In addition, deterministic formulas have been derived to predict the accuracy of genomic prediction across breeds as a function of population parameters (e.g. heritability, genetic correlation) and also using selection index theory15,16. However, these deterministic formulas mostly apply to best linear unbiased predictors17, which are not classically used in human studies. Consequently, a theoretical understanding of the trans-ancestry predictive capacities of standard PGS is still missing. Although the key factors causing the loss of accuracy have been enumerated in previous studies, quantification of their relative contributions has not been done systematically. Note that quantifying the relative contributions of all these factors is critical for understanding aetiological differences between ancestries, which may have important clinical implications. Here, we develop an approximation of the theoretical relative accuracy of PGS in an ancestry divergent sample as a function of population genetics parameters. Our method only requires GWAS summary statistics and ancestry-specific reference panels. We evaluate the performances of our theory through extensive simulations and apply it to GWAS of 5 quantitative traits and 3 common diseases with different genetic architectures in ~350,000 unrelated UK Biobank participants.
