- 1 Getting started
- 2 Running VSN on data from a single two-colour array
- 3 Running VSN on data from multiple arrays (“single colour normalisation”)
- 4 Running VSN on Affymetrix genechip data
- 5 Running VSN on RGList objects
- 6 Missing values
- 7 Normalisation with ‘spike-in’ probes
- 8 Normalisation against an existing reference dataset
- 9 The calibration parameters
- 10 Variance stabilisation without calibration
- 11 Assessing the performance of VSN
- 12 VSN, shrinkage and background correction
- 13 Quality assessment
- 14 Acknowledgements
- 15 Session info
- References

This is an unfinished port of the package’s “old” Sweave/PDF vignette into Rmarkdown/HTML. There are still bugs in here, like unevaluated LaTeX markup (incl. footnotes), unmapped cross-references, figure formatting. Please bear with me. In doubt, please consult the existing PDF vignette.

VSN is a method to preprocess microarray intensity data. This can be as simple as

```
library("vsn")
data("kidney")
xnorm = justvsn(kidney)
```

where `kidney`

is an `ExpressionSet`

object with unnormalised data and `xnorm`

the resulting `ExpressionSet`

with calibrated and glog\(_2\)-transformed data.

`M = exprs(xnorm)[,1] - exprs(xnorm)[,2]`

produces the vector of generalised log-ratios between the data in the first and second column.

VSN is a model-based method, and the more explicit way of doing the above is

```
fit = vsn2(kidney)
ynorm = predict(fit, kidney)
```

where `fit`

is an object of class `vsn`

that contains the fitted calibration and transformation parameters, and the method `predict`

applies the fit to the data. The two-step protocol is useful when you want to fit the parameters on a subset of the data, e.,g. a set of control or spike-in features, and then apply the model to the complete set of data (see Section~ for details). Furthermore, it allows further inspection of the `fit`

object, e.,g. for the purpose of quality assessment.

Besides `ExpressionSet`

s, there are also `justvsn`

methods for `AffyBatch`

objects from the *affy* package and `RGList`

objects from the *limma* package. They are described in this vignette.

The so-called glog\(_2\) (short for generalised logarithm) is a function that is like the logarithm (base 2) for large values (large compared to the amplitude of the background noise), but is less steep for smaller values. Differences between the transformed values are the generalised log-ratios. These are shrinkage estimators of the logarithm of the fold change. The usual log-ratio is another example for an estimator of log fold change. There is also a close relationship between background correction of the intensities and the variance properties of the different estimators. Please see Section~ for more explanation of these issues.

How does VSN work? There are two components: First, an affine transformation whose aim is to calibrate systematic experimental factors such as labelling efficiency or detector sensitivity. Second, a glog\(_2\) transformation whose aim is variance stabilisation.

An affine transformation is simply a shifting and scaling of the data, i.,e. a mapping of the form \(x\mapsto (x-a)/s\) with offset \(a\) and scaling factor \(s\). By default, a different offset and a different scaling factor are used for each column, but the same for all rows within a column. There are two parameters of the function `vsn2`

to control this behaviour: With the parameter `strata`

, you can ask `vsn2`

to choose different offset and scaling factors for different groups (“strata”) of rows. These strata could, for example, correspond to sectors on the array. With the parameter `calib`

, you can ask `vsn2`

to choose the same offset and scaling factor throughout. This can be useful, for example, if the calibration has already been done by other means, e.g., quantile normalisation.

Note that VSN’s variance stabilisation only addresses the dependence of the variance on the mean intensity. There may be other factors influencing the variance, such as gene-inherent properties or changes of the tightness of transcriptional control in different conditions. These need to be addressed by other methods.

The dataset `kidney`

contains example data from a spotted cDNA two-colour microarray on which cDNA from two adjacent tissue samples of the same kidney were hybridised, one labeled in green (Cy3), one in red (Cy5). The two columns of the matrix `exprs(kidney)`

contain the green and red intensities, respectively. A local background estimate was calculated by the image analysis software and subtracted, hence some of the intensities in `kidney`

are close to zero or negative. In Figure @ref{fig:nkid-scp} you can see the scatterplot of the calibrated and transformed data. For comparison, the scatterplot of the log-transformed raw intensities is also shown.

```
library("ggplot2")
allpositive = (rowSums(exprs(kidney) <= 0) == 0)
## some data shuffling to bring data into the right shape and data.frame for ggplot
df1 = data.frame(log2(exprs(kidney)[allpositive, ]),
type = "raw",
allpositive = TRUE)
df2 = data.frame(exprs(xnorm),
type = "vsn",
allpositive = allpositive)
df = rbind(df1, df2)
names(df)[1:2] = c("x", "y")
ggplot(df, aes(x, y, col = allpositive)) + geom_hex(bins = 40) +
coord_fixed() + facet_grid( ~ type)
```

`meanSdPlot`

. For each feature \(k=1,\ldots,n\) it shows the empirical standard deviation \(\hat{\sigma}_k\) on the \(y\)-axis versus the rank of the average \(\hat{\mu}_k\) on the \(x\)-axis.
\begin{equation}
\hat{\mu}_k =\frac{1}{d} \sum_{i=1}^d h_{ki}\quad\quad
\hat{\sigma}_k^2=\frac{1}{d-1}\sum_{i=1}^d (h_{ki}-\hat{\mu}_k)^2
\end{equation}
`meanSdPlot(xnorm, ranks = TRUE)`