Associations between each thresholded CROSS PRS and GENSUB were tested using ordinary least squares regression. Multinomial logistic regression was then used to test associations across each level of involvement (i.e., no/non-regular use, non-problem use, mild problems, moderate dependence, and severe dependence) for specific substances and individual disorder PRS. Due to the large number of non-independent tests performed, an empirical significance threshold for α = 0.05 was determined using 10,000 label-swapping permutations (see Supplementary Materials and Methods for details). The lowest level of involvement was used as the reference group; thus, resulting odds-ratios (ORs) reflect increases or decreases in association for each level of substance involvement relative to the lowest level (i.e., no/non-regular use). Wald chi-square tests (for 1° of freedom) were used to examine whether the magnitude of these resulting ORs could be equated to each other and thus establish whether differences in PRS existed across involvement levels (e.g., comparison of the OR between no use and use with no problems vs. the OR between no use and use with 1–2 symptoms). To determine whether specific disorder-substance associations were driven
