Multivariate analysis of microarray data: differential expression and differential connection

Background: Typical analysis of microarray data ignores the correlation between gene expression values. In this paper we present a model for microarray data which specifically allows for correlation between genes. As a result we combine gene network ideas with linear models and differential expression. Results: We use sparse inverse covariance matrices and their associated graphical representation to capture the notion of gene networks. An important issue in using these models is the identification of the pattern of zeroes in the inverse covariance matrix. The limitations of existing methods for doing this are discussed and we provide a workable solution for determining the zero pattern. We then consider a method for estimating the parameters in the inverse covariance matrix which is suitable for very high dimensional matrices. We also show how to construct multivariate tests of hypotheses. These overall multivariate tests can be broken down into two components, the first one being similar to tests for differential expression and the second involving the connections between genes. Conclusion: The methods in this paper enable the extraction of a wealth of information concerning the relationships between genes which can be conveniently represented in graphical form. Differentially expressed genes can be placed in the context of the gene network and places in the gene network where unusual or interesting patterns have emerged can be identified, leading to the formulation of hypotheses for future experimentation.