Notably, our expression for E [Zk2] bears a great resemblance to expressions for the expected value of the squared Z statistic when accounting for LD, population stratification, and polygenicity [38, 43, 44]. Consider the scenario where the CGR between two samples of equal size is positive one. Based of Eq 1, we then have that E [Zk2]≈1+hSNP2MNT for a trait-affecting haplotype block, where NT = 2N denotes the total sample size. This expression is equivalent to the expected squared Z statistic from the linear regression analysis for a trait-affecting variant reported in Section 4.2 of the Supplementary Note to [44] as well as the first equation in [38] when assuming that confounding biases and LD are absent.
