A new variance stabilizing transformation for gene expression data analysis

Kelmansky Diana M., Martínez Elena J. and Leiva Víctor ()
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Kelmansky Diana M.: Instituto de Cálculo, FCEN, Universidad de Buenos Aires, Argentina
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

Statistical Applications in Genetics and Molecular Biology, 2013, vol. 12, issue 6, 653-666

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.

Keywords: classical and robust estimators; linear models; microarrays; Monte Carlo method; power transformations; R software; regression methods (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1515/sagmb-2012-0030

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