Fig. 3: Evaluating the utility of PGS for confounder adjustment.
a, A DAG illustrates the causal structure between PGS, confounder (C), treatment (X) and outcome (Y). The PGS serves as an imperfect proxy variable for the confounder. The effects of the C on the exposure (X) and outcome (Y) are denoted as bCX and bCY, respectively. The true unconfounded effect of X on Y is bXY = 1. b, Simulation study—under 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 bCX and bCY. 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. \(\frac{{{b}_{{CX}}}^{2}}{{\mathrm{Var}}(X)}\) = \(\frac{{{b}_{{CY}}}^{2}}{{\mathrm{Var}}(Y)}\) = 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, r2 = 0.5)—an unlikely scenario, given the correlation between PGS and traits is generally lower—correcting for PGS does not completely account for the bias introduced by the confounder.
