controls, and public controls. Under both scenarios, we began with a baseline model in which a study has 2,000 cases and 2,000 controls genotyped, providing 80 % power to detect an additive SNP effect size of 1 % variance explained in the phenotype at genome-wide significance (P ≤ 5 × 10−8). This is equivalent to detecting a minimum odds ratio of 1.545, 1.405, 1.355, and 1.335 for SNPs with MAFs of 10, 20, 30, and 40 %, respectively, with the same sample size. The calculations were made following Zheng et al. (2011) simulation of power by imputation accuracy (average R2) for a standard 1 degree of freedom test under an additive genetic model for imputed allele dosage. Modification to sample size and proportion of controls to cases were made taking the harmonic mean of the numbers of cases and controls multiplied by two to produce the overall sample size for a given scenario. We applied a given level of average R2 to proportionately reduce sample size to effective sample size (Pritchard and Przeworski 2001; Pasaniuc et al. 2012) due to imputation inaccuracy, and then used Elston’s Excellent Estimator (Tiwari et al. 2011) via the web tool Analytic Power Calculation (http://gwatestdriver.ssg.uab.edu/)
