The success in eliminating the bias of imputing SNPs across arrays by using the intersection approach must be balanced with practical considerations of using public controls genotyped on multiple arrays. Two scenarios are most relevant. The first is to consider adding public controls to an existing sample, which increases sample size but necessitates SNP imputation to generate a common set of SNPs for analysis and engenders imputation error that reduces effective sample size. To examine the balance of these two effects on statistical power, we examined a simplified scenario in which a study has 2,000 cases and 2,000 controls genotyped, providing 80 % power to detect an effect size of 1 % variance explained at genome-wide significance (P ≤ 5 × 10−8). Figure 4 presents the power estimates by level of imputation accuracy (average R2) for differing numbers of public controls added to the baseline design. Compared to the baseline model (blue diamond), adding 500 public controls (pink curve) does not improve and may worsen power: showing equivalent power to the baseline model when R2 = 0.9 but steadily declining
