The GenomicSEM package30 within R was used for genomic structural equation modeling (gSEM). The gSEM implemented multivariable LDSC function within this package was used to calculate single-nucleotide polymorphism heritability on the observed and liability scale (prevalence of 10%), genetic covariance matrices, and genetic correlation. The LD scores from 1000 Genomes Project phase 3 European70 were used as the reference population in this calculation. The sampling genetic covariance matrix is expanded to incorporate SNP effects by including the covariances between SNPs and each cohort. This expanded sampling genetic covariance includes the multivariate LDSC estimated genetic variances and covariances, along with the sampling covariance matrix of the SNP effects on the cohorts, which are estimated using cross-trait LDSC with the sampling correlation weighted by the sample overlap. With the gSEM implemented LDSC, the overlap of samples between GENOA, MVP meta-analysis, and PGC-SUD is not a concern.
