varianceStabilizingTransformation: Apply a variance stabilizing transformation (VST) to the count data

Description

This function calculates a variance stabilizing transformation (VST) from the fitted dispersion-mean relation(s) and then transforms the count data (normalized by division by the size factors or normalization factors), yielding a matrix of values which are now approximately homoskedastic (having constant variance along the range of mean values). The transformation also normalizes with respect to library size. The rlog is less sensitive to size factors, which can be an issue when size factors vary widely. These transformations are useful when checking for outliers or as input for machine learning techniques such as clustering or linear discriminant analysis.

Usage

varianceStabilizingTransformation(object, blind = TRUE,
  fitType = "parametric")
getVarianceStabilizedData(object)

Arguments

object

a DESeqDataSet or matrix of counts

blind

logical, whether to blind the transformation to the experimental design. blind=TRUE should be used for comparing samples in an manner unbiased by prior information on samples, for example to perform sample QA (quality assurance). blind=FALSE should be used for transforming data for downstream analysis, where the full use of the design information should be made. blind=FALSE will skip re-estimation of the dispersion trend, if this has already been calculated. If many of genes have large differences in counts due to the experimental design, it is important to set blind=FALSE for downstream analysis.

fitType

in case dispersions have not yet been estimated for object, this parameter is passed on to estimateDispersions (options described there).

Value

varianceStabilizingTransformation returns a DESeqTransform if a DESeqDataSet was provided, or returns a a matrix if a count matrix was provided. Note that for DESeqTransform output, the matrix of transformed values is stored in assay(vsd). getVarianceStabilizedData also returns a matrix.

Details

For each sample (i.e., column of counts(dds)), the full variance function is calculated from the raw variance (by scaling according to the size factor and adding the shot noise). We recommend a blind estimation of the variance function, i.e., one ignoring conditions. This is performed by default, and can be modified using the 'blind' argument.

Note that neither rlog transformation nor the VST are used by the differential expression estimation in DESeq, which always occurs on the raw count data, through generalized linear modeling which incorporates knowledge of the variance-mean dependence. The rlog transformation and VST are offered as separate functionality which can be used for visualization, clustering or other machine learning tasks. See the transformation section of the vignette for more details.

The transformation does not require that one has already estimated size factors and dispersions.

A typical workflow is shown in Section Variance stabilizing transformation in the package vignette.

If estimateDispersions was called with:

fitType="parametric", a closed-form expression for the variance stabilizing transformation is used on the normalized count data. The expression can be found in the file vst.pdf which is distributed with the vignette.

fitType="local", the reciprocal of the square root of the variance of the normalized counts, as derived from the dispersion fit, is then numerically integrated, and the integral (approximated by a spline function) is evaluated for each count value in the column, yielding a transformed value.

fitType="mean", a VST is applied for Negative Binomial distributed counts, 'k', with a fixed dispersion, 'a': ( 2 asinh(sqrt(a k)) - log(a) - log(4) )/log(2).

In all cases, the transformation is scaled such that for large counts, it becomes asymptotically (for large values) equal to the logarithm to base 2 of normalized counts.

The variance stabilizing transformation from a previous dataset can be frozen and reapplied to new samples. See the 'Data quality assessment' section of the vignette for strategies to see if new samples are sufficiently similar to previous datasets. The frozen VST is accomplished by saving the dispersion function accessible with dispersionFunction, assigning this to the DESeqDataSet with the new samples, and running varianceStabilizingTransformation with 'blind' set to FALSE (see example below). Then the dispersion function from the previous dataset will be used to transform the new sample(s). Limitations: In order to preserve normalization, the same transformation has to be used for all samples. This results in the variance stabilizition to be only approximate. The more the size factors differ, the more residual dependence of the variance on the mean will be found in the transformed data. rlog is a transformation which can perform better in these cases. As shown in the vignette, the function meanSdPlot from the package vsn can be used to see whether this is a problem.

References

Reference for the variance stabilizing transformation for counts with a dispersion trend:

Simon Anders, Wolfgang Huber: Differential expression analysis for sequence count data. Genome Biology 2010, 11:106. http://dx.doi.org/10.1186/gb-2010-11-10-r106

Examples

Run this code

dds <- makeExampleDESeqDataSet(m=6)
vsd <- varianceStabilizingTransformation(dds)
dists <- dist(t(assay(vsd)))
plot(hclust(dists))

# learn the dispersion function of a dataset
design(dds) <- ~ 1
dds <- estimateSizeFactors(dds)
dds <- estimateDispersions(dds)

# use the previous dispersion function for a new sample
ddsNew <- makeExampleDESeqDataSet(m=1)
ddsNew <- estimateSizeFactors(ddsNew)
dispersionFunction(ddsNew) <- dispersionFunction(dds)
vsdNew <- varianceStabilizingTransformation(ddsNew, blind=FALSE)

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