Systematic genotyping errors (over or under calling of the susceptibility allele) decreased power modestly for the one-stage design with only study controls (Table 4). For the one-stage designs that included public controls, genotyping errors in opposite directions on the two genotyping platforms (e.g. over calling susceptibility allele in public controls and under calling susceptibility allele in study samples) had a major impact on power. For the single-stage study with only public controls, in the absence of batch effects (for both the individual SNP and for all other SNPs across the genome) the power was 0.90. Over calling the susceptibility allele in the public controls and under calling the susceptibility allele in cases (each with probability of 0.01 per allele) resulted in power decreasing to 0.53. Conversely, if the susceptibility allele was under called in the public controls and over called in the cases then power increased to 0.99. A similar pattern, but less dramatic differences, were observed for the single-stage study design with both public and study controls. Both single-stage studies that include public controls experienced some loss in power
