Design and Analysis of three- and multi-armed "gold-standard" non-inferiority trials

Due to limitations in the development of more efficient therapies, non-inferiority trials are becoming increasingly important in clinical research. The proof of non-inferiority is of particular interest if the new treatment has other advantages like lower costs, better safety profiles or an increased efficacy with regard to secondary endpoints. A major difficulty with non-inferiority trials is the problem of lack of assay sensitivity, i.e. the potential that in the specific trial the treatment effect is generally small, e.g. due to unsatisfactory compliance or the inclusion of a high proportion of insufficiently responding patients. Therefore trial designs with active reference and placebo groups, often denoted as "three-armed gold-standard designs'', are considered preferable to two-armed non-inferiority designs whenever it is ethical to include the placebo.

In this researchl the statistical methodology for placebo controlled non-inferiority trials was enhanced and extended to designs with multiple treatment arms. A particular focus of the project was the construction of simultaneous confidence intervals for the three-arm non-inferiority trials but also for graphical test procedures in general. Designs with absolute and relative non-inferiority margins where both considered. For designs with absolute non-inferiority margins, methods for simultaneous testing and interval estimation of non-inferiority and efficacy were a theme. The goal is to develop methods that account for the fact that the clinical relevance of the non-inferiority claim depends on the observed efficacy of the active comparator. To this single-sateg adaptive designs  have been  considered in which there is the possibility of switching the focus from non-inferiority to an enhanced superiority of the experimental treatment to placebo that provides an inderict proof of non.ineferirity in cases where the reference is not sufficiently efficient. We also did research on specific adaptive design phase II/III in oncology and on dose finding studies in phase II.

Project start: November 2014
Project End: December 2108
Funding: DFG
Project members: W. Brannath, G. Gutjahr and S. Schmidt
Project partner: J. Röhmel, I. Pigerot (BIPS, Bremen), M. Carreras (Roche), B. Bornkamp (Novartis)


Brannath W, Schmidt S (2014). A new class of powerful and informative simultaneous confidence intervals. Statistics in Medicine, 33(19):3365–3386. (

Schmidt S, Brannath W (2014). Informative simultaneous confidence intervals in hierarchical testing. Methods of Information in Medicine, 53(4):278–283. (

Schmidt S, Brannath W  (2015). Informative simultaneous confidence intervals for the fall-back procedure. Biometrical Journal, 57(4):712–719. (

Carreras M, Gutjahr G, Brannath W (2015). Adaptive seamless designs with interim treatment selection: a case study in oncology. Statistics in Medicine, 34(8):1317-1333. (

Graf A, Gutjahr G, Brannath W (2016). Precision of maximum likelihood estimation in adaptive designs. Statistics in Medicine, 35(6): 922-941 (

Gutjahr G, Bornkamp B (2017). Likelihood Ratio Tests for a Dose-Response Effect using Multiple Nonlinear Regression Models. Biometrics, Journal of the International Biometric Society 73(1): 197-205. (