When TOB was added to the model, the standardized coefficient estimates for the PRS decreased by 0.041 (28%) (B1 to B2). PRS Change R2 decreased by 0.010 (50%) (B1 to B2). When the phenotypic PCs were added to the model, the standardized coefficient estimate for the PRS increased by 0.029 (20%) (B2 to B3). PRS Change R2 increased by 0.007 (35%) (B2 to B3). These results suggest that the phenotypic PCs provide a modest correction for the collider bias that results from the correlation between PRS and TOB (r = 0.140). The decrease in PRS effect from models B1 to B2 suggests some magnitude of collider bias may be present. The subsequent increase in PRS effect from models B2 to B3 represents a correction for this bias under the assumption that the phenotypic PCs are proxies for the correlated error structure driven by both observed and unobserved factors.
