In the univariate case where ρ is estimated within the same dataset as the PGI analysis is conducted, we show that while uncertainty in R^2 causes downward bias in the standard error, uncertainty in h^SNP2 causes upward bias, and the net effect is likely to be standard errors that are slightly conservative. We conjecture that the standard errors will also typically be conservative in multivariate settings. If the ρ estimate is from a different dataset, then ignoring the uncertainty in ρ will unambiguously cause the standard errors to be anticonservative. In such settings and in settings when there is meaningful uncertainty in the estimate of ρ, we recommend that users calculate bootstrapped standard errors. The bootstrapped standard errors correctly account for uncertainty in ρ and will be larger than the unbootstrapped standard errors.
