Are a set of microarrays independent of each other?

TL;DR

This paper develops nonparametric and normal-theory statistical tests to assess the independence of columns in a microarray data matrix, accounting for potential row correlations that complicate analysis.

Contribution

It introduces new testing methods specifically designed for microarray data, addressing the challenge of correlated gene expression levels affecting independence tests.

Findings

New nonparametric tests for column independence in microarrays

Normal-theory tests adapted for correlated gene expression data

Analysis of how row correlations impact test accuracy

Abstract

Having observed an $m\times n$ matrix $X$ whose rows are possibly correlated, we wish to test the hypothesis that the columns are independent of each other. Our motivation comes from microarray studies, where the rows of $X$ record expression levels for $m$ different genes, often highly correlated, while the columns represent $n$ individual microarrays, presumably obtained independently. The presumption of independence underlies all the familiar permutation, cross-validation and bootstrap methods for microarray analysis, so it is important to know when independence fails. We develop nonparametric and normal-theory testing methods. The row and column correlations of $X$ interact with each other in a way that complicates test procedures, essentially by reducing the accuracy of the relevant estimators.