We performed a two-locus GWA scan including epistasis in T2D by selecting variants tagging common variation across the human genome. We obtained genome-wide evidence for joint two-locus effects at 79 pairs of markers, all of which included a single variant (rs11196205) in TCF7L2. Our conditional test results and permutation results indicate that the genome-wide significant joint two-locus effects are due to the strong main-effects at TCF7L2 and not to genome-wide significant epistatic effects. We obtained interesting signals for epistasis at five pairs of regions and more detailed analyses of the SNP-pair with the strongest evidence for epistasis (rs1935683 in RFPL4B and rs11196205 in TCF7L2) gave an indication into potential underlying multilocus models.
Overall, we found weak evidence that epistatic effects contribute to the multilocus joint effects obtained in this study. These results are likely in part influenced by the strong single-locus effects of rs11196205 in TCF7L2 in our dataset. Previous studies have shown that although multilocus approaches have on average more power than single-locus approaches to detect susceptibility loci in the presence of epistasis, that is not necessarily the case when one of the loci in the pair has strong single-locus effects that are large relative to the interaction effects and are sufficient to detect this locus in a single-locus GWAS (Marchini et al., 2005). Our findings confirm that in multilocus association testing very strong single locus effects can obscure the two-locus positive results. For example, for one of the observed suggestive models of epistasis in Figure 2, we estimated over 94% power to detect susceptibility variants under the joint two-locus test, however, power to detect the effects of the secondary locus (rs1935683 in RFPL4B) in the pair under the conditional test was only 28.6%. These results suggest that although interactions may contribute to T2D, there is currently insufficient power to detect them even in the single largest GWA study for T2D to date (WTCCC, 2007). Power to detect loci in the presence of epistasis depends on many factors, including sample-size, underlying model of epistasis, and disease allele frequencies at the two loci. Several approaches to detect genetic interactions exist (see Cordell, 2009) and the majority of methods used in our study focus on detecting susceptibility variants in the presence of epistasis, rather than targeting interactions alone. Tests for epistasis in GWA data may prove challenging, both computationally and due to the effect of allele frequency on the corresponding epistatic variance components. Computationally tractable methods to detect epistasis alone have previously been developed (Ritchie et al., 2001; Purcell et al., 2007; Steffens et al., 2010; Wan et al., 2010), and one of these has been applied to the T2D data used in our study (Wan et al., 2010) also reporting negative evidence for epistasis among genome-wide SNPs at least 1Mb away from each other. These findings confirm our results for the conditional and epistasis-only tests, when interpreted in a genome-wide context. In our study, single-locus tests together with the conditional test indicate the relative magnitude of epistatic effects. The joint two-locus analyses may provide a sense of the proportion of two locus effects in the genome that are epistatic, for example, the joint two-locus test results and associated quantile–quantile plot show that the majority of the deviation from the null model of no two-locus association is due to TCF7L2 alone, although there is some minimal enrichment of two-locus signals for tests excluding TCF7L2 (Fig. S1). Based on these findings, it is unlikely that interactions between common variants will be detected at genome-wide significant thresholds in present-day single GWA scans, even if they contribute appreciably to the missing heritability in T2D. Replication of our negative findings is important, but the replication sets for our study will be smaller than the original sample set used, therefore obscuring the distinction between lack of power to detect signals and negative results. Larger sample sizes and meta-analysis approaches may help detect epistatic effects, but do not address the problems of low power to detect epistasis under certain underlying genetic models, and interpreting the epistatic effects in the context of the allele frequency spectrum. Furthermore, the best strategy to perform meta-analyses on results from multiple two-locus GWA scans remains unclear.
Although we did not find evidence for epistasis genome-wide, our few interaction-only analysis findings point towards loci for which there is weak or no evidence for single-locus association. Previous studies have shown that association analyses can detect large epistatic effects in the complete absence of main effects (Culverhouse et al., 2002), but another factor which can influence the power of multilocus GWA search strategy is the presence of LD between marker and disease locus (Marchini et al., 2005). We applied a tagging approach to select a subset of markers for the joint two-locus GWA tests, as this approach significantly reduced the computational load of the analyses. However, tagging may both reduce power to detect multilocus association, and may yield misleading inferences from interaction follow-up results due to the effect of linkage disequilibrium on the underlying two-locus models (Lynch & Walsh, 1998; Hill et al., 2008). Future studies need to improve our understanding of the effect of linkage disequilibrium on the epistatic components of the test statistic under various underlying models of epistasis.
The extent to which findings of statistical interactions relate to biological epistasis remains unclear. As pointed out by Lynch and Walsh (1998), unless the allele frequencies are known, the estimated variance components provide limited insight into the biological gene action. Some approaches incorporate additional biological data to prioritize, improve, or interpret statistical interaction analyses (Aylor & Zeng, 2008; Emily et al., 2009). However, there are many genetic models of epistasis for which the biological mechanisms are difficult to envision. The optimal approach would be to test for statistical epistasis in a situation where biological epistasis exists, unfortunately, examples of such studies are rare. The underlying genetic models for most complex traits are likely models of higher-dimensional biological complexity. However, an assessment of pair-wise joint effects is useful as a first step towards obtaining further insight into the genetic etiology of common complex traits.