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Gene set analysis for longitudinal gene expression data

Ke Zhang1*, Haiyan Wang2*, Arne C Bathke3, Solomon W Harrar4, Hans-Peter Piepho5 and Youping Deng6

Author Affiliations

1 School of Medicine & Health Sciences, University of North Dakota, Grand Forks, ND 58202, USA

2 Department of Statistics, Kansas State University, Manhattan, KS 66506, USA

3 Department of Statistics, University of Kentucky, Lexington, KY 40506, USA

4 Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA

5 Institut für Kulturpflanzenzüchtung, Universität Hohenheim, D70599 Stuttgart, Germany

6 Department of Internal Medicine, Rush University Medical Center, Chicago, IL 60612, USA

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BMC Bioinformatics 2011, 12:273  doi:10.1186/1471-2105-12-273

Published: 3 July 2011



Gene set analysis (GSA) has become a successful tool to interpret gene expression profiles in terms of biological functions, molecular pathways, or genomic locations. GSA performs statistical tests for independent microarray samples at the level of gene sets rather than individual genes. Nowadays, an increasing number of microarray studies are conducted to explore the dynamic changes of gene expression in a variety of species and biological scenarios. In these longitudinal studies, gene expression is repeatedly measured over time such that a GSA needs to take into account the within-gene correlations in addition to possible between-gene correlations.


We provide a robust nonparametric approach to compare the expressions of longitudinally measured sets of genes under multiple treatments or experimental conditions. The limiting distributions of our statistics are derived when the number of genes goes to infinity while the number of replications can be small. When the number of genes in a gene set is small, we recommend permutation tests based on our nonparametric test statistics to achieve reliable type I error and better power while incorporating unknown correlations between and within-genes. Simulation results demonstrate that the proposed method has a greater power than other methods for various data distributions and heteroscedastic correlation structures. This method was used for an IL-2 stimulation study and significantly altered gene sets were identified.


The simulation study and the real data application showed that the proposed gene set analysis provides a promising tool for longitudinal microarray analysis. R scripts for simulating longitudinal data and calculating the nonparametric statistics are posted on the North Dakota INBRE website webcite. Raw microarray data is available in Gene Expression Omnibus (National Center for Biotechnology Information) with accession number GSE6085.