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The widespread use of generalized linear models in case-control geneticstudies has helped identify many disease-associated risk factors typicallydefined as DNA variants, or single nucleotide polymorphisms (SNPs). Up to now,most literature has focused on selecting a unique best subset of SNPs based onsome statistical perspectives. In the presence of pronounced noise, however,multiple biological paths are often found to be equally supported by a givendataset when dealing with complex genetic diseases. We address the ambiguityrelated to SNP selection by constructing a list of models called variableselection confidence set (VSCS), which contains the collection of allwell-supported SNP combinations at a user-specified confidence level. The VSCSextends the familiar notion of confidence intervals in the variable selectionsetting and provides the practitioner with new tools aiding the variableselection activity beyond trusting a single model. Based on the VSCS, weconsider natural graphical and numerical statistics measuring the inclusionimportance of a SNP based on its frequency in the most parsimonious VSCSmodels. This work is motivated by available case-control genetic data onage-related macular degeneration, a widespread complex disease and leadingcause of vision loss.

Ranking genetic factors related to age-related maculardegeneration by variable selection confidence sets