1.5.2.1 Probe level summary
The multi-probe design of Affymetrix GeneChips requires that individual probe- level signals are combined to give a single intensity value for each transcript. Typical probe level summary methods for Affymetrix GeneChip microarrays were discussed in Section 1.4.2. The choice of summary method has been found to play a significant role in determining the comparability of the results of data analysis, and was found to be the largest source of error in meta-analyses between data sets produced by different laboratories (Bammler et al., 2005; Irizarry et al., 2005). A lot of thought must therefore be given to the choice of algorithm to use to summarise and normalise the probe-level data. It is necessary to be aware of the negative effects of using each of the available methods.
102 For instance, while RMA is more precise, specific and sensitive than MAS 5.0, resulting in reduced noise at the lower expression level values and fewer false positives (Figure 1.4.3), it also suffers from a reduction in accuracy and an increase in false negatives (Irizarry et al., 2003a; Wu et al., 2004). This results in fewer transcripts identified as differentially expressed when using RMA as compared to MAS 5.0. The information lost by using RMA can never be recovered; false positives can be confirmed or rejected with validation studies, whilst false negative results are gone forever. GC-RMA maintains the improvements seen with RMA, but uses a weighting based on the probe affinity to estimate NSB, which increases accuracy to levels comparable to MAS 5.0.
GC-RMA is typically considered to be one of the best probe level normalisation techniques, with other model-based probe-level normalisation methods such as dChip from Li and Wong (2001) performing well also. Due to the reliance on MM signal estimates for NSB, MAS 5.0 is often considered the least suitable of the techniques, however studies by Choe et al. (2005) have found that MAS 5.0 outperformed GC-RMA in determining differential expression for their spike in data set (although the data set and experimental design leading to these conclusions have been criticised (Dabney and Storey, 2006; Irizarry et al., 2006)). Also, Pepper et al. (2007) found that false positives in MAS 5.0 can be greatly minimised when used alongside the detection calls described in Section 1.4.3.1. Interestingly, it has recently been discovered that GC-RMA can result in severe artefacts in the data, leading to overestimation of pairwise correlation and inaccuracies in the calculation of network structures (Lim et al., 2007). Thus, in this context, MAS 5.0 may prove to be more reliable.
The choice of algorithm can depend largely on the data being analysed. Typically, if differential expression is suspected to be low, MAS 5.0 may be preferred in order to avoid the loss of interesting changes. However, if differential expression is suspected to be mainly of a high level, or if inter-replicate variation is high, GC- RMA is generally preferred in order to reduce false positives.
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1.5.2.2 Normalisation
To allow analysis of relative expression of genes across arrays, it is important to perform normalisation to remove systematic errors from the data and ensure that data distributions are comparable. Often, this is achieved by scaling such that the distribution of each gene is centred with a mean of 0 and a standard deviation of 1. In a gene-expression context, it is the log gene-expression that is scaled, as microarray data is thought to follow a roughly log-normal distribution (Giles and Kipling, 2003). This process removes bias and noise from the data that may be present due to technical variation that may obscure the interesting biological variation under study. The method used by Affymetrix is to simply scale the expression values such that all arrays have the same mean. Another often used method is to normalise to a reference array, which can be constructed by taking the median gene-expression across all arrays (Parmigiani et al., 2002).
In a comparison test of 5 commonly used normalisation procedures, Bolstad et al.
(2003), quantile normalisation was found to perform preferably in terms of speed, minimising variance and reducing bias. The process of quantile normalisation transforms the data such that the distribution of gene abundance is roughly equal across all arrays. Typically, the pooled distribution across all arrays is used as the reference distribution (𝐹𝑟𝑒𝑓) to which each individual array‟s signal distribution
(𝐹𝑖 for arrays 𝑖 = 1, … 𝐼) should be scaled. Thus for each array i, points are taken
regularly at intervals along the cumulative distribution function (quantiles), and for each quantile x the transformation 𝑥𝑛𝑜𝑟𝑚 = Fi−1 Fref x is applied. The
resulting set of normalised quantiles is used to build up the normalised signal distribution for array i. That is to say that the intensity values across the arrays are scaled in such a way as to be equal at specified intervals on the cumulative frequency plots. In a graphical sense, this can be thought of as adjusting the distribution of the probe intensities such that the I-dimensional quantile-quantile plot (a plot of the discretised cumulative distributions of 2 or more data distributions for comparison) approaches the identity as closely as possible. Model based normalisation techniques such as RMA, GC-RMA and dChip
104 incorporate the quantile normalisation procedure into their algorithms to allow calculation of summarised, normalised and background corrected expression data from probe-level intensity values.