Fourth, we performed null simulations with a nonzero genetic correlation and differential power for the two traits, reducing the sample size from 100k to 20k for trait 2. 0.5% of SNPs were causal for L with effects q1=q2=0.5 on each trait, and 8% were causal for each trait exclusively (Figure 2d, Table S2k-m). Because per-SNP heritability was higher for shared causal SNPs than for non-shared causal SNPs, shared causal SNPs were more likely to reach genome-wide significance in the smaller trait 1 sample (N=20k), leading to a similar imbalance as in Figure 2c. As a result, Bidirectional MR (as well as other MR Methods) produced excess false positives, while LCV produced well-calibrated p-values.
