vsn {vsn} | R Documentation

## Variance stabilization and calibration for microarray data.

### Description

Robust estimation of variance-stabilizing and calibrating transformations for microarray data. This is the main function of this package; see also the vignette vsn.pdf.

### Usage

    vsn(intensities,
        lts.quantile = 0.5,
        verbose      = interactive(),
        niter        = 10,
        cvg.check    = NULL,
        describe.preprocessing = TRUE,
        subsample,
        pstart,
        strata)

### Arguments

`intensities` | An object that contains intensity values from a microarray experiment. See `getIntensityMatrix` for details. The intensities are assumed to be the raw scanner data, summarized over the spots by an image analysis program, and possibly "background subtracted". The intensities must not be logarithmically or otherwise transformed, and not thresholded or "floored". NAs are not accepted. See details.
`lts.quantile` | Numeric. The quantile that is used for the resistant least trimmed sum of squares regression. Allowed values are between 0.5 and 1. A value of 1 corresponds to ordinary least sum of squares regression.
`verbose` | Logical. If TRUE, some messages are printed.
`niter` | Integer. The number of iterations to be used in the least trimmed sum of squares regression.
`cvg.check` | List. If non-NULL, this allows finer control of the iterative least trimmed sum of squares regression. See details.
`pstart` | Array. If not missing, user can specify start values for the iterative parameter estimation algorithm. See `vsnh` for details.
`describe.preprocessing` | Logical. If TRUE, calibration and transformation parameters, plus some other information are stored in the `preprocessing` slot of the returned object. See details.
`subsample` | Integer. If specified, the model parameters are estimated from a subsample of the data only, the transformation is then applied to all data. This can be useful for performance reasons.
`strata` | Integer vector. Its length must be the same as nrow(intensities). This parameter allows for the calibration and error model parameters to be stratified within each array, e.g to take into account probe sequence properties, print-tip or plate effects. If `strata` is not specified, one pair of parameters is fitted for every sample (i.e. for every column of `intensities`). If `strata` is specified, a pair of parameters is fitted for every stratum within every sample. The strata are coded for by the different integer values. The integer vector `strata` can be obtained from a factor `fac` through `as.integer(fac)`, from a character vector `str` through `as.integer(factor(fac))`.

### Details

Overview: The function calibrates for sample-to-sample variations through shifting and scaling, and transforms the intensities to a scale where the variance is approximately independent of the mean intensity. The variance stabilizing transformation is equivalent to the natural logarithm in the high-intensity range, and to a linear transformation in the low-intensity range. In an intermediate range, the arsinh function interpolates smoothly between the two. For details on the transformation, please see the help page for `vsnh`. The parameters are estimated through a robust variant of maximum likelihood. This assumes that for the majority of genes the expression levels are not much different across the samples, i.e., that only a minority of genes (less than a fraction `1-lts.quantile`) is differentially expressed.

Even if most genes on an array are differentially expressed, it may still be possible to use the estimator: if a set of non-differentially expressed genes is known, e.g. because they are external controls or reliable 'house-keeping genes', the transformation parameters can be fitted with `vsn` from the data of these genes, then the transformation can be applied to all data with `vsnh`.

Format: The format of the matrix of intensities is as follows: for the two-color printed array technology, each row corresponds to one spot, and the columns to the different arrays and wave-lengths (usually red and green, but could be any number). For example, if there are 10 arrays, the matrix would have 20 columns, columns 1...10 containing the green intensities, and 11...20 the red ones. In fact, the ordering of the columns does not matter to `vsn`, but it is your responsibility to keep track of it for subsequent analyses. For one-color arrays, each row corresponds to a probe, and each column to an array.

Performance: This function is slow. That is due to the nested iteration loops of the numerical optimization of the likelihood function and the heuristic that identifies the non-outlying data points in the least trimmed squares regression. For large arrays with many tens of thousands of probes, you may want to consider random subsetting: that is, only use a subset of the e.g. 10-20,000 rows of the data matrix `intensities` to fit the parameters, then apply the transformation to all the data, using `vsnh`. An example for this can be seen in the function `normalize.AffyBatch.vsn`, whose code you can inspect by typing `normalize.AffyBatch.vsn` on the R command line.

Iteration control: By default, if `cvg.check` is `NULL`, the function will run the fixed number `niter` of iterations in the least trimmed sum of squares regression. More fine-grained control can be obtained by passing a list with elements `eps` and `n`. If the maximum change between transformed data values is smaller than `eps` for `n` subsequent iterations, then the iteration terminates.

Estimated transformation parameters: If `describe.preprocessing` is `TRUE`, the transformation parameters are returned in the `preprocessing` slot of the `description` slot of the resulting `exprSet` object, in the form of a `list` with three elements

- `vsnParams`: the parameter array (see `vsnh` for details)
- `vsnParamsIter`: an array with dimensions `c(dim(vsnParams, niter))` that contains the parameter trajectory during the iterative fit process (see also `vsnPlotPar`).
- `vsnTrimSelection`: a logical vector that for each row of the intensities matrix reports whether it was below (TRUE) or above (FALSE) the trimming threshold.

If `intensities` has class `exprSet`, and its `description` slot has class `MIAME`, then this list is appended to any existing entries in the `preprocessing` slot. Otherwise, the `description` object and its `preprocessing` slot are created.

### Value

An object of class `exprSet`. Differences between the columns of the transformed intensities are "generalized log-ratios", which are shrinkage estimators of the natural logarithm of the fold change. For the transformation parameters, please see the Details.

### Author(s)

Wolfgang Huber http://www.ebi.ac.uk/huber

### References

Variance stabilization applied to microarray data calibration and to the quantification of differential expression, Wolfgang Huber, Anja von Heydebreck, Holger Sueltmann, Annemarie Poustka, Martin Vingron; Bioinformatics (2002) 18 Suppl.1 S96-S104.

Parameter estimation for the calibration and variance stabilization of microarray data, Wolfgang Huber, Anja von Heydebreck, Holger Sueltmann, Annemarie Poustka, and Martin Vingron; Statistical Applications in Genetics and Molecular Biology (2003) Vol. 2 No. 1, Article 3. http://www.bepress.com/sagmb/vol2/iss1/art3.

### See Also

`vsnh`, `vsnPlotPar`, `exprSet-class`, `MIAME-class`, `normalize.AffyBatch.vsn`

### Examples

    data(kidney)
    log.na = function(x) log(ifelse(x>0, x, NA))

    if(interactive()) {
      x11(width=9, height=4.5)
      par(mfrow=c(1,2))
    }
    plot(log.na(exprs(kidney)), pch=".", main="log-log")

    vsnkid = vsn(kidney)   ## transform and calibrate
    plot(exprs(vsnkid), pch=".", main="h-h")

    if (interactive()) {
      x11(width=9, height=4)
      par(mfrow=c(1,3))
    }

    meanSdPlot(vsnkid)
    vsnPlotPar(vsnkid, "factors")
    vsnPlotPar(vsnkid, "offsets")

    ## this should always hold true
    params = preproc(description(vsnkid))$vsnParams
    stopifnot(all(vsnh(exprs(kidney), params) == exprs(vsnkid)))

[Package vsn version 1.10.0 Index]