A multivariate linear model for investigating the association between gene-module co-expression and a continuous covariate.

A way to enhance our understanding of the development and progression of complex diseases is to investigate the influence of cellular environments on gene co-expression (i.e. gene-pair correlations). Often, changes in gene co-expression are investigated across two or more biological conditions defined by categorizing a continuous covariate. However, the selection of arbitrary cut-off points may have an influence on the results of an analysis. To address this issue, we use a general linear model (GLM) for correlated data to study the relationship between gene-module co-expression and a covariate like metabolite concentration. The GLM specifies the gene-pair correlations as a function of the continuous covariate. The use of the GLM allows for investigating different (linear and non-linear) patterns of co-expression. Furthermore, the modeling approach offers a formal framework for testing hypotheses about possible patterns of co-expression. In our paper, a simulation study is used to assess the performance of the GLM. The performance is compared with that of a previously proposed GLM that utilizes categorized covariates. The versatility of the model is illustrated by using a real-life example. We discuss the theoretical issues related to the construction of the test statistics and the computational challenges related to fitting of the proposed model.