In what follows, we sketch the derivation of an estimator for αg (for details, see the Supplementary Methods). The derivation assumes that the error in the PGI, ei, is uncorrelated with zi and wi. In the Supplementary Methods, we show that this condition holds exactly if the PGI weights γ^ are unbiased estimates of γ. We also show that if the PGI weights γ^ are estimated using LDpred-inf—as is true for the Repository PGIs—then the bias in our estimator due to plausible violations of this condition will typically be negligible.
