Sub-array normalization subject to differentiation

From microarray measurement, we seek differentiation of mRNA expressions among different biological samples. However, each array has a 'block effect' due to uncontrolled variation. The statistical treatment of reducing the block effect is usually referred to as normalization. Our perspective is to find a transformation that matches the distributions of hybridization levels of those probes corresponding to undifferentiated genes between arrays. We address two important issues. First, array-specific spatial patterns exist due to uneven hybridization and measurement process. Second, in some cases a substantially large portion of genes are differentially expressed between a target and a reference array. For the purpose of normalization we need to identify a subset that exclude those probes corresponding to differentially expressed genes and abnormal probes due to experimental variation. Least trimmed squares (LTS) is a natural choice to achieve this goal. Substantial differentiation is protected in LTS by setting an appropriate trimming fraction. To take into account any spatial pattern of hybridization, we divide each array into sub-arrays and normalize probe intensities within each sub-array. We illustrate the problem and solution through an Affymetrix spike-in dataset with defined perturbation and a dataset of primate brain expression.