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Bayes factors in the presence of population stratification

Author

Listed:
  • Wang, Linglu
  • Li, Qizhai
  • Li, Zhaohai
  • Zheng, Gang

Abstract

Hidden population stratification (PS) is a main concern in the analysis of case-control genetic association studies. All methods to correct for hidden PS have been focused on classical hypothesis testing, and cannot be directly applied to Bayesian analysis. In this paper, to study the impact and the correction of hidden PS on Bayes factor (BF), we use a simple approximation of BF in terms of the maximum likelihood estimates of the odds ratio (OR) and its asymptotic variance. One advantage is that the commonly used principal components analysis method with a large panel of null markers scanned from existing genome-wide association studies can be directly employed to correct for hidden PS in estimating the OR and its asymptotic variance, through which a correction to BF for hidden PS can be achieved. Using simulations, we examine the impact of ignoring hidden PS on BF and show that the proposed method yields an appropriate correction in Bayesian analysis.

Suggested Citation

  • Wang, Linglu & Li, Qizhai & Li, Zhaohai & Zheng, Gang, 2011. "Bayes factors in the presence of population stratification," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 836-841, July.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:836-841
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    References listed on IDEAS

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    1. Li, Zhaohai & Zhang, Hong & Zheng, Gang & Gastwirth, Joseph L. & Gail, Mitchell H., 2009. "Excess false positive rate caused by population stratification and disease rate heterogeneity in case-control association studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1767-1781, March.
    2. B. Devlin & Kathryn Roeder, 1999. "Genomic Control for Association Studies," Biometrics, The International Biometric Society, vol. 55(4), pages 997-1004, December.
    3. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    4. Kai Yu & Zhaoming Wang & Qizhai Li & Sholom Wacholder & David J Hunter & Robert N Hoover & Stephen Chanock & Gilles Thomas, 2008. "Population Substructure and Control Selection in Genome-Wide Association Studies," PLOS ONE, Public Library of Science, vol. 3(7), pages 1-14, July.
    5. Gang Zheng & Zhaohai Li & Mitchell H. Gail & Joseph L. Gastwirth, 2010. "Impact of Population Substructure on Trend Tests for Genetic Case–Control Association Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 196-204, March.
    6. Valen E. Johnson, 2005. "Bayes factors based on test statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 689-701, November.
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