In one common experimental design, DNA microarrays are built by printing or spotting an array of cDNA on a glass slide, which provides gene-specific probes for hybridization to targets. Two different samples of mRNA are labeled with different fluorescent dyes and simultaneously hybridized onto each probe. The data for each probe (gene) consists of two fluorescence intensity measurements, typically red and green, representing the expression levels of the same gene in the red-labeled (with the dye Cy5) and the green-labeled (with Cy3) mRNA samples. Early analyses of the data obtained through these microarrays will identify differentially expressed genes by taking the ratio of red intensity to green intensity, i.e., the intensity ratio, and choosing an arbitrary cut-off above or below which the genes will be interpreted as being differentially expressed in the two samples. The crucial point is that one typically does not use the absolute measure of intensity, but uses, instead, the ratio or degree of difference between samples.
In one of the earliest uses of this design, Schena et al.  called a gene differentially expressed if the expression level in the two mRNA samples differed by more than a factor of 5. DeRisi et al.  called genes differentially expressed if the logarithm of their ratio differed by more than a factor of 3, after standardizing the intensity measurements using a set of "housekeeping" genes. More recently, sophisticated statistical techniques have been developed to provide more reliable calculations of the intensity ratios by taking into account the distribution of the intensities across the whole microarray. In the first statistical analysis of these data, Chen et al.  proposed a method to identify statistically significant changes between the two mRNA samples, under several assumptions on the distribution of the intensities, including normality, null intercept, and constant variation coefficient. Newton et al.  offered a bayesian approach to the problem, using a hierarchical model for intensities and identified differentially expressed genes on the basis of the posterior odds of change. It is worthwhile to mention that Arfin et al. , in a study involving cDNA arrays expression profiling of E. coli, found little correlation between fold difference in the reported expression levels of a gene and its accuracy.
Using synthetic oligonucleotide microarrays, on the other hand, one identifies differentially expressed genes by comparing expression measurements made on two separate microarrays. On these microarrays, there is no simple measure of intensity: instead, 16 to 20 probe pairs are used to interrogate each gene. Each probe pair has a PM and MM intensity signal. In an ideal setting, if a gene is truly present, each of the PM probes would have a high intensity and each of the MM probes would have a near-zero intensity. The ratio PM/MM closely resembles the intensity ratio used with spotted microarrays; however, here we are using this ratio to determine an absolute expression level for this gene. Since each gene is represented by many probe pairs, the average log(PM/MM) is called the Log Average Ratio. A probe pair would be considered positive if PM MM is greater than or equal to a threshold, and if PM/MM is greater than or equal to another threshold (similarly, MM PM and PM/MM are calculated in considering a probe pair negative). The average of the PM MM differences for all probe pairs in a probe set is called the Average Difference, and this value is used as the absolute amount of expression for a gene.
In order to determine whether a gene expression is significantly different, current experimental protocols require the (possibly repeated) pairwise comparison of two microarrays, each hybridized to each of the different samples being compared. The intensity ratio used in the spotted arrays is thus replaced by the indirectly calculated ratio between the the average difference of each gene in the two different arrays. Typically, a cut-off threshold is arbitrarily selected between 2 and 3 (see, e.g., [97, 198]). That is, the expression level of a gene will be considered differentially expressed in an experiment if the (indirectly calculated) average difference is two or three times higher in one microarray than in the other. However, this threshold has been set as low as 1.7 .
The major manufacturer of these microarrays  provides software implementing a different measure of differential expression. Let x represent the average difference of a gene on one microarray and y its average difference on the second microarray. For each gene, the level of change across the two microarrays is computed by a weighted ratio:
If y e x, then +1 is added to W, otherwise W-1. Qc is the maximum noise level of the two microarrays, or the difference in pixel intensities seen in the lowest intensity probes, and Qm is a constant depending on the resolution of the microarray—2.1 for 50 1Am feature microarrays and 2.8 for 24 1Am feature microarrays. However, the decision of whether a gene is significantly differentially expressed in the two microarrays is based on a complicated interpretation of the change of each of its 14 to 20 probe pairs. Let (PM MM)x be the difference between PM and MM for a probe pair in the first array and (PM MM)y be the same difference for the same probe pair on the second array. A probe pair shows a significant change (increased or decreased) across two microarrays if:
1. the difference (PM MM)y - (PM MM)x is higher than an arbitrary threshold called the Change Threshold, and
2. the ratio, exceeds another arbitrary threshold called the Percent Change Threshold, where Q represents the noise on the chip.
Given this definition of a significantly increased or decreased probe pair, a gene is considered significantly differentially expressed based on four aggregate measures:
1. The number of increased or decreased probe pairs, which ever is higher.
2. The ratio of the number of increased probe pairs to the number of decreased probe pairs.
3. The difference or subtraction of the log average ratios of the gene in the two microarrays.
4. The difference in the number of positive probe pairs minus the difference in the number of negative probe pairs, divided by the number of probe pairs.
The decision of whether a gene is significantly differentially expressed between two microarrays is decided by a user-modifiable matrix indexed by the above four results. The user can set thresholds to define the boundaries where each metric changes the decision. Default values for these thresholds have been set by the manufacturer through in-house empirical testing.'51 Since systematic variations are expected to occur between any two microarrays—due to biological noise, changed environmental conditions, or other factors affecting equally all genes on an array— various normalization techniques are used to render comparable the expression levels across the two microarrays. Section 3.4.1 discusses the various techniques used.
It should be clear that there is a great deal of difference in the interpretation of intensity measurements, intensity ratios, and gene expression levels across the two systems. Fundamentally, spotted arrays are currently used to measure a difference in transcription levels between two samples, whereas oligonucleotide arrays are used to measure absolute transcription levels in a single sample. Even if one discounts the differences in the quantitative and differencing algorithms, it should be obvious to the reader that the "results" of an experiment involving spotted arrays are going to be significantly influenced by the choice of the reference or control sample, already implying that the resulting values are not directly comparable.
[51As complicated as this methodology sounds in our description here, we are ignoring the fact that in the actual algorithm, not all available probe pairs are used in these calculations. Probe pairs with an intensity difference significantly beyond the mean intensity difference are considered outliers and are ignored in these calculations.
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