As is shown in S1 Derivations, in case the CGR between the two sets of studies, C1 and C2, is zero, meta-analyzing the two sets jointly yields power βC1∪C2≤max{βC1,βC2} and βC1∪C2≥min{βC1,βC2}, where βA denotes the power in set of studies A. In particular, when βC1=βC2 we have under a CGR of zero between the sets, that βC1∪C2=βC1=βC2. Since in Fig 5 we considered two equally-powered sets, the power of a meta-analysis using both sets, under zero CGR between sets, is identical to the power obtained when meta-analyzing, for instance, only the first set. However, as CGR between sets increases, so does power. For instance, when a total sample size of 250,000 individuals is spread across 2 clusters, each cluster consisting of 50 studies (i.e., sample size of 125,000 individuals per cluster and 2,500 individuals per study), under hSNP2=50% due to 1k causal SNPs, a CGR of one within each cluster, and CGR of zero between clusters, the power is expected to be 49%, which is identical to the power of a meta-analysis of either the first or the second cluster.
