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+<blockquote>

+<p>Microarray data then was preprocessed using the RMA method [bolstad] and subsequently batch corrected [Alberts et al]. In this study, RNA was extracted at three different points in time for the Treg samples and also microarray processing was performed at three different points in time. Similarly, the Th samples were processed in two batches. Therefore, we performed a batch correction for both cell types using the following ANOVA model before further analysis of the data.<br />

+<em>y<sub>i</sub> = </em><em>&mu;</em><em> + B<sub>i</sub> + e<sub>i</sub></em><br />

+Where <em>y<sub>i</sub></em> is the expression level of the <em>i</em><sup>th</sup> microarray, <em>&mu;</em> is the overall mean, B<em><sub>i</sub> </em>is the batch to which the <em>i</em>th individual belongs and <em>e<sub>i</sub> </em>is the residual error.<br />

+Batch corrected data sets were then preprocessed before transferring them to the GeneNetwork (GN) database: Adding an offset of 1 unit to each signal intensity value to ensure that the logarithm of all values were positive, computing the log2 value, performing a quantile normalization of the log2 values for the total set of arrays using the same initial steps used by the RMA transform, computing the Z scores for each cell value, multiplying all Z scores by 2 and adding 8 to the value of all Z scores. The advantage of this variant of a Z transformation is that all values are positive and that 1 unit represents approximately a 2-fold difference in expression as determined using the spike-in control probe sets. The mean values were subsequently calculated if multiple samples from one BXD line were recorded (male and females or replicates).</p>

+</blockquote>