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Statistical Applications in Genetics and Molecular Biology

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1544-6115
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The Joint Null Criterion for Multiple Hypothesis Tests

Jeffrey T Leek1 / John D. Storey2

1Johns Hopkins Bloomberg School of Public Health

2Princeton University

Citation Information: Statistical Applications in Genetics and Molecular Biology. Volume 10, Issue 1, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.2202/1544-6115.1673, June 2011

Publication History

Published Online:
2011-06-01

This article offers supplementary material which is provided at the end of the article.

Simultaneously performing many hypothesis tests is a problem commonly encountered in high-dimensional biology. In this setting, a large set of p-values is calculated from many related features measured simultaneously. Classical statistics provides a criterion for defining what a “correct” p-value is when performing a single hypothesis test. We show here that even when each p-value is marginally correct under this single hypothesis criterion, it may be the case that the joint behavior of the entire set of p-values is problematic. On the other hand, there are cases where each p-value is marginally incorrect, yet the joint distribution of the set of p-values is satisfactory. Here, we propose a criterion defining a well behaved set of simultaneously calculated p-values that provides precise control of common error rates and we introduce diagnostic procedures for assessing whether the criterion is satisfied with simulations. Multiple testing p-values that satisfy our new criterion avoid potentially large study specific errors, but also satisfy the usual assumptions for strong control of false discovery rates and family-wise error rates. We utilize the new criterion and proposed diagnostics to investigate two common issues in high-dimensional multiple testing for genomics: dependent multiple hypothesis tests and pooled versus test-specific null distributions.

Keywords: false discovery rate; multiple testing dependence; pooled null statistics

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