The Joint Null Criterion for Multiple Hypothesis Tests

Leek Jeffrey T and Storey John D.

Statistical Applications in Genetics and Molecular Biology, 2011, vol. 10, issue 1, 1-22

Abstract: 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 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.2202/1544-6115.1673

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