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How to analyze many contingency tables simultaneously in genetic association studies

Author

Listed:
  • Dickhaus Thorsten

    (Humboldt-University, Berlin)

  • Straßburger Klaus

    (German Diabetes Center, Düsseldorf)

  • Schunk Daniel

    (Johannes Gutenberg-Universität Mainz and University of Zurich)

  • Morcillo-Suarez Carlos

    (Universitat Pompeu Fabra, Barcelona)

  • Illig Thomas

    (Helmholtz Zentrum München)

  • Navarro Arcadi

    (ICREA and Universitat Pompeu Fabra, Barcelona)

Abstract

We study exact tests for (2 x 2) and (2 x 3) contingency tables, in particular exact chi-squared tests and exact tests of Fisher type. In practice, these tests are typically carried out without randomization, leading to reproducible results but not exhausting the significance level. We discuss that this can lead to methodological and practical issues in a multiple testing framework when many tables are simultaneously under consideration as in genetic association studies.Realized randomized p-values are proposed as a solution which is especially useful for data-adaptive (plug-in) procedures. These p-values allow to estimate the proportion of true null hypotheses much more accurately than their non-randomized counterparts. Moreover, we address the problem of positively correlated p-values for association by considering techniques to reduce multiplicity by estimating the "effective number of tests" from the correlation structure.An algorithm is provided that bundles all these aspects, efficient computer implementations are made available, a small-scale simulation study is presented and two real data examples are shown.

Suggested Citation

  • Dickhaus Thorsten & Straßburger Klaus & Schunk Daniel & Morcillo-Suarez Carlos & Illig Thomas & Navarro Arcadi, 2012. "How to analyze many contingency tables simultaneously in genetic association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-33, July.
    • Handle: RePEc:bpj:sagmbi:v:11:y:2012:i:4:n:12
    DOI: 10.1515/1544-6115.1776
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    References listed on IDEAS

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    1. Laurent Barras & Olivier Scaillet & Russ Wermers, 2010. "False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas," Journal of Finance, American Finance Association, vol. 65(1), pages 179-216, February.
    2. Helmut Finner & Veronika Gontscharuk, 2009. "Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1031-1048, November.
    3. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    4. Mette Langaas & Bo Henry Lindqvist & Egil Ferkingstad, 2005. "Estimating the proportion of true null hypotheses, with application to DNA microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 555-572, September.
    5. Bryan N Howie & Peter Donnelly & Jonathan Marchini, 2009. "A Flexible and Accurate Genotype Imputation Method for the Next Generation of Genome-Wide Association Studies," PLOS Genetics, Public Library of Science, vol. 5(6), pages 1-15, June.
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    Citations

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    Cited by:

    1. Marina Bogomolov & Ruth Heller, 2018. "Assessing replicability of findings across two studies of multiple features," Biometrika, Biometrika Trust, vol. 105(3), pages 505-516.
    2. Stange, Jens & Dickhaus, Thorsten & Navarro, Arcadi & Schunk, Daniel, 2016. "Multiplicity- and dependency-adjusted p-values for control of the family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 32-40.
    3. Dickhaus Thorsten, 2015. "Simultaneous Bayesian analysis of contingency tables in genetic association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(4), pages 347-360, August.
    4. Marta Cousido‐Rocha & Jacobo de Uña‐Álvarez & Sebastian Döhler, 2022. "Multiple comparison procedures for discrete uniform and homogeneous tests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 219-243, January.
    5. Anh-Tuan Hoang & Thorsten Dickhaus, 2022. "On the usage of randomized p-values in the Schweder–Spjøtvoll estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 289-319, April.

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