SNPs, each with three genotypes (i.e., AA, Aa, and aa), would have nine possible genotypes, while a model containing four SNPs would have 81 possible genotypes (i.e., 3# of SNPs). Capturing epistatic effects is further complicated by the fact that the power to detect a genetic effect is dependent upon the minor allele frequency (MAF) of the risk allele being studied. Specifically, the power to detect relatively modest genotypic risk ratios observed in AD GWAS increases as the MAF of the risk allele being tested increases. However, in the case of epistatic studies we would be dealing with the MAF of different combinations of risk alleles, which further increases the likelihood of obtaining a false positive result. Recently, it has been suggested that the inclusion of epistatic effects, as well as gene-environment interaction effects (discussed in section 4.2) in association studies provides a slight improvement in predictive power; notably, predictive power increases as (1) the number of risk factors increases and (2) the effect size of causal variants increases (Aschard et al., 2012).
