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The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies

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  • Hunt, Daniel L.
  • Cheng, Cheng
  • Pounds, Stanley

Abstract

In differential expression analysis of microarray data, it is common to assume independence among null hypotheses (and thus gene expression levels). The independence assumption implies that the number of false rejections V follows a binomial distribution and leads to an estimator of the empirical false discovery rate (eFDR). The number of false rejections V is modeled with the beta-binomial distribution. An estimator of the beta-binomial false discovery rate (bbFDR) is then derived. This approach accounts for how the correlation among non-differentially expressed genes influences the distribution of V. Permutations are used to generate the observed values for V under the null hypotheses and a beta-binomial distribution is fit to the values of V. The bbFDR estimator is compared to the eFDR estimator in simulation studies of correlated non-differentially expressed genes and is found to outperform the eFDR for certain scenarios. As an example, this method is also used to perform an analysis that compares the gene expression of soft-tissue sarcoma samples to normal-tissue samples.

Suggested Citation

  • Hunt, Daniel L. & Cheng, Cheng & Pounds, Stanley, 2009. "The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1688-1700, March.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:5:p:1688-1700
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    References listed on IDEAS

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    1. Cheng Cheng & Pounds Stanley B. & Boyett James M. & Pei Deqing & Kuo Mei-Ling & Roussel Martine F., 2004. "Statistical Significance Threshold Criteria For Analysis of Microarray Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-32, December.
    2. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 1-20, March.
    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. Chen-An Tsai & Huey-miin Hsueh & James J. Chen, 2003. "Estimation of False Discovery Rates in Multiple Testing: Application to Gene Microarray Data," Biometrics, The International Biometric Society, vol. 59(4), pages 1071-1081, December.
    5. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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    3. David E. Giles, 2012. "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications," Econometrics Working Papers 1201, Department of Economics, University of Victoria.

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