Parameter estimation for the calibration and variance stabilization of 
microarray data

Huber, Wolfgang; von Heydebreck, Anja; Sültmann, Holger; Poustka, Annemarie; Vingron, Martin

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Parameter estimation for the calibration and variance stabilization of microarray data

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von Heydebreck, Anja
Max Planck Society;

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Vingron, Martin
Gene regulation (Martin Vingron), Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society;

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Citation

Huber, W., von Heydebreck, A., Sültmann, H., Poustka, A., & Vingron, M. (2003). Parameter estimation for the calibration and variance stabilization of microarray data. Statistical Applications in Genetics and Molecular Biology, 2(1), article 3-article 3.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-8A6D-B

Abstract

We derive and validate an estimator for the parameters of a transformation for the joint calibration (normalization) and variance stabilization of microarray intensity data. With this, the variances of the transformed intensities become approximately independent of their expected values. The transformation is similar to the logarithm in the high intensity range, but has a smaller slope for intensities close to zero. Applications have shown better sensitivity and specificity for the detection of differentially expressed genes. In this paper, we describe the theoretical aspects of the method. We incorporate calibration and variance-mean dependence into a statistical model and use a robust variant of the maximum-likelihood method to estimate the transformation parameters. Using simulations, we investigate the size of the estimation error and its dependence on sample size and the presence of outliers. We find that the error decreases with the square root of the number of probes per array and that the estimation is robust against the presence of differentially expressed genes. Software is publicly available as an R package through the Bioconductor project (http://www.bioconductor.org).