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Simultaneous Bayesian analysis of contingency tables in genetic association studies

Author

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  • Dickhaus Thorsten

    (Institute for Statistics, University of Bremen, P.O. Box 330 440, D-28344 Bremen, Germany)

Abstract

Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus consists of a contingency table containing the numbers of observed genotype-phenotype combinations. Under case-control design, the row counts of every table are identical and fixed, while column counts are random. The aim of the statistical analysis is to test independence of the phenotype and the genotype at every locus. We present an objective Bayesian methodology for these association tests, which relies on the conjugacy of Dirichlet and multinomial distributions. Being based on the likelihood principle, the Bayesian tests avoid looping over all tables with given marginals. Making use of data generated by The Wellcome Trust Case Control Consortium (WTCCC), we illustrate that the ordering of the Bayes factors shows a good agreement with that of frequentist p-values. Furthermore, we deal with specifying prior probabilities for the validity of the null hypotheses, by taking linkage disequilibrium structure into account and exploiting the concept of effective numbers of tests. Application of a Bayesian decision theoretic multiple test procedure to the WTCCC data illustrates the proposed methodology. Finally, we discuss two methods for reconciling frequentist and Bayesian approaches to the multiple association test problem.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sagmbi:v:14:y:2015:i:4:p:347-360:n:2
    DOI: 10.1515/sagmb-2014-0052
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    References listed on IDEAS

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    1. 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.
    2. Sellke T. & Bayarri M. J. & Berger J. O., 2001. "Calibration of rho Values for Testing Precise Null Hypotheses," The American Statistician, American Statistical Association, vol. 55, pages 62-71, February.
    3. Kim‐Anh Do & Peter Müller & Feng Tang, 2005. "A Bayesian mixture model for differential gene expression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 627-644, June.
    4. Alan Agresti & David B. Hitchcock, 2005. "Bayesian inference for categorical data analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 297-330, December.
    5. Peter Muller & Giovanni Parmigiani & Christian Robert & Judith Rousseau, 2004. "Optimal Sample Size for Multiple Testing: The Case of Gene Expression Microarrays," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 990-1001, December.
    6. W. M. Patefield, 1981. "An Efficient Method of Generating Random R × C Tables with Given Row and Column Totals," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(1), pages 91-97, March.
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