  The widespread use of generalized linear models in case-control genetic
studies has helped identify many disease-associated risk factors typically
defined as DNA variants, or single nucleotide polymorphisms (SNPs). Up to now,
most literature has focused on selecting a unique best subset of SNPs based on
some statistical perspectives. In the presence of pronounced noise, however,
multiple biological paths are often found to be equally supported by a given
dataset when dealing with complex genetic diseases. We address the ambiguity
related to SNP selection by constructing a list of models called variable
selection confidence set (VSCS), which contains the collection of all
well-supported SNP combinations at a user-specified confidence level. The VSCS
extends the familiar notion of confidence intervals in the variable selection
setting and provides the practitioner with new tools aiding the variable
selection activity beyond trusting a single model. Based on the VSCS, we
consider natural graphical and numerical statistics measuring the inclusion
importance of a SNP based on its frequency in the most parsimonious VSCS
models. This work is motivated by available case-control genetic data on
age-related macular degeneration, a widespread complex disease and leading
cause of vision loss.
