Variance stabilization

Normalization by variance stabilization (8) comprises data calibration, the quantification of differential expression, and the quantification of measurement error. In particular, this normalization method leads to the correction of the variance-versus-mean dependence that can typically be observed when examining the variance-to-mean plots of background-corrected microarray intensity data. 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. The difference statistic Ah has approximately constant variance for the whole intensity range of the array. Note that for high intensities, h coincides with the logarithmic transformation. For low intensities the arsinh-transformation is continuous in contrast to logarithmic transformations. This is because there is no singularity around zero as in the case of logarithmic transformation. The parameters of h together with those of the calibration between experiments are estimated with a robust variant of maximum-likelihood estimation. The variance stabilizing model was introduced by Huber et al. (8) and Durbin et al. (9) and is implemented in the vsn-package in Bioconductor (; library: vsn).

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