Inference on low-rank data matrices with applications to microarray data

TL;DR

This paper introduces a statistical framework for testing whether microarray data matrices can be adequately summarized by a single dimension, revealing complex features in probe set data.

Contribution

It proposes a low-rank matrix model and a testing procedure for unidimensionality, addressing the challenge of inference on non-i.i.d. matrix data.

Findings

The test effectively detects deviations from unidimensionality in simulated data.

Applications to GeneChip data reveal meaningful biological features.

The method has good small sample performance in simulations.

Abstract

Probe-level microarray data are usually stored in matrices, where the row and column correspond to array and probe, respectively. Scientists routinely summarize each array by a single index as the expression level of each probe set (gene). We examine the adequacy of a unidimensional summary for characterizing the data matrix of each probe set. To do so, we propose a low-rank matrix model for the probe-level intensities, and develop a useful framework for testing the adequacy of unidimensionality against targeted alternatives. This is an interesting statistical problem where inference has to be made based on one data matrix whose entries are not i.i.d. We analyze the asymptotic properties of the proposed test statistics, and use Monte Carlo simulations to assess their small sample performance. Applications of the proposed tests to GeneChip data show that evidence against a unidimensional model is often indicative of practically relevant features of a probe set.