  When searching for gene pathways leading to specific disease outcomes,
additional information on gene characteristics is often available that may
facilitate to differentiate genes related to the disease from irrelevant
background when connections involving both types of genes are observed and
their relationships to the disease are unknown. We propose method to single out
irrelevant background genes with the help of auxiliary information through a
logistic regression, and cluster relevant genes into cohesive groups using the
adjacency matrix. Expectation-maximization algorithm is modified to maximize a
joint pseudo-likelihood assuming latent indicators for relevance to the disease
and latent group memberships as well as Poisson or multinomial distributed link
numbers within and between groups. A robust version allowing arbitrary linkage
patterns within the background is further derived. Asymptotic consistency of
label assignments under the stochastic blockmodel is proven. Superior
performance and robustness in finite samples are observed in simulation
studies. The proposed robust method identifies previously missed gene sets
underlying autism related neurological diseases using diverse data sources
including de novo mutations, gene expressions and protein-protein interactions.
