vsn 3.70.0

- 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
- Session info
- References

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 7 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 estimator1 In statistics, the term estimator is used to denote an algorithm that calculates a value from measured data. This value is intended to correspond to the true value of a parameter of the underlying process that generated the data. Depending on the amount of the available data and the quality of the estimator, the intention may be more or less satisfied. 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 12 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
array2 See Section 5.2.. With the parameter
`calib`

, you can ask `vsn2`

to choose the same
offset and scaling factor throughout3 See
Section 10.. 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 estimate4 See Section 12 for more
on the relationship between background correction and variance
stabilising transformations. was calculated by the image analysis
software and subtracted, hence some of the intensities in
`kidney`

are close to zero or negative. In
Figure 1 you can see the scatterplot of the
calibrated and transformed data. For comparison, the scatterplot of
the log-transformed raw intensities is also shown. The code below involves
some data shuffling to move the data into datasframes for `ggplot`

.

```
library("ggplot2")
allpositive = (rowSums(exprs(kidney) <= 0) == 0)
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)
```

To verify the variance stabilisation, there is the function `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)`

`meanSdPlot(xnorm, ranks = FALSE) `

The red dots, connected by lines, show the running median of the standard
deviation5 The parameters used were: window width 10%, window
midpoints 5%, 10%, 15%, … . It should be said that the proper
way to do is with quantile regression such as provided by the
*quantreg* package—what is done here for these plots is
simple, cheap and should usually be good enough due to the abundance
of data.. The aim of these plots is to see whether there is a
systematic trend in the standard deviation of the data as a function
of overall expression. The assumption that underlies the usefulness of
these plots is that most genes are not differentially expressed, so
that the running median is a reasonable estimator of the standard
deviation of feature level data conditional on the mean. After
variance stabilisation, this should be approximately a horizontal
line. It may have some random fluctuations, but should not show an
overall trend. If this is not the case, that usually indicates a data
quality problem, or is a consequence of inadequate prior data
preprocessing. The rank ordering distributes the data evenly along
the \(x\)-axis. A plot in which the \(x\)-axis shows the average
intensities themselves is obtained by calling the `plot`

command with the argument `ranks=FALSE`

; but this is
less effective in assessing variance and hence is not the default.

The histogram of the generalized log-ratios:

`hist(M, breaks = 100, col = "#d95f0e")`

The package includes example data from a series of 8 spotted cDNA arrays on which cDNA samples from different lymphoma were hybridised together with a reference cDNA (Alizadeh et al. 2000).

```
data("lymphoma")
dim(lymphoma)
```

```
## Features Samples
## 9216 16
```

The 16 columns of the `lymphoma`

object contain the red and
green intensities, respectively, from the 8 slides.

`pData(lymphoma)`

```
## name sample dye
## lc7b047.reference lc7b047 reference Cy3
## lc7b047.CLL-13 lc7b047 CLL-13 Cy5
## lc7b048.reference lc7b048 reference Cy3
## lc7b048.CLL-13 lc7b048 CLL-13 Cy5
## lc7b069.reference lc7b069 reference Cy3
## lc7b069.CLL-52 lc7b069 CLL-52 Cy5
## lc7b070.reference lc7b070 reference Cy3
## lc7b070.CLL-39 lc7b070 CLL-39 Cy5
## lc7b019.reference lc7b019 reference Cy3
## lc7b019.DLCL-0032 lc7b019 DLCL-0032 Cy5
## lc7b056.reference lc7b056 reference Cy3
## lc7b056.DLCL-0024 lc7b056 DLCL-0024 Cy5
## lc7b057.reference lc7b057 reference Cy3
## lc7b057.DLCL-0029 lc7b057 DLCL-0029 Cy5
## lc7b058.reference lc7b058 reference Cy3
## lc7b058.DLCL-0023 lc7b058 DLCL-0023 Cy5
```

We can call `justvsn`

on all of them at once:

`lym = justvsn(lymphoma)`

`meanSdPlot(lym)`

We see that the variance stabilisation worked. As above, we can obtain the generalised log-ratios for each slide by subtracting the common reference intensities from those for the 8 samples:

```
iref = seq(1, 15, by=2)
ismp = seq(2, 16, by=2)
M = exprs(lym)[,ismp]-exprs(lym)[,iref]
A =(exprs(lym)[,ismp]+exprs(lym)[,iref])/2
colnames(M) = lymphoma$sample[ismp]
colnames(A) = colnames(M)
j = "DLCL-0032"
smoothScatter(A[,j], M[,j], main=j, xlab="A", ylab="M", pch=".")
abline(h=0, col="red")
```