For the current cross-trait GWAS, we maintained the same QC metrics and only analyzed SNPs that were present in all four input GWAS, i.e., variants that passed QC thresholds at all levels, resulting in 3,513,381 SNPs in samples of European ancestry and 5,303,643 SNPs in samples of African American ancestry. The LD scores used for the genomic structural equation modeling (GenomicSEM)47 were estimated in the European ancestry samples only using the 1000 Genomes European data48. We restricted analyses to HapMap3 SNPs49 as these tend to be well imputed and produce accurate estimates of heritability. We used the effective N, which was estimated for each GWAS50. For traits with a binary distribution, the effective sample size for an equivalently powered case-control study under a 50–50 case control balance was estimated using the equation: Neffective = 4/((1/Ncase) + (1/Ncontrol))51. Continuous and quasi-continuous traits used the given N or if from MTAG, the equation Neffective = ((Z/β)2)/(2*MAF*(1-MAF))8 to approximate an equivalently powered GWAS of a single trait. Effective Ns ranged from 46,351 (CUD) to 300,789 (PAU) and are described for each substance-specific GWAS in the Results below. Individual GWAS details can be found in the Online Methods.
