The impact of batch genotype effects on power were evaluated under the null hypothesis of no association and under the alternative model described above for the one and two-stage designs. These calculations were performed under the assumption that either the specific SNP under consideration was the only SNP subject to batch effects or that there existed a systematic bias due to batch effects that impacted all SNPs. Under the former scenario, we used the same significance thresholds described previously for the one- and two-stage studies. For the latter scenario, we assumed a baseline 10% mean systematic inflation of the chi-square test statistics across the genome (mean value test statistic, μ=1.10) for all SNPs evaluated in the one-stage study design based only on public controls. We assumed no inflation (μ=1.00) for the test statistics of the one-stage study design based only on study controls and for the test statistics from stage 2 analyses of the replication-based two-stage study designs (because cases and controls would be genotyped at the same time in stage 2). The mean systematic inflation of the test statistics,
