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Open Access Open Badges Methodology article

Clustering of time-course gene expression profiles using normal mixture models with autoregressive random effects

Kui Wang1, Shu Kay Ng2 and Geoffrey J McLachlan1*

Author Affiliations

1 Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia

2 School of Medicine, Griffith Health Institute, Griffith University, Meadowbrook, QLD 4131, Australia

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BMC Bioinformatics 2012, 13:300  doi:10.1186/1471-2105-13-300

Published: 14 November 2012



Time-course gene expression data such as yeast cell cycle data may be periodically expressed. To cluster such data, currently used Fourier series approximations of periodic gene expressions have been found not to be sufficiently adequate to model the complexity of the time-course data, partly due to their ignoring the dependence between the expression measurements over time and the correlation among gene expression profiles. We further investigate the advantages and limitations of available models in the literature and propose a new mixture model with autoregressive random effects of the first order for the clustering of time-course gene-expression profiles. Some simulations and real examples are given to demonstrate the usefulness of the proposed models.


We illustrate the applicability of our new model using synthetic and real time-course datasets. We show that our model outperforms existing models to provide more reliable and robust clustering of time-course data. Our model provides superior results when genetic profiles are correlated. It also gives comparable results when the correlation between the gene profiles is weak. In the applications to real time-course data, relevant clusters of coregulated genes are obtained, which are supported by gene-function annotation databases.


Our new model under our extension of the EMMIX-WIRE procedure is more reliable and robust for clustering time-course data because it adopts a random effects model that allows for the correlation among observations at different time points. It postulates gene-specific random effects with an autocorrelation variance structure that models coregulation within the clusters. The developed R package is flexible in its specification of the random effects through user-input parameters that enables improved modelling and consequent clustering of time-course data.

Time-course data; Mixtures of linear mixed models; Autoregressive random effects; EMMIX-WIRE procedure