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Distinguishing genetic correlation from causation across 52 diseases and complex traits


Mendelian randomization, a method to infer causal relationships, is confounded by genetic correlations reflecting shared etiology. We developed a model in which a latent causal variable mediates the genetic correlation; trait 1 is partially genetically causal for trait 2 if it is strongly genetically correlated with the latent causal variable, quantified using the genetic causality proportion. We fit this model using mixed fourth moments \({\it{E}}({\it{\alpha }}_1^2{\it{\alpha }}_1{\it{\alpha }}_2)\) and \({\it{E}}\left( {{\it{\alpha }}_2^2{\it{\alpha }}_1{\it{\alpha }}_2} \right)\) of marginal effect sizes for each trait; if trait 1 is causal for trait 2, then SNPs affecting trait 1 (large \({\it{\alpha }}_1^2\)) will have correlated effects on trait 2 (large α1α2), but not vice versa. In simulations, our method avoided false positives due to genetic correlations, unlike Mendelian randomization. Across 52 traits (average n = 331,000), we identified 30 causal relationships with high genetic causality proportion estimates. Novel findings included a causal effect of low-density lipoprotein on bone mineral density, consistent with clinical trials of statins in osteoporosis.

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Change history

  • 06 November 2018

    In the version of this article originally published, there were errors in equations. In the HTML and PDF, the initial term of equation 10 was estimated GCP but should have been estimated standard error, while a ‘hat’ was missing from the first alpha in the second term of the expression at the end of the paragraph following equation (6) in the Methods. In addition, in the abstract in the PDF, a subscript 1 was used instead of a subscript 2 for the final term of the first fourth-moment expression. These errors have been corrected in the HTML, PDF and print versions of the paper.


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We are grateful to B. Neale, S. Raychaudhuri, C. Patel, S. Kathiresan, B. Pasaniuc, and H. Finucane for helpful discussions and to P.-R. Loh and S. Gazal for producing BOLT-LMM summary statistics for UK Biobank traits. This research was conducted using the UK Biobank Resource under Application #16549 and was funded by National Institutes of Health grants R01 MH107649, U01 CA194393, and R01 MH101244.

Author information

L.J.O. and A.L.P. conceived the methods, designed the analyses, and wrote the manuscript. L.J.O. performed the analyses.

Competing interests

The authors declare no competing interests.

Correspondence to Luke J. O’Connor or Alkes L. Price.

Integrated supplementary information

  1. Supplementary Figure 1 Null and causal simulations with no LD and LCV model violations.

    ag, We report the positive rate (α = 0.05 for null simulations, α = 0.001 for causal simulations) for two-sample MR, MR-Egger, Bidirectional MR and LCV. ac correspond to Gaussian mixture model extensions of the models in Fig. 2b-d. f and g correspond to causal analogs of the models in a and d, respectively. We also display scatterplots illustrating the bivariate distribution of true SNP effect sizes on the two traits. a, Null simulation with nonzero SNP effects drawn from a mixture of Gaussian distributions; one mixture component has correlated effects on each trait. b, Null simulation with SNP effects drawn from a mixture of Gaussian distributions, and differential polygenicity between the two traits. c, Null simulation with SNP effects drawn from a mixture of Gaussian distributions and unequal power between the two traits. d, Null simulation with two intermediaries having different effects on each trait. e, Null simulation with two intermediaries having different effects on each trait and unequal polygenicity for the two intermediaries. f, Causal simulation with SNP effects drawn from a mixture of Gaussian distributions; all SNPs affecting trait 1 also affect trait 2, but the relative effect sizes were noisy. g, Causal simulation with an additional genetic confounder (i.e., a second intermediary) mediating part of the genetic correlation. Results for each panel are based on 1,000 simulations. Numerical results are reported in Supplementary Tables 4 and 5, which also include comparisons to MR-WME and MR-MBE.

  2. Supplementary Figure 2 Mean GCP estimates in simulations with LCV model violations.

    Error bars show s.d. based on 1,000 simulations. a, Null simulation with two intermediaries having possibly unequal polygenicity. The two intermediaries had either a slightly, moderately, or highly heterogenous effect on the two traits; that is, when heterogeneity was high, intermediary 1 had a much larger effect on trait 1 while intermediary 2 had a much larger effect on trait 2. Then, we specified a certain difference in polygenicity between the two traits (measured by the proportion of causal SNPs). b, Causal simulation with an additional latent confounder. The latent confounder explained a low, medium, or high proportion of the genetic correlation. We varied the polygenicity of the confounder and of the causal trait, such that a 16× difference in polygenicity indicates that 16× more SNPs were causal for the causal trait than for the genetic confounder.

  3. Supplementary Figure 3 Unbiasedness of posterior mean GCP estimates in simulations with LD and random true GCP values.

    Estimated values of GCP were binned and averaged, and mean true values of GCP are plotted for each bin, with standard errors. Points above the line indicate that GCP estimates were downward biased (toward –1). a, Ascertained simulations (43%) with significant genetic correlation (P < 0.05) and evidence for partial causality (P < 0.001). Only bins with a count of at least 10 are plotted. b, All 10,000 simulations.

Supplementary information

  1. Supplementary Text and Figures

    Supplementary Figures 1–3, Supplementary Tables 2–11 and 13–17, and Supplementary Note

  2. Reporting Summary

  3. Supplementary Table 1

    Simulation parameters

  4. Supplementary Table 12

    LCV and MR results for all trait pairs

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Further reading

Fig. 1: Illustration of the LCV model.
Fig. 2: Null simulations with no LD to assess calibration.
Fig. 3: Causal simulations with no LD to assess power.
Fig. 4: Partially or fully genetically causal relationships between selected complex traits.
Supplementary Figure 1: Null and causal simulations with no LD and LCV model violations.
Supplementary Figure 2: Mean GCP estimates in simulations with LCV model violations.
Supplementary Figure 3: Unbiasedness of posterior mean GCP estimates in simulations with LD and random true GCP values.