Reverse graphical approaches for multiple test procedures

ABSTRACT

The graphical approach has been proposed as a general framework for clinical trial designs involving multiple hypotheses, where decisions are made only based on the observed marginal $p$-values. The graphical approach starts from a graph that includes all hypotheses as vertices and gradually removes some vertices when their corresponding hypotheses are rejected. In this paper, we propose a reverse graphical approach, which starts from a set of singleton graphs and gradually adds vertices into graphs until rejection of a set of hypotheses is made. Proofs of familywise error rate control are provided. A simulation study is conducted for statistical power analysis, and a case study is included to illustrate how the proposed approach can be applied to clinical studies.

KEYWORDS:

• Clinical trials
• graphical approach
• Hochberg procedure
• Holm procedure
• multiple tests

Acknowledgement

The authors thank Ajit C. Tamhane for bringing Xi and Bretz (2019) to our attention. We thank Ajit C. Tamhane and Dong Xi for helpful discussion. The authors thank editor, associate editor and two anonymous referees for suggestions that improved this paper.

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No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

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Funding

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