  Network-based analyses of high-throughput genomics data provide a holistic,
systems-level understanding of various biological mechanisms for a common
population. However, when estimating multiple networks across heterogeneous
sub-populations, varying sample sizes pose a challenge in the estimation and
inference, as network differences may be driven by differences in power. We are
particularly interested in addressing this challenge in the context of
proteomic networks for related cancers, as the number of subjects available for
rare cancer (sub-)types is often limited. We develop NExUS (Network Estimation
across Unequal Sample sizes), a Bayesian method that enables joint learning of
multiple networks while avoiding artefactual relationship between sample size
and network sparsity. We demonstrate through simulations that NExUS outperforms
existing network estimation methods in this context, and apply it to learn
network similarity and shared pathway activity for groups of cancers with
related origins represented in The Cancer Genome Atlas (TCGA) proteomic data.
