One of the most difficult challenges of GWAS is how to deal with the large p, small n problem that arises when the number of variables considered (p) is much larger than the number of subjects (n). The problem becomes even more pronounced when one seeks to test interactions between SNPs and one or more environmental exposures in addition to determining the main effect of each SNP. One approach commonly used to reduce the number of tests performed is to select a subset of SNPs to be tested for interactions with known or hypothesized environmental predictors of the phenotype. This can be done by first conducting a single-SNP analysis for each SNP in the genome-wide data, in which one SNP at a time, along with relevant covariates, is tested for association with the phenotype, and then only the most significant SNPs are followed up in G×E interaction testing. Several Group 10 contributions showed that the use of this strategy may miss potentially important SNPs that have a very small main effect, but a significant G×E effect. For example, Arya et
