  The estimation of covariance matrices of gene expressions has many
applications in cancer systems biology. Many gene expression studies, however,
are hampered by low sample size and it has therefore become popular to increase
sample size by collecting gene expression data across studies. Motivated by the
traditional meta-analysis using random effects models, we present a
hierarchical random covariance model and use it for the meta-analysis of gene
correlation networks across 11 large-scale gene expression studies of diffuse
large B-cell lymphoma (DLBCL). We suggest to use a maximum likelihood estimator
for the underlying common covariance matrix and introduce an EM algorithm for
estimation. By simulation experiments comparing the estimated covariance
matrices by cophenetic correlation and Kullback-Leibler divergence the
suggested estimator showed to perform better or not worse than a simple pooled
estimator. In a posthoc analysis of the estimated common covariance matrix for
the DLBCL data we were able to identify novel biologically meaningful gene
correlation networks with eigengenes of prognostic value. In conclusion, the
method seems to provide a generally applicable framework for meta-analysis,
when multiple features are measured and believed to share a common covariance
matrix obscured by study dependent noise.
