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Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests
Author(s) -
Bretz Frank,
Posch Martin,
Glimm Ekkehard,
Klinglmueller Florian,
Maurer Willi,
Rohmeyer Kornelius
Publication year - 2011
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201000239
Subject(s) - bonferroni correction , multiple comparisons problem , weighting , parametric statistics , computer science , statistical hypothesis testing , mathematics , data mining , statistics , machine learning , medicine , radiology
The confirmatory analysis of pre‐specified multiple hypotheses has become common in pivotal clinical trials. In the recent past multiple test procedures have been developed that reflect the relative importance of different study objectives, such as fixed sequence, fallback, and gatekeeping procedures. In addition, graphical approaches have been proposed that facilitate the visualization and communication of Bonferroni‐based closed test procedures for common multiple test problems, such as comparing several treatments with a control, assessing the benefit of a new drug for more than one endpoint, combined non‐inferiority and superiority testing, or testing a treatment at different dose levels in an overall and a subpopulation. In this paper, we focus on extended graphical approaches by dissociating the underlying weighting strategy from the employed test procedure. This allows one to first derive suitable weighting strategies that reflect the given study objectives and subsequently apply appropriate test procedures, such as weighted Bonferroni tests, weighted parametric tests accounting for the correlation between the test statistics, or weighted Simes tests. We illustrate the extended graphical approaches with several examples. In addition, we describe briefly the gMCP package in R , which implements some of the methods described in this paper.