Estimating a common covariance matrix for network meta-analysis of gene expression datasets in diffuse large B-cell lymphoma

Estimating gene networks in combination with posthoc analysis based on data from malignant tissue is a major challenge in cancer systems biology as it allows us to improve our understanding of disease pathology and eventually identify new drug targets. Motivated by the need for improving the inherently unstable covariance estimation compounded by noisy gene expression data, we present a hierarchical random covariance model applied as a meta-analysis of gene networks across eleven large-scale gene expression studies of diffuse large B-cell lymphoma (DLBCL). The approach was inspired by traditional meta-analysis using random effects models and we derive and compare basic properties and estimators of the model. Simple inference and interpretation of an introduced parameter measuring the inter-class homogeneity is suggested. The methods are generally applicable where multiple classes are present and believed to share a common covariance matrix of interest that is obscured by class-dependent noise. As such, it provides a basis for meta- or integrative analysis of covariance matrices where the classes are formed by datasets. In a posthoc analysis of the estimated common covariance matrix for the DLBCL data we were able to identify biologically meaningful gene networks of prognostic value. Of particular interest was the identification of a network with the S100 family of calcium-binding proteins as central players which further fuels the indications that knock down of these proteins may improve the immunotherapy strategies and outcome of lymphoma patients.