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

Abstract

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.

The Monday effect revisited: An alternative testing approach

“…We also call this test procedure "closed F-test", since all primary and auxiliary hypotheses are tested using F-statistics. 7 5 For further results and applications of closed test procedures see, for example, Alt (2005), Hochberg and Tamhane (1987), Hommel et al (2007), Hsu (1996), Pigeot (2000), and Sonnemann (2008). 6 To see an example of a primary hypothesis together with all subhypotheses, please refer to Table 7.…”

A Dunnett–Bonferroni‐based parallel gatekeeping procedure for dose–response clinical trials with multiple endpoints

“…We do note that there are other gatekeeping approaches that share in overlapping ways some of the ideas in our approach but are different in their entireties. For instance, the idea of applying the Dunnett adjustment within each family and splitting a using the Bonferroni inequality among families is conceptually similar to a gatekeeping procedure based on weighted hypotheses introduced by Hommel et al [12,Section 3.1]. The procedure in [12, Section 3.1] groups hypotheses for high doses across all endpoints as the primary family and hypotheses for low doses across all endpoints as the secondary family.…”

“…The independence condition means that the inference made in the primary family should be independent of, or in other words, not affected by, the inference made in the subsequent families. It is worth noting that relaxing the independence condition may result in some power gain when doing so is in line with the objectives of clinical studies (see [6;11,Section 2.7.3;12]). …”

Gatekeeping procedures with clinical trial applications

“…Generalizations of the Bonferroni-based parallel gatekeeping procedure were studied by Dmitrienko et al [17] and Hommel et al [11]. Dmitrienko et al discussed procedures with an extended parallel gatekeeping property.…”