We next attempted to determine the expected genomic distances over which rare variants could create synthetic associations. To do so, we simulated a 10-Mb region with a typical recombination rate (1 cM/Mb), nine rare causal variants, 2,000 cases and 2,000 controls, and GRR = 4. We then identified the most distal causal variant that was confirmed to actually contribute to the signal of synthetic association. We did this by finding the most distal variant that resulted in a minimum of a one-log drop in p-value when its effect was statistically removed (by incorporation as a covariate into the regression). We found that when a synthetic association reached genome-wide significance, the most distant causal variant that affected the significance of the synthetic association was closer than 2 Mb from a synthetic association in fewer than 13% of the simulations and at least 9 Mb away in 4% of the simulations. The median distance of the most distant causal variant was 5 Mb. A simulated Manhattan plot showing a 10-Mb region with average recombination and nine causal variants with GRR = 4 shows an example of a signature created by synthetic association (Figure 6).
