For the replication-based two-stage design, we observed that the optimal choice of the proportion of cases, πcases, to be genotyped in stage 1 varied considerably between the different choices of stage 2 genotyping platforms (as expected, a larger proportion of cases were necessary to be genotyped in stage 1 for the smaller follow-up platforms) but, importantly, varied little within a given platform across the considered range of GRRs and disease allele frequencies (Table 2). We note that for a given follow-up platform, the optimal choice of πcases was also insensitive to analytic strategy (i.e. similar optimal values of πcases were observed for the general 2-df test as for the trend test) (Supplementary Table 5) and genetic inheritance model (i.e., similar optimal values of πcases were also observed for the dominant and recessive models) (Supplementary Tables 6 and 7). These results suggest that it is reasonable to use the proportion of cases, πcases, to be genotyped in stage 1 that optimizes power for a replication-based two-stage study design based on a single specific alternative model and expect that power should be near optimized by this choice of πcases across a range of alternative genetic models when using the same follow-up platform.
