For significant rgs detected in LDSC where both the individual eating disorder and substance use-related phenotypes each had ~10 or more significant GWAS SNPs (Zhu et al., 2018), bidirectional Mendelian randomization (MR) analyses (Smith and Ebrahim, 2003) were conducted using Generalised Summary-data-based Mendelian Randomisation (GSMR; Zhu et al., 2018) to preliminarily investigate potentially causal relationships between liability to these phenotypes. As GSMR requires a reference sample with individual genotypes to account for LD, we used the 1000 Genomes Phase 3 European ancestries sample as our reference panel (1000 Genomes Project Consortium et al., 2015). SNPs with evidence of horizontal pleiotropy were excluded (using the HEIDI-Outlier method; default p-value threshold=0.01). We only included genome-wide significant SNPs (p<5x10−8) as possible instruments, and SNPs were clumped to ensure independence (i.e., amongst a set of genome-wide significant SNPs correlated at r2>0.05 within a 1-Mb window, only the SNP with the lowest p-value was retained). As MR analyses are sensitive to sample overlap, we scanned the published papers to determine which samples were included in the discovery GWAS, and any known samples in common across the two discovery GWAS were excluded from the eating disorder GWAS and summary statistics were regenerated for MR analyses.
