Across the full set of GWAS results contributing to the gSEM GWAS (i.e., GENOA, MVP-SAGE-YP, PGC-SUD, and PH) there are additional OA definitions (MVP and PH used Electronic Health Record ICD-9 or ICD-10 codes for opioid use disorder [OUD]) and variation in type of controls used. GENOA cohorts used a combination of controls (opioid exposed, unexposed, and unknown exposure public controls). MVP and PH used opioid exposed controls, and the PGC-SUD results used here were based on unexposed controls. Regardless of the approach to defining OA or the type of controls, the LDSC genetic correlations across cohorts were very high (all pairwise rg > 0.9, Supplementary Table 2). These heritabilities and genetic correlations show that the genetics contributing to OA are highly shared regardless of OA case definition or opioid exposure status of controls to which the cases are compared.