The phenotypic value of a trait in individual i, denoted yi, can be decomposed into the sum of the additive genetic variance component and a residual: yi=gi+εiy.We denote the GWAS- and MTAG-based polygenic scores for the trait by g^GWAS,i and g^MTAG,i, respectively. Note that GWAS and MTAG produce consistent estimates of the SNP effect sizes, and LDpred22 produces a consistent estimate of the additive genetic variance component. Therefore, each polygenic score k∈{GWAS,MTAG} is approximately equal to gi plus estimation error: g^k,i=gi+ek,i.
