Note on simultaneous inferences about non-inferiority and superiority for a primary and a secondary endpoint

In their review of challenges to multiple testing in clinical trials, Hung and Wang (2010) considered the situation where a treatment is to be compared with an active comparator and the aim is to show non-inferiority and (if possible) superiority with respect to a primary and a secondary endpoint. This note extends their discussion of this particular situation, taking the sequentially rejective procedure they used for illustration as a starting point. Some alternative multiple testing procedures (MTPs) are considered, and corresponding simultaneous confidence regions are discussed that provide additional information "for free". The choice may then be based on the properties of these MTPs and corresponding confidence regions.