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A Bayesian decision procedure for testing multiple hypotheses in DNA microarray experiments

Author

Listed:
  • Gómez-Villegas Miguel A.

    (Dpto. de Estadística e I.O., Facultad de Ciencias Matemáticas, Plaza de las Ciencias, 3, Universidad Complutense de Madrid, 28040–Madrid, Spain)

  • Salazar Isabel

    (Dpto. de Producción Animal, Facultad de Veterinaria, Universidad Complutense de Madrid, 28040–Madrid, Spain)

  • Sanz Luis

    (Dpto. de Estadística e I.O., Facultad de Ciencias Matemáticas, Plaza de las Ciencias, 3, Universidad Complutense de Madrid, 28040–Madrid, Spain)

Abstract

DNA microarray experiments require the use of multiple hypothesis testing procedures because thousands of hypotheses are simultaneously tested. We deal with this problem from a Bayesian decision theory perspective. We propose a decision criterion based on an estimation of the number of false null hypotheses (FNH), taking as an error measure the proportion of the posterior expected number of false positives with respect to the estimated number of true null hypotheses. The methodology is applied to a Gaussian model when testing bilateral hypotheses. The procedure is illustrated with both simulated and real data examples and the results are compared to those obtained by the Bayes rule when an additive loss function is considered for each joint action and the generalized loss 0–1 function for each individual action. Our procedure significantly reduced the percentage of false negatives whereas the percentage of false positives remains at an acceptable level.

Suggested Citation

  • Gómez-Villegas Miguel A. & Salazar Isabel & Sanz Luis, 2014. "A Bayesian decision procedure for testing multiple hypotheses in DNA microarray experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 49-65, February.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:1:p:49-65:n:4
    DOI: 10.1515/sagmb-2012-0076
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    References listed on IDEAS

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    1. Wenguang Sun & Alexander C. McLain, 2012. "Multiple Testing of Composite Null Hypotheses in Heteroscedastic Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 673-687, June.
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    3. Peter Muller & Giovanni Parmigiani & Christian Robert & Judith Rousseau, 2004. "Optimal Sample Size for Multiple Testing: The Case of Gene Expression Microarrays," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 990-1001, December.
    4. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517, August.
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