Simulation studyunder this model (Methods), we changed the correlation between C and PGS simply by varying r and the effect of confounding factor C on X and Y by varying b CX and b CY . Under each condition, we measured the observed effect of X on Y, conditioned on PGS and calculated the bias as a percentage of the inflated effect of X on Y . = = 0.1 for small confounding effect, 0.2 for small-medium confounding effect, 0.3 for medium-large confounding effect and 0.5 for large confounding effect. Under each condition, we carried out experiments for 100 iterations (each n = 100,000). Data are presented as mean values and 95% tolerance intervals (1.96 s.d.). These simulations show that even if PGS is strongly correlated with the confounder (that is, r 2 = 0.5)an unlikely scenario, given the correlation between PGS and traits is generally lowercorrecting for PGS does not completely account for the bias introduced by the confounder.
