The harmonic mean p -value for combining dependent tests
Open Access
- 4 January 2019
- journal article
- research article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America
- Vol. 116 (4), 1195-1200
- https://doi.org/10.1073/pnas.1814092116
Abstract
Analysis of “big data” frequently involves statistical comparison of millions of competing hypotheses to discover hidden processes underlying observed patterns of data, for example, in the search for genetic determinants of disease in genome-wide association studies (GWAS). Controlling the familywise error rate (FWER) is considered the strongest protection against false positives but makes it difficult to reach the multiple testing-corrected significance threshold. Here, I introduce the harmonic mean p-value (HMP), which controls the FWER while greatly improving statistical power by combining dependent tests using generalized central limit theorem. I show that the HMP effortlessly combines information to detect statistically significant signals among groups of individually nonsignificant hypotheses in examples of a human GWAS for neuroticism and a joint human–pathogen GWAS for hepatitis C viral load. The HMP simultaneously tests all ways to group hypotheses, allowing the smallest groups of hypotheses that retain significance to be sought. The power of the HMP to detect significant hypothesis groups is greater than the power of the Benjamini–Hochberg procedure to detect significant hypotheses, although the latter only controls the weaker false discovery rate (FDR). The HMP has broad implications for the analysis of large datasets, because it enhances the potential for scientific discovery.Funding Information
- Wellcome (101237/Z/13/Z)
- Royal Society (101237/Z/13/Z)
- RCUK | Medical Research Council (MR/K01532X/1)
This publication has 20 references indexed in Scilit:
- Modeling interactions with known risk loci-a Bayesian model averaging approachAnnals of Human Genetics, 2010
- A general framework for multiple testing dependenceProceedings of the National Academy of Sciences of the United States of America, 2008
- Estimation of the multiple testing burden for genomewide association studies of nearly all common variantsGenetic Epidemiology, 2008
- Estimation of significance thresholds for genomewide association scansGenetic Epidemiology, 2008
- To permute or not to permuteBioinformatics, 2006
- A haplotype map of the human genomeNature, 2005
- The control of the false discovery rate in multiple testing under dependencyThe Annals of Statistics, 2001
- An improved Bonferroni procedure for multiple tests of significanceBiometrika, 1986
- On closed testing procedures with special reference to ordered analysis of varianceBiometrika, 1976
- The Large-Sample Distribution of the Likelihood Ratio for Testing Composite HypothesesThe Annals of Mathematical Statistics, 1938