Bioinformatics Advance Access published online on May 3, 2006
Bioinformatics, doi:10.1093/bioinformatics/btl165
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1 Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia
* To whom correspondence should be addressed.
Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries, and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real data sets, representing typical microarray experimental designs, covering time-course, repeated-measurement, and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic data set is considered too. Availability: A Fortran program blue called EMMIX-WIRE (EM-based MIXture analysis WIth Random Effects) is available on request from the correspondence author. Supplementary Information: http://www.maths.uq.edu.au/~gjm/bioinf0602_supp.pdf.
Received February 15, 2006
Revised April 10, 2006
Accepted April 26, 2006
Article
A mixture model with random-effects components for clustering correlated gene-expression profiles
S. K. Ng 1,
G. J. McLachlan 2 *,
K. Wang 3,
L. Ben-Tovim Jones 4,
and
S.-W. Ng 5
2 Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia; Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072, Australia; ARC Centre for Complex Systems, University of Queensland, Brisbane, QLD 4072, Australia
3 ARC Centre for Complex Systems, University of Queensland, Brisbane, QLD 4072, Australia
4 Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072, Australia
5 Laboratory of Gynecologic Oncology, Department of Obstetrics, Gynecology and Reproductive Biology, Brigham and Women's Hospital, Boston, MA 02115, USA
G. J. McLachlan, E-mail: gjm{at}maths.uq.edu.au
Abstract
Associate Editor: Martin Bishop
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