Variance stabilization applied to microarray data calibration and to the quantification of differential expression

TLDR

The study introduces a statistical model for microarray gene expression data that integrates data calibration, differential expression quantification, and measurement error estimation. The authors derive a variance‑stabilizing transformation h(x)=arsinh(a+bx) and a difference statistic Δh, estimating parameters via robust maximum‑likelihood to calibrate intensity data across experiments. The method yields a variance‑stable transformation that aligns with log‑ratio at high intensities and enables reliable inference, as demonstrated on two‑colour cDNA and Affymetrix oligonucleotide arrays. Software is freely available as an R package at http://www.dkfz.de/abt0840/whuber (contact [e-mail]).

Abstract

Abstract 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 Δh 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 Δh 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: [e-mail]