Distinguishing genetic correlation from causation across 52 diseases and complex traits.

Illustration of the latent causal variable model. We display the relationship between genotypes X, latent causal variable L and trait values Y1 and Y2. (a) Full LCV model. The genetic correlation between traits Y1 and Y2 is mediated by L, which has normalized effects q1 and q2 on each trait. (See Supplementary Table 17 for a list of random variables vs. parameters.) (b) When q1 = 1, Y1 is perfectly genetically correlated with L (so L does not need to be shown in the diagram), and we say that Y1 is fully genetically causal for Y2. (c) Example genetic architecture of genetically correlated traits with no genetic causality (gcp = 0, i.e. q2 = q1 < 1). Slight noise is added to SNP effects for illustration. Orange SNPs have correlated effects on both traits via L, while blue SNPs do not. (d) Example genetic architecture of genetically correlated traits with partial genetic causality (gcp = 0.8, i.e. q2 < q1 < 1). (e) Example genetic architecture of genetically correlated traits with full genetic causality (gcp = 1, i.e. q2 < q1 = 1).

Null simulations with no LD to assess calibration. We compared LCV to three main MR methods (two-sample MR, MR-Egger and Bidirectional MR). We report the positive rate (α = 0.05) for a causal (or partially causal) effect. Scatterplots illustrate the bivariate effect size distribution. (a) Null simulation (gcp=0) with uncorrelated pleiotropic effects and zero genetic correlation. (b) Null simulation with nonzero genetic correlation. (c) Null simulation with nonzero genetic correlation and differential polygenicity between the two traits. (d) Null simulation with nonzero genetic correlation and differential power for the two traits. Results for each panel are based on 4000 simulations. Numerical results are reported in Supplementary Table 1.

Causal simulations with no LD to assess power. We compared LCV to three main MR methods (two-sample MR, MR-Egger and Bidirectional MR). We report the positive rate (α = 0.001) for a causal (or partially causal) effect. (a) Causal simulations with default parameters: N1 = N2 = 25k; M = 50k; q1 = 1, q2 = 0.2 (results also displayed as dashed lines in panels b-e). (b) Higher (unfilled) or lower (filled) sample size for trait 1 (N1 = 50k and N1 = 12.5k respectively). (c) Higher (unfilled) or lower (filled) sample size for trait 2 (N2 = 50k and N2 = 12.5k respectively). (d) Higher (unfilled) or lower (filled) causal effect size of trait 1 on trait 2 (q2 = 0.4 and q2 = 0.1 respectively). (e) Lower (unfilled) or higher (filled) polygenicity for trait 1. Results for each panel are based on 1000 simulations. Numerical results are reported in Supplementary Table 3.

Partially or fully genetically causal relationships between selected complex traits. Shaded squares indicate significant evidence for a causal or partially causal effect of the row trait on the column trait (FDR <1%). Color scale indicates posterior mean gcp^ for the effect of the row trait on the column trait; blue color indicates gcp^ > 0.6, grey color indicates gcp^ < 0.6. ``+" or ``−" signs indicate trait pairs with a nominally significant (positive or negative) genetic correlation (p<.05), and the size of the "+" or "-" size is proportional to the genetic correlation. Results for the 30 trait pairs with gcp^>0.6 are reported in Table 1, results for all 59 significant trait pairs are reported in Supplementary Table 11, and results for all 429 genetically correlated trait pairs are reported in Supplementary Table 12. HTHY: hypothyroidism. FG: fasting glucose. PDW: platelet distribution width. BPD: bipolar disorder. SCZ: schizophrenia. BrCa: breast cancer: PrCa: prostate cancer.