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Simultaneous Bayesian analysis of contingency tables in genetic association studies

  • Thorsten Dickhaus EMAIL logo
Published/Copyright: July 28, 2015

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.


Corresponding author: Thorsten Dickhaus, Institute for Statistics, University of Bremen, P.O. Box 330 440, D-28344 Bremen, Germany, e-mail:

Acknowledgments

This work makes use of data generated by the Wellcome Trust Case Control Consortium. A full list of the investigators who contributed to the generation of the data is available from http://www.wtccc.org.uk. Funding for the Wellcome Trust Case Control Consortium project was provided by the Wellcome Trust under award 076113. The author is grateful to two anonymous referees for their careful reading of the manuscript and constructive comments which have improved the presentation.

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Published Online: 2015-7-28
Published in Print: 2015-8-1

©2015 by De Gruyter

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