in each interim analysis keeping the predefined confidence coefficient. In each interim analysis, the sample size for the next part of the trial can be determined in a completely adaptive way based on all the unblinded data collected so far. Exact formulas for sample size updating are provided. Moreover, in each interim analysis, it is possible to switch, in the sample size planning, from showing noninferiority of T compared to R to showing superiority of T over R, that is, we set the noninferiority margin equal to zero in the second testing problem.

**Keywords:** Noninferiority trial; Hierarchical testing; Repeated confidence interval; Adaptive sample size planning

**Biography:** Dr. Knapp is a statistician from Dortmund University in Germany, where he also got his PhD in 1996. His current position is equivalent to an assistant professor. Besides adaptive clinical trials, meta-analysis of clinical trials or observational studies is his second major research area.