First, we performed null simulations (gcp=0) with uncorrelated pleiotropic effects (via γ; Figure 1a) and zero genetic correlation. 1% of SNPs were causal for both traits (with independent effect sizes, explaining 20% of heritability for each trait), and 4% of SNPs were causal for each trait exclusively (Figure 2a, Supplementary Table 2a-d). LCV produced conservative p-values (0.0% false positive rate at α = 0.05); our normalization of the test statistic can lead to conservative p-values when the genetic correlation is low (see Methods). All three main MR methods produced well-calibrated p-values. Even though the ``exclusion restriction" assumption of MR is violated here, these results confirm that uncorrelated pleiotropic effects do not confound random-effect MR at large sample sizes[21]. (Such pleiotropy is known to cause false positives if a less conservative fixed-effect approach is used[22].) In these simulations, all methods except LCV used the set of approximately 170 SNPs (on average) that were genome-wide significant (p < 5 × 10−8) for trait 1 (or approximately 330 SNPs that were genome-wide significant for either trait, in the case of Bidirectional MR).
