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A new variance stabilizing transformation for gene expression data analysis

Author

Listed:
  • Kelmansky Diana M.
  • Martínez Elena J.

    (Instituto de Cálculo, FCEN, Universidad de Buenos Aires, Argentina)

  • Leiva Víctor

    (Departamento de Estadística, Universidad de Valparaíso, Avda. Gran Bretaña 1111, Playa Ancha, Valparaíso, Chile)

Abstract

In this paper, we introduce a new family of power transformations, which has the generalized logarithm as one of its members, in the same manner as the usual logarithm belongs to the family of Box-Cox power transformations. Although the new family has been developed for analyzing gene expression data, it allows a wider scope of mean-variance related data to be reached. We study the analytical properties of the new family of transformations, as well as the mean-variance relationships that are stabilized by using its members. We propose a methodology based on this new family, which includes a simple strategy for selecting the family member adequate for a data set. We evaluate the finite sample behavior of different classical and robust estimators based on this strategy by Monte Carlo simulations. We analyze real genomic data by using the proposed transformation to empirically show how the new methodology allows the variance of these data to be stabilized.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sagmbi:v:12:y:2013:i:6:p:653-666:n:1
    DOI: 10.1515/sagmb-2012-0030
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    References listed on IDEAS

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    1. Samuel Kotz & Víctor Leiva & Antonio Sanhueza, 2010. "Two New Mixture Models Related to the Inverse Gaussian Distribution," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 199-212, March.
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    4. Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
    5. 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.
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