Testing a sequence of pre-ordered hypotheses to decide which of these can be rejected or accepted while controlling the familywise error rate (FWER) is of importance in many scientific studies such as clinical trials. In this paper, we first introduce a generalized fixed sequence procedure whose critical values are defined by using a function of the numbers of rejections and acceptances, and wh...

2 Methods 5 2.1 Multiple hypothesis testing framework . . . . . . . . . . . . . 5 2.2 Test statistics null distribution . . . . . . . . . . . . . . . . . 11 2.3 Single-step procedures for control of general Type I error rates θ(FVn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Step-down procedures for control of the family-wise error rate 16 2.5 Augmentation multiple tes...

We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant. The trial uses a group sequential procedure with two stages. The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α. The type I error rate for the primary endpoint is cont...

Diverging diamond interchanges (DDIs) have been growing in usage over the past few years and have gained considerable attention and interest. The advantage of the DDI over a conventional diamond interchange is that DDIs eliminate the need for left turn phases at the two intersections of the diamond, while occupying roughly the same geometric footprint as the conventional diamond. At the beginni...