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The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies

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  • Ian Barnett
  • Rajarshi Mukherjee
  • Xihong Lin

Abstract

It is of substantial interest to study the effects of genes, genetic pathways, and networks on the risk of complex diseases. These genetic constructs each contain multiple SNPs, which are often correlated and function jointly, and might be large in number. However, only a sparse subset of SNPs in a genetic construct is generally associated with the disease of interest. In this article, we propose the generalized higher criticism (GHC) to test for the association between an SNP set and a disease outcome. The higher criticism is a test traditionally used in high-dimensional signal detection settings when marginal test statistics are independent and the number of parameters is very large. However, these assumptions do not always hold in genetic association studies, due to linkage disequilibrium among SNPs and the finite number of SNPs in an SNP set in each genetic construct. The proposed GHC overcomes the limitations of the higher criticism by allowing for arbitrary correlation structures among the SNPs in an SNP-set, while performing accurate analytic p-value calculations for any finite number of SNPs in the SNP-set. We obtain the detection boundary of the GHC test. We compared empirically using simulations the power of the GHC method with existing SNP-set tests over a range of genetic regions with varied correlation structures and signal sparsity. We apply the proposed methods to analyze the CGEM breast cancer genome-wide association study. Supplementary materials for this article are available online.

Suggested Citation

  • Ian Barnett & Rajarshi Mukherjee & Xihong Lin, 2017. "The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 64-76, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:64-76
    DOI: 10.1080/01621459.2016.1192039
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    References listed on IDEAS

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    1. Armin Schwartzman & Xihong Lin, 2011. "The effect of correlation in false discovery rate estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 199-214.
    2. Zhang, Yu & Liu, Jun S., 2011. "Fast and Accurate Approximation to Significance Tests in Genome-Wide Association Studies," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 846-857.
    3. Yu I. Ingster & Alexandre B. Tsybakov & N. Verzelzn, 2010. "Detection Boundary in Sparse Regression," Working Papers 2010-28, Center for Research in Economics and Statistics.
    4. Teri A. Manolio & Francis S. Collins & Nancy J. Cox & David B. Goldstein & Lucia A. Hindorff & David J. Hunter & Mark I. McCarthy & Erin M. Ramos & Lon R. Cardon & Aravinda Chakravarti & Judy H. Cho &, 2009. "Finding the missing heritability of complex diseases," Nature, Nature, vol. 461(7265), pages 747-753, October.
    5. Ian J. Barnett & Xihong Lin, 2014. "Analytical p-value calculation for the higher criticism test in finite-d problems," Biometrika, Biometrika Trust, vol. 101(4), pages 964-970.
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