Test and power considerations for multiple endpoint analyses using sequentially rejective graphical procedures

A variety of powerful test procedures are available for the analysis of clinical trials addressing multiple objectives, such as comparing several treatments with a control, assessing the benefit of a new drug for more than one endpoint, etc. However, some of these procedures have reached a level of complexity that makes it difficult to communicate the underlying test strategies to clinical teams. Graphical approaches have been proposed instead that facilitate the derivation and communication of Bonferroni-based closed test procedures. In this paper we give a coherent description of the methodology and illustrate it with a real clinical trial example. We further discuss suitable power measures for clinical trials with multiple primary and/or secondary objectives and use a generic example to illustrate our considerations.