Bioinformatics Vol. 18 no. 90001 2002
Pages S96-S104
© 2002 Oxford University Press
Variance stabilization applied to microarray data calibration and to the quantification of differential expression
1 Department of Molecular Genome Analysis, German Cancer Research Center,
INF 280, Heidelberg, 69120, Germany
2 Department of Computational Molecular Biology, Max-Planck-Institute for Molecular Genetics,
Dahlem, Berlin, 14195, Germany
Received on January 24, 2002
; revised on March 30, 2002
; accepted on March 30, 2002
We introduce a statistical model for microarray gene expression data
that comprises data calibration, the quantification of differential
expression, and the quantification of measurement error.
In particular, we derive a transformation h for intensity measurements,
and a difference statistic 
h whose variance is approximately constant
along the whole intensity range.
This forms a basis for statistical inference from microarray data,
and provides a rational data pre-processing strategy for multivariate
analyses.
For the transformation h, the parametric form h(x)=arsinh(a+bx)
is derived from a model of the variance-versus-mean dependence for
microarray intensity data, using the method of variance stabilizing
transformations.
For large intensities, h coincides with the logarithmic transformation,
and h with the log-ratio.
The parameters of h together with those of the calibration between experiments
are estimated with a robust variant of maximum-likelihood estimation.
We demonstrate our approach on data sets from different experimental
platforms, including two-colour cDNA arrays and a series of
Affymetrix oligonucleotide arrays.
Availability: Software is freely available for academic use as an R package at http://www.dkfz.de/abt0840/whuber
Contact: w.huber{at}dkfz.de
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