In Method 3, we propose genotyping a small number of additional controls alongside the cases and performing a preliminary step of filtering SNPs by comparing these additional controls to the original controls. This approach also improves results, but at increased monetary cost. It should, however, retain more non-artifactual SNPs while reducing the number of artifactual SNPs. In our example of 1000 cases and 1000 controls, it appeared that genotyping 300 additional controls alongside cases would allow researchers to filter out most of the false positives — with α = 0.2, only 5 highly significant SNPs were left among the SNPs genotyped on Illumina and imputed on Affy, with 264,519 (74%) remaining for analysis. We believe these results would be the same if we had new cases and controls on Illumina and a separate control group on Affy — we merely consider this setting because it made best use of the subjects available on each chip. This method is in line with the discussion in McCarthy et al. (2008) regarding the use of historical controls. McCarthy et al. listed many possible
