Across the conditions we have studied, not only is it possible to achieve genome-wide significance for common variants when one or more rare variants are the only contributors to disease, it is often the likely outcome (Figure 2). Overall, 30% of the simulations were able to detect an association with a common SNP at genome-wide significance (p<10−8). Three factors—GRR, sample size, and the number of rare causal variants—had a notable impact on power to detect an association with a common SNP. As expected, greater proportions of synthetic associations were created when GRR increased for the rare causal variants and when sample size increased. As the number of rare causal variants increased, the probability of creating a synthetic association did as well. One possible explanation for this increase due to increasing the number of rare causal variants is that adding more causal variants increases the size of the disease class, which is the proportion of haplotypes that carry one or more disease alleles [8]. The size of the disease class varied in the simulations both because the frequency of causal variants
