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Parameter estimation for the calibration and variance stabilization of microarray data

Author

Listed:
  • Huber Wolfgang

    (German Cancer Research Center, Heidelberg, Germany)

  • von Heydebreck Anja

    (Max-Planck-Institute for Molecular Genetics, Berlin, Germany)

  • Sueltmann Holger

    (German Cancer Research Center, Heidelberg, Germany)

  • Poustka Annemarie

    (German Cancer Research Center, Heidelberg, Germany)

  • Vingron Martin

    (Max-Planck-Institute for Molecular Genetics, Berlin, Germany)

Abstract

We derive and validate an estimator for the parameters of a transformation for the joint calibration (normalization) and variance stabilization of microarray intensity data. With this, the variances of the transformed intensities become approximately independent of their expected values. The transformation is similar to the logarithm in the high intensity range, but has a smaller slope for intensities close to zero. Applications have shown better sensitivity and specificity for the detection of differentially expressed genes. In this paper, we describe the theoretical aspects of the method. We incorporate calibration and variance-mean dependence into a statistical model and use a robust variant of the maximum-likelihood method to estimate the transformation parameters. Using simulations, we investigate the size of the estimation error and its dependence on sample size and the presence of outliers. We find that the error decreases with the square root of the number of probes per array and that the estimation is robust against the presence of differentially expressed genes. Software is publicly available as an R package through the Bioconductor project (http://www.bioconductor.org).

Suggested Citation

  • Huber Wolfgang & von Heydebreck Anja & Sueltmann Holger & Poustka Annemarie & Vingron Martin, 2003. "Parameter estimation for the calibration and variance stabilization of microarray data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 2(1), pages 1-24, April.
    • Handle: RePEc:bpj:sagmbi:v:2:y:2003:i:1:n:3
    DOI: 10.2202/1544-6115.1008
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    Citations

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    Cited by:

    1. Ambroise Jérôme & Bearzatto Bertrand & Robert Annie & Macq Benoit & Gala Jean-Luc, 2012. "Combining Multiple Laser Scans of Spotted Microarrays by Means of a Two-Way ANOVA Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-20, February.
    2. Seppe Goovaerts & Hanne Hoskens & Ryan J. Eller & Noah Herrick & Anthony M. Musolf & Cristina M. Justice & Meng Yuan & Sahin Naqvi & Myoung Keun Lee & Dirk Vandermeulen & Heather L. Szabo-Rogers & Pau, 2023. "Joint multi-ancestry and admixed GWAS reveals the complex genetics behind human cranial vault shape," Nature Communications, Nature, vol. 14(1), pages 1-21, December.
    3. Leiva, Vctor & Sanhueza, Antonio & Kelmansky, Diana M. & Martnez, Elena J., 2009. "On the glog-normal distribution and its application to the gene expression problem," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1613-1621, March.
    4. McLachlan, G. J. & Khan, N., 2004. "On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 90-105, July.
    5. Lama, Nicola & Boracchi, Patrizia & Biganzoli, Elia, 2009. "Exploration of distributional models for a novel intensity-dependent normalization procedure in censored gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1906-1922, March.
    6. Kelmansky Diana M. & Martínez Elena J. & Leiva Víctor, 2013. "A new variance stabilizing transformation for gene expression data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 653-666, December.

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