To validate substance-specific SNPs, we used ASSET for discovery of these variants and, in the European ancestry GWAS, also examined Q-SNP results derived from GenomicSEM. Q-SNP14 indexes violation of the null hypothesis that a SNP acts on a trait entirely through a common factor (e.g., addiction-rf). For example, if a SNP has a particular effect on one SUD trait (such as SNPs in CHRNA5 influencing PTU), then it should have significant Q-SNP statistics because it violates the assumption that its effect on PTU is via the addiction-rf. We identified Q-SNPs by estimating the association between each SNP and the addiction-rf. Then, we fit a model where the SNP predicted the indicators underlying the addiction-rf, i.e., PAU, PTU, CUD, OUD. We compared the Chi-square difference statistic between the two models; those with significant decrement of fit (X2 for Δdf = 4) in the model where the SNP predicted the addiction-rf alone relative to the SNP predicting the indicators themselves was considered a significant Q-SNP above genome-wide significance (i.e. Q p < 5e-8). SNPs with significant Q-SNP statistics were removed from the
