We assumed an investigator had a sample of NA study cases, NU study controls and access to free genotype data on NPU public controls. We further assumed that study controls were screened for disease and that public controls were not screened for disease. We performed a series of calculations over a range of alternative models comparing the power achieved in an association study using four different sampling approaches: 1) a single-staged association study that used all NA study cases and NU study controls; 2) a single-staged association study that utilized all NA study cases and NPU public controls; 3) a single-staged association study that used all NA cases and combined all NU study and NPU public controls; 4) a two-staged replication-based study that used all NPU public controls in stage 1, all NU study controls in stage 2 and all NA cases apportioned between stages 1 and 2. We assumed an underlying multiplicative genetic mode-of-inheritance risk model for a bi-allelic locus with alleles D and d and corresponding allele frequencies of fD and fd, respectively. For each alternative model, we
