Normalization
A microarray experiment is carried out to discover variation between samples - usually as a result of some disease, treatment, or phenotypic difference. However, there are many other factors that cause variations in microarrays - pipetting errors, printing differences, electrical fluctuations during scanning, etc. The goal of normalization is to remove these undesirable variations. True normalization, in the stastical sense, refers only to modifying the signal distribution of arrays to be more directly comparable. Most of the time, the term "normalization" in microarrays includes a background correction step.
Background Correction
Background correction seeks to eliminate the low levels of noise that are present on any microarray. Background noise is caused when the scanning laser is reflected by a surface, and can never be completely eliminated. Occasionally, high levels of background can be caused by debris or salts left over from hybridization, or by increasing the sensitivity of the scanning device.
The dotted circle shows the local neighborhood of the spot. This neighborhood defines the background noise that will be subtracted from the spots signal.
The most basic kind of background correction is local neighborhood detection. With this type of correction, the area immediately surrounding the spot is examined and averaged, and then subtracted from the signal of the spot as background. This type of correction is very robust, accounting for small variations in background across the array. However, it requires that the spots be fairly widely spaced, so that the neighborhood of each spot does not include other spots. This type of background correction is applied to spotted arrays, as well as being an element of the correction on Applied Biosystems arrays.
Another common background correction uses negative controls. These controls can be random oligos, bacterial genes, or some other sequence that will not be hybridized by the genome being queried. Therefore, these controls provide a measure of the random cross-hybridization that occurred. This is a global background - it does not account for local variations. This correction is applied to some Combimatrix arrays, as well as being an element of the correction on Applied Biosystems arrays.
An extension of the negative control scheme is to use mismatch probes. For every probe on the array, there is an additional probe with one or two of the nucleotides changed. This provides a similar measure of cross-hybridization as negative controls, while also providing local background information (since mismatches are usually adjacent to perfect matches). However, this requires twice as many spots on the array, and occasionally the mismatch will align somewhere on the genome. All Affymetrix and some Combimatrix arrays have mismatch spots, and mismatch data is used by the Affymetrix MAS 5 algorithm.
A final method of background correction is model-based. There is some evidence that mismatch probes do not provide a good picture of background, and so most recent algorithms for analyzing Affymetrix data do not even consider them. Instead, they calculate background based on a statistical model. The exact model differs, and is in fact the largest difference between the algorithms. The most common algorithms that use a model for background correction are RMA and MBEI.
Statistical Normalization
The simplest type of normalization is scaling. Scaling makes the assumption that the distribution of signal intensities on an array is normal (or Gaussian), and merely shifts the distribution to be centered at a particular point. Essentially, each signal is multiplied by a scaling factor, calculated such that a certain point in the distribution has a certain value. For instance, Affymetrix's MAS 5 algorithm throws out the top and bottom 1% of an array (as outliers), then scales the mean of the remaining signals to a certain value. Other common algorithms scale the median of the distribution, or even one of the quartiles. This normalization works surprisingly well, but has a tendency to leave too much variation at low intensities.
Ratio vs Intensity plots for an array - the left is raw data, the right is after Lowess normalization. A strong bias toward one dye is evident at lower intensities in the raw data, and is absent after normalization
Two-color arrays are frequently corrected by Lowess (or Loess) normalization. This normalization seeks to eliminate intensity-dependent bias from the ratio values (which is why it can only be applied to two-color arrays). A Lowess curve is calculated by fitting a line to the local neighborhood of each data point, and aggregating the line segments into a curve. This curve is then used to adjust each spot's value. A Lowess curve calculated after normalization should be a straight line with zero slope, indicating that ratio values are no longer dependent on intensity.
The final common type of microarray normalization is quantile. In this scheme, the arrays of signal values are sorted. The highest signal from each array is replaced by the average of all of the highest signals, the second highest on each array is replaced by the average of all of the second highest, and so forth. This results in data that is not heavily skewed by outliers, still retains the differences between the separate values, and has an identical distribution for each array. The downside is that some data can be lost, especially in the lower signals. However, quantile normalization has proven to be robust despite this drawback, and is widely used. The RMA and MBEI algorithms for Affymetrix arrays use quantile normalization, and it is the recommended normalization for Applied Biosystems arrays and the Affymetrix PLIER algorithm.
