Equation 1 makes clear the dependence of power on the frequency of the risk allele. The results in Figure 2 are averaged over putative causative SNPs with a risk allele frequency (RAF) in the range 5–95%. Figure 3 shows that this hides quite different behaviour depending on whether the putative disease SNP is rare or common, and that the conclusions in the preceding subsection apply principally for common causative SNPs. The Figure shows a substantial difference in power for common and rare alleles with the same effect size and that power is minimal for the rare alleles when the effect size is small. These results refer to single-SNP analyses. While there are definitely more powerful analysis methods for rare alleles [14], this is not a major factor in the loss of power, and neither is the incomplete coverage of the SNPs on the commercially available chips: even using a sample size of 3000 cases and controls and genotyping the causal locus directly (black line) is unlikely to lead to a test statistic which will reach the small levels of significance thought appropriate for GWAS.
