Using the formulas described above for one-stage power, we calculated power for a replication-based two-stage design. For a replication-based two-stage design, the overall power for a SNP was simply calculated as the product of the power for the first stage times the power of the second stage. Following the notation in Skol et al. (Skol et al., 2006), the power for the first-stage was calculated using a significance threshold defined as the proportion of markers followed in stage 2, πmarkers. Power for the second-stage was calculated using a significance threshold equal to 2α/(M π markers), i.e. the Bonferroni corrected cutoff for a one-sided test that requires the direction of the SNP main effect to be the same in stage 1 and 2 samples.
