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

TL;DR

This paper reveals complex correlation patterns in gene expression data that can be exploited to improve statistical inference, especially in testing differential gene expression with greater accuracy and robustness.

Contribution

It demonstrates that correlation structures in microarray data contain valuable information that enhances statistical methods beyond traditional approaches.

Findings

Identification of distinct correlation substructures in gene expression data

A new method for testing differential expression with improved error control

Correlation analysis offers insights with broad biological and statistical implications

Abstract

It is well known that correlations in microarray data represent a serious nuisance deteriorating the performance of gene selection procedures. This paper is intended to demonstrate that the correlation structure of microarray data provides a rich source of useful information. We discuss distinct correlation substructures revealed in microarray gene expression data by an appropriate ordering of genes. These substructures include stochastic proportionality of expression signals in a large percentage of all gene pairs, negative correlations hidden in ordered gene triples, and a long sequence of weakly dependent random variables associated with ordered pairs of genes. The reported striking regularities are of general biological interest and they also have far-reaching implications for theory and practice of statistical methods of microarray data analysis. We illustrate the latter point with a method for testing differential expression of nonoverlapping gene pairs. While designed for testing a different null hypothesis, this method provides an order of magnitude more accurate control of type 1 error rate compared to conventional methods of individual gene expression profiling. In addition, this method is robust to the technical noise. Quantitative inference of the correlation structure has the potential to extend the analysis of microarray data far beyond currently practiced methods.