The Sequential Rejection Principle of Familywise Error Control

By Jelle J. Goeman, Aldo Solari. 2010

127 citations recorded by the source corpus.

Closed testing and partitioning are recognized as fundamental principles of familywise error control. In this paper, we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing. We present a general sequentially rejective multiple testing procedure and show that many well-known familywise error controlling methods can be constructed as special cases of this procedure, among which are the procedures of Holm, Shaffer and Hochberg, parallel and serial gatekeeping procedures, modern procedures for multiple testing in graphs, resampling-based multiple testing procedures and even the closed testing and partitioning procedures themselves. We also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step. The sequential rejection principle gives a novel theoretical perspective on many well-known multiple testing procedures, emphasizing the sequential aspect. Its main practical usefulness is for the development of multiple testing procedures for null hypotheses, possibly logically related, that are structured in a graph. We illustrate this by presenting a uniform improvement of a recently published procedure.

Subfields: Statistics and Probability, Transplantation

View Paper: https://www.semanticscholar.org/paper/1086643c453895287174269eb2121491ef270c75

How researchers see this paper

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In Statistics and Probability

1. Peter Buhlmann
2. Robert Tibshirani
3. Jelle J. Goeman
4. Nicolai Meinshausen
5. Aldo Solari
6. Marloes H. Maathuis
7. Jesse Hemerik
8. Stefan Wager

In Transplantation

1. Jelle J. Goeman
2. Aldo Solari
3. Jesse Hemerik

Citations in the corpus

• Only closed testing procedures are admissible for controlling false discovery proportions (2019, methodology): “As proposed by Goeman and Solari (2011), procedures that fulfil (1) or (2) allow a different, flexible way of using multiple testing methods.”
• Asymptotic optimality of the Westfall--Young permutation procedure for multiple testing under dependence (2011, background): “Subset-pivotality is not a necessary condition for strong control; see, for example, Romano and Wolf [29], Westfall and Troendle [31] and Goeman and Solari [13].”
• Sequential selection procedures and false discovery rate control (2013, background): “Related Work Although there is an extensive literature on FDR control and its variants (e.g., Benjamini and Hochberg, 1995; Benjamini and Yekutieli, 2001; Blanchard and Roquain, 2008; Efron et al., 2001; Goeman and Solari, 2010; Romano and Shaikh, 2006; Storey et al., 2004), no definitive procedure ”
• Multiple hypothesis testing in genomics (2014, background): “A valid permutation is a null-invariant transformation of the data, which means that it does not change the joint distribution of the p -values corresponding to true hypotheses [37].”
• Multiple Testing for Exploratory Research (2011, methodology): “Examples of such procedures are the tree-based testing procedure of Meinshausen (2008), recently improved by Goeman and Solari (2010), the focus level procedure of Goeman and Mansmann (2008), and the gatekeeping method of Edwards and Madsen (2007).”