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Error-Rate and Decision-Theoretic Methods of Multiple Testing: Which Genes Have High Objective Probabilities of Differential Expression?

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  • Bickel David R.

    (Medical College of Georgia (currently at Pioneer Hi-Bred International))

Abstract

Given a multiple testing situation, the null hypotheses that appear to have sufficiently low probabilities of truth may be rejected using a simple, nonparametric method based on decision theory. This applies not only to posterior levels of belief, but also to conditional probabilities in the sense of relative frequencies, as seen from their equality to local false discovery rates (dFDRs). This approach neither requires the estimation of probability densities, nor of their ratios. Decision theory can also inform the selection of false discovery rate weights. An application to gene expression microarrays is presented with a discussion of the applicability of the assumption of "clumpy dependence."

Suggested Citation

  • Bickel David R., 2004. "Error-Rate and Decision-Theoretic Methods of Multiple Testing: Which Genes Have High Objective Probabilities of Differential Expression?," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-22, May.
    • Handle: RePEc:bpj:sagmbi:v:3:y:2004:i:1:n:8
    DOI: 10.2202/1544-6115.1043
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    Cited by:

    1. David R. Bickel, 2011. "Estimating the Null Distribution to Adjust Observed Confidence Levels for Genome-Scale Screening," Biometrics, The International Biometric Society, vol. 67(2), pages 363-370, June.
    2. Debashis Ghosh, 2006. "Shrunken p-Values for Assessing Differential Expression with Applications to Genomic Data Analysis," Biometrics, The International Biometric Society, vol. 62(4), pages 1099-1106, December.

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