We then examined the effect of a PRS for alcohol problems on alcohol use disorder clinical criteria in our application of the method in observed data. We tested two heritable environments as sources of collider bias: tobacco use (TOB) and educational attainment (EDU). Inclusion of the phenotypic PCs in the TOB models increased the PRS beta and change R2 modestly. The same pattern was observed in the EDU models, but the differences were very modest. This likely reflects the difference in correlation between the PRS and heritable environment, which influences the magnitude of collider bias. The correlation of −0.051 between PRS and EDU was likely too small to suppress the PRS effect and induce a measurable bias. On the other hand, the correlation between PRS and TOB (r = 0.140) was high enough to cause a detectable decrease in PRS effect and subsequent correction via PCA.
