Abstract
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.