A structural mixed model to shrink covariance matrices for time-course differential gene expression studies

Time-course microarray studies require a particular modelling of covariance matrices when measures are repeated on the same individuals. Taking into account the within-subject correlation in the test statistics for differential gene expression, however, requires a large number of parameters when a gene-specific approach is used, which often results in a lack of power due to the small number of individuals usually considered in microarray experiments. Shrinkage approaches can improve this detection power in differential gene expression studies by reducing the number of parameters, while offering a good flexibility and a small rate of false positives. A natural extension of the shrinkage approach based on a structural mixed model to variance-covariance matrices is proposed. The structural model was used in three configurations to shrink (i) the eigenvalues in an eigenvalue/eigenvector decomposition, (ii) the innovation variances in a Cholesky decomposition, (iii) both the variances and correlation parameters of a gene-by-gene covariance matrix using a Fisher transformation. The proposed methods were applied both to a publicly available data set and to simulated data. They were found to perform well, compared to previously proposed empirical Bayesian approaches, and outperformed the gene-specific or common-covariance methods in many cases.

Bayesian recursive mixed linear model for gene expression analyses with continuous covariates

[EN] The analysis of microarray gene expression data has experienced a remarkable growth in scientific research over the last few years and is helping to decipher the genetic background of several productive traits. Nevertheless, most analytical approaches have relied on the comparison of 2 (or a few) well-defined groups of biological conditions where the continuous covariates have no sense (e. g., healthy vs. cancerous cells). Continuous effects could be of special interest when analyzing gene expression in animal production-oriented studies (e. g., birth weight), although very few studies address this peculiarity in the animal science framework. Within this context, we have developed a recursive linear mixed model where not only are linear covariates accounted for during gene expression analyses but also hierarchized and the effects of their genetic, environmental, and residual components on differential gene expression inferred independently. This parameterization allows a step forward in the inference of differential gene expression linked to a given quantitative trait such as birth weight. The statistical performance of this recursive model was exemplified under simulation by accounting for different sample sizes (n), heritabilities for the quantitative trait (h(2)), and magnitudes of differential gene expression (lambda). It is important to highlight that statistical power increased with n, h(2), and lambda, and the recursive model exceeded the standard linear mixed model with linear (nonrecursive) covariates in the majority of scenarios. This new parameterization would provide new insights about gene expression in the animal science framework, opening a new research scenario where within-covariate sources of differential gene expression could be individualized and estimated. The source code of the program accommodating these analytical developments and additional information about practical aspects on running the program are freely available by request to the corresponding author of this article.This research was funded by grant AGL2008-04818-C03 (Ministerio de Ciencia e Innovacion, Madrid, Spain). The research contract of J. Casellas was partially financed by the Ministerio de Ciencia e Innovacion of Spain (program Ramon y Cajal, reference RYC-2009-04049). The authors are also indebted to 2 anonymous referees for their helpful comments on the manuscript.Casellas, J.; Ibáñez-Escriche, N. (2012). Bayesian recursive mixed linear model for gene expression analyses with continuous covariates. Journal of Animal Science. 90(1):67-75. https://doi.org/10.2527/jas.2010-3750S6775901Bernard, C., Cassar-Malek, I., Le Cunff, M., Dubroeucq, H., Renand, G., & Hocquette, J.-F. (2007). New Indicators of Beef Sensory Quality Revealed by Expression of Specific Genes. 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