Adding publically available controls to augment existing study controls or using such public controls in lieu of study controls would be an attractive option to substantially increase sample size and power in the absence of cross array imputation-induced bias (Ho and Lange 2010). However, imputation engenders error in the estimated allele count across imputed SNPs, indicated by average R2, which reduces effective sample size (Pritchard and Przeworski 2001; Pasaniuc et al. 2012). We compared the effects of increasing sample size and potentially poorer imputation accuracy as the number of samples genotyped on different arrays increases under two scenarios: (1) adding public controls to a fixed sample of 2,000 study cases and 2,000 study controls; and (2) focusing on the study design stage where we have fixed resources to ascertain and genotype 4,000 individuals with differing mixes of study cases, study 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
