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

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

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 (λ). It is important to highlight that statistical power increased with n, h(2), and λ, 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.