  Genome-wide association studies (GWA studies or GWAS) investigate the
relationships between genetic variants such as single-nucleotide polymorphisms
(SNPs) and individual traits. Recently, incorporating biological priors
together with machine learning methods in GWA studies has attracted increasing
attention. However, in real-world, nucleotide-level bio-priors have not been
well-studied to date. Alternatively, studies at gene-level, for example,
protein--protein interactions and pathways, are more rigorous and legitimate,
and it is potentially beneficial to utilize such gene-level priors in GWAS. In
this paper, we proposed a novel two-level structured sparse model, called
Sparse Group Lasso with Group-level Graph structure (SGLGG), for GWAS. It can
be considered as a sparse group Lasso along with a group-level graph Lasso.
Essentially, SGLGG penalizes the nucleotide-level sparsity as well as takes
advantages of gene-level priors (both gene groups and networks), to identifying
phenotype-associated risk SNPs. We employ the alternating direction method of
multipliers algorithm to optimize the proposed model. Our experiments on the
Alzheimer's Disease Neuroimaging Initiative whole genome sequence data and
neuroimage data demonstrate the effectiveness of SGLGG. As a regression model,
it is competitive to the state-of-the-arts sparse models; as a variable
selection method, SGLGG is promising for identifying Alzheimer's
disease-related risk SNPs.
