control group) from the genotype dosages using Plink’s ‘--score’ method, with default arguments. However the PRS scores for ADHD, were generated using the approach described Demontis et al.33. For each P-value threshold the variance in the phenotype explained by PRS was estimated using Nagelkerke’s R (R package ‘BaylorEdPsych’), and association of PRS with CUD was estimated using logistic regression including the same covariates used in the GWAS analysis (PCs from PCA and the psychiatric disorders listed in Supplementary Table 1). In PRS analyses of psychiatric disorders (ADHD, schizophrenia and depression related phenotypes) individuals with a diagnosis of the disorder being analysed were excluded. The number of individuals excluded with ADHD, schizophrenia and major depressive disorder are listed in Supplementary Table 1.
