  In cancer research, the comparison of gene expression or DNA methylation
networks inferred from healthy controls and patients can lead to the discovery
of biological pathways associated to the disease. As a cancer progresses, its
signalling and control networks are subject to some degree of localised
re-wiring. Being able to detect disrupted interaction patterns induced by the
presence or progression of the disease can lead to the discovery of novel
molecular diagnostic and prognostic signatures. Currently there is a lack of
scalable statistical procedures for two-network comparisons aimed at detecting
localised topological differences. We propose the dGHD algorithm, a methodology
for detecting differential interaction patterns in two-network comparisons. The
algorithm relies on a statistic, the Generalised Hamming Distance (GHD), for
assessing the degree of topological difference between networks and evaluating
its statistical significance. dGHD builds on a non-parametric permutation
testing framework but achieves computationally efficiency through an asymptotic
normal approximation. We show that the GHD is able to detect more subtle
topological differences compared to a standard Hamming distance between
networks. This results in the dGHD algorithm achieving high performance in
simulation studies as measured by sensitivity and specificity. An application
to the problem of detecting differential DNA co-methylation subnetworks
associated to ovarian cancer demonstrates the potential benefits of the
proposed methodology for discovering network-derived biomarkers associated with
a trait of interest.
