In the Yale–Penn EUR subsample, the PRS of PAU was associated with 123 traits, including 26 in alcohol, 39 in opioid, 24 in cocaine and 17 in tobacco categories (Supplementary Table 19 and Extended Data Fig. 5), indicating high comorbidity and shared genetic components across SUDs. In the Yale–Penn AFR subsample, the AUD PRS was associated with six alcohol-related traits, including DSM-5 AUD criterion count, alcohol-induced blackouts and frequency of alcohol use (Supplementary Table 20 and Extended Data Fig. 6).