The larger the variance in the Z statistic, the higher the probability of rejecting the null. The ratio of hSNP2 and M can be regarded as the theoretical R2 of each associated SNP with respect to the phenotype. Eq 1 reveals that (i) when sample size increases, power increases, (ii) when hSNP2 increases, the R2 per associated SNP increases and therefore power increases, (iii) when the number of associated SNPs increases, the R2 per associated SNP decreases and therefore power decreases, (iv) when the CGR is zero the power of the meta-analysis is identical to the power obtained in each of the two studies when analyzed separately, yielding no strict advantage to meta-analyzing, and (v) when the CGR is positive one, the additional variance in the Z statistic—compared to the variance under the null—is twice the additional variance one would have when analyzing the studies separately, yielding a strong advantage to meta-analyzing.
