For intuition, we here present an approximation for prediction in a hold-out sample, with SNP weights based on a GWAS in a single discovery study with sample size N, where both studies have SNP heritability hSNP2, and with CGR ρG, between the studies. Under high polygenicity, the R2 of the PGS in the hold-out sample is then given by the following expression: R2≈hSNP2ρG2hSNP2SN+hSNP2.(2) In case the CGR is one, and we consider the R2 between the PGS and the genetic value (i.e., the genetic component of the phenotype) instead of the phenotype itself, the first two terms in Eq 2 disappear, yielding an expression equivalent to the first equation in [40]. Assuming a CGR of one and that all SNPs are associated, Eq 2 is equivalent to the expression in [23] for the R2 between the PGS and the phenotype in the hold-out sample.
