the same batch effect, effecting any cases and controls genotyped together equally. Over or under calling of the susceptibility allele was allowed to occur with different probabilities for each genotyping platform (e.g. for our proposed two-stage design there were three different genotyping platforms where the susceptibility allele could either be over or under called – the platform used for public controls, the genome-wide panel for a subset of the cases, and the follow-up platform for the remaining cases and all study controls). Genotype batch effects were modeled by modifying the genotype probabilities in our power calculator. For example, under Model 1 the probabilities of the three genotypes for public controls (fD = 0.30) when there were no genotype batch effects were set to 0.09, 0.42 and 0.49 for the DD, Dd and dd genotypes, respectively. If the batch effects resulted in the susceptibility allele D systematically being over-called with error probability + 0.01 (i.e. the non-susceptibility allele d is erroneously reported as the susceptibility allele D with probability 0.01), then the probabilities for the three genotypes DD, Dd and dd were set to 0.094249 [0.09 + 0.01(0.42) + (0.01)2(0.49)], 0.425502 [(0.99)(0.42) + 2(0.99)(0.01)(0.49)] and 0.480249 [(0.99)2(0.49)], respectively. This calculation takes
