Powerful short-cuts for multiple testing procedures with special reference to gatekeeping strategies.

In this paper we present a general testing principle for a class of multiple testing problems based on weighted hypotheses. Under moderate conditions, this principle leads to powerful consonant multiple testing procedures. Furthermore, short-cut versions can be derived, which simplify substantially the implementation and interpretation of the related test procedures. It is shown that many well-known multiple test procedures turn out to be special cases of this general principle. Important examples include gatekeeping procedures, which are often applied in clinical trials when primary and secondary objectives are investigated, and multiple test procedures based on hypotheses which are completely ordered by importance. We illustrate the methodology with two real clinical studies.