  For the etiology, progression, and treatment of complex diseases,
gene-environment (G-E) interactions have important implications beyond the main
G and E effects. G-E interaction analysis can be more challenging with the
higher dimensionality and need for accommodating the "main effects,
interactions" hierarchy. In the recent literature, an array of novel methods,
many of which are based on the penalization technique, have been developed. In
most of these studies, however, the structures of G measurements, for example
the adjacency structure of SNPs (attributable to their physical adjacency on
the chromosomes) and network structure of gene expressions (attributable to
their coordinated biological functions and correlated measurements), have not
been well accommodated. In this study, we develop the structured G-E
interaction analysis, where such structures are accommodated using penalization
for both the main G effects and interactions. Penalization is also applied for
regularized estimation and selection. The proposed structured interaction
analysis can be effectively realized. It is shown to have the consistency
properties under high dimensional settings. Simulations and the analysis of
GENEVA diabetes data with SNP measurements and TCGA melanoma data with gene
expression measurements demonstrate its competitive practical performance.
