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It is well known that correlations in microarray data represent a seriousnuisance deteriorating the performance of gene selection procedures. This paperis intended to demonstrate that the correlation structure of microarray dataprovides a rich source of useful information. We discuss distinct correlationsubstructures revealed in microarray gene expression data by an appropriateordering of genes. These substructures include stochastic proportionality ofexpression signals in a large percentage of all gene pairs, negativecorrelations hidden in ordered gene triples, and a long sequence of weaklydependent random variables associated with ordered pairs of genes. The reportedstriking regularities are of general biological interest and they also havefar-reaching implications for theory and practice of statistical methods ofmicroarray data analysis. We illustrate the latter point with a method fortesting differential expression of nonoverlapping gene pairs. While designedfor testing a different null hypothesis, this method provides an order ofmagnitude more accurate control of type 1 error rate compared to conventionalmethods of individual gene expression profiling. In addition, this method isrobust to the technical noise. Quantitative inference of the correlationstructure has the potential to extend the analysis of microarray data farbeyond currently practiced methods.

Diverse correlation structures in gene expression data and their utility in improving statistical inference