Variance stabilization applied to microarray data calibration and to the quantification of differential expression.
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 Deltah 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 Deltah 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.
Huber
Wolfgang
W
Department of Molecular Genome Analysis, German Cancer Research Center, INF 280, Heidelberg, 69120, Germany. w.huber@dkfz.de
von Heydebreck
Anja
A
Sültmann
Holger
H
Poustka
Annemarie
A
Vingron
Martin
M
D000465:Algorithms; D000704:Analysis of Variance; D002138:Calibration / Q000592:standards; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling / Q000295:instrumentation* / Q000379:methods* / Q000592:standards; D016013:Likelihood Functions; D008957:Models, Genetic; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000295:instrumentation* / Q000379:methods* / Q000592:standards; D012015:Reference Standards; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012984:Software