λ=NANU[∑i=02xi(PAi−PUi)]2∑i=02xi2(NAPAi+NUPUi)−[∑i=02xi(NAPAi+NUPUi)]2/(NA+NU) where NA and NU (or optionally NPU) were the sample sizes of the cases and screened (or public) controls, respectively, xi was the score for the i-th genotype (i = 0, 1, 2 for genotypes dd, Dd, DD), and PAi and PUi were the probabilities of the i-th genotype for the cases and controls, respectively. Power was then taken to be 1 − β, where β was the type II error of the non-central χ2 distribution with 1 degree of freedom and non-centrality parameter λ, evaluated at the 100(1 −αBonferroni) percentile of the central χ2 distribution with 1 degree of freedom. For single-stage designs, the overall family-wise error rate was set to α = 0.05 by using a Bonferroni corrected significance threshold αBonferroni = 0.05/M, where M was the number of markers evaluated.
