We examined associations between EduYears-GPS and the SUD criterion counts in separate linear mixed models using the nlme package version 3.1–128 [43] for R version 3.2.3 [44]. We conducted preliminary analyses to identify the EduYears-GPS most strongly associated with criterion counts for each SUD (see Supporting Information Table 1), and present results using the threshold with the strongest association. We conducted these preliminary analyses separately for polygenic scores meeting increasingly stringent p-value thresholds using linear mixed models, which allowed us to account for the nested structure of the COGA family-based data; other methods for optimizing the p-value threshold [e.g., PRSice; 45] do not allow for nested data. In addition to the covariates described above, we also included a count measure of the number of SNPs available for scoring for each participant. Marginal effect sizes for fixed effects were calculated using the MuMIn package version 1.15.6 [46].
