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Estimation of empirical null using a mixture of normals and its use in local false discovery rate

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  • Park, DoHwan
  • Park, Junyong
  • Zhong, Xiaosong
  • Sadelain, Michel

Abstract

When high dimensional microarray data is given, it is of interest to select significant genes by controlling a given level of Type-I error. One popular way to control the level is the false discovery rate (FDR). This paper considers gene selection based on the local false discovery rate. In most of the previous studies, the null distribution of gene expression is commonly assumed to be a normal distribution. However, if the null distribution has heavier tail than that of normal, there may exist too many false discoveries leading to the failure of controlling the given level of FDR. We propose a novel procedure which enriches a class of null distribution based on a mixture of normals. We present simulation studies to show that our proposed procedure is less sensitive to variation of null distribution than local false discovery rate with a single normal for the null. We also provide real example of gene expression profiles of antigen-specific human CD8+ T-lymphocytes treated with cytokine Interleukin-2 (IL-2) and Interleukin-15 (IL-15) for comparison.

Suggested Citation

  • Park, DoHwan & Park, Junyong & Zhong, Xiaosong & Sadelain, Michel, 2011. "Estimation of empirical null using a mixture of normals and its use in local false discovery rate," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2421-2432, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2421-2432
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    References listed on IDEAS

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    1. 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.
    2. van der Laan Mark J. & Birkner Merrill D. & Hubbard Alan E., 2005. "Empirical Bayes and Resampling Based Multiple Testing Procedure Controlling Tail Probability of the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, October.
    3. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    4. Robin, Stephane & Bar-Hen, Avner & Daudin, Jean-Jacques & Pierre, Laurent, 2007. "A semi-parametric approach for mixture models: Application to local false discovery rate estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5483-5493, August.
    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.
    6. Pounds, Stan & Rai, Shesh N., 2009. "Assumption adequacy averaging as a concept for developing more robust methods for differential gene expression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1604-1612, March.
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    Cited by:

    1. Iris Ivy M. Gauran & Junyong Park & Johan Lim & DoHwan Park & John Zylstra & Thomas Peterson & Maricel Kann & John L. Spouge, 2018. "Empirical null estimation using zero†inflated discrete mixture distributions and its application to protein domain data," Biometrics, The International Biometric Society, vol. 74(2), pages 458-471, June.

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