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A Bayesian False Discovery Rate for Multiple Testing

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  • Alice Whittemore

Abstract

Case-control studies of genetic polymorphisms and gene-environment interactions are reporting large numbers of statistically significant associations, many of which are likely to be spurious. This problem reflects the low prior probability that any one null hypothesis is false, and the large number of test results reported for a given study. In a Bayesian approach to the low prior probabilities, Wacholder et al. (2004) suggest supplementing the p-value for a hypothesis with its posterior probability given the study data. In a frequentist approach to the test multiplicity problem, Benjamini & Hochberg (1995) propose a hypothesis-rejection rule that provides greater statistical power by controlling the false discovery rate rather than the family-wise error rate controlled by the Bonferroni correction. This paper defines a Bayes false discovery rate and proposes a Bayes-based rejection rule for controlling it. The method, which combines the Bayesian approach of Wacholder et al. with the frequentist approach of Benjamini & Hochberg, is used to evaluate the associations reported in a case-control study of breast cancer risk and genetic polymorphisms of genes involved in the repair of double-strand DNA breaks.

Suggested Citation

  • Alice Whittemore, 2007. "A Bayesian False Discovery Rate for Multiple Testing," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 1-9.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:1:p:1-9
    DOI: 10.1080/02664760600994745
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    Citations

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    Cited by:

    1. Lin, Wan-Yu & Lee, Wen-Chung, 2011. "Floating prioritized subset analysis: A powerful method to detect differentially expressed genes," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 903-913, January.
    2. Bickel David R., 2013. "Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(4), pages 529-543, August.
    3. Xiaoquan Wen, 2017. "Robust Bayesian FDR Control Using Bayes Factors, with Applications to Multi-tissue eQTL Discovery," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(1), pages 28-49, June.

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