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Cited by 208Genetic Associations and EpidemiologyAdvanced Causal Inference TechniquesGenetic and phenotypic traits in livestock

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Mendelian randomization analysis using mixture models for robust and efficient estimation of causal effects.

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Qi, Guanghao, Chatterjee, Nilanjan·2019·Nature Communications
DOI 10.1038/s41467-019-09432-2PMC PMC6486646

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Abstract

Abstract Mendelian randomization (MR) has emerged as a major tool for the investigation of causal relationship among traits, utilizing results from large-scale genome-wide association studies. Bias due to horizontal pleiotropy, however, remains a major concern. We propose a novel approach for robust and efficient MR analysis using large number of genetic instruments, based on a novel spike-detection algorithm under a normal-mixture model for underlying effect-size distributions. Simulations show that the new method, MRMix, provides nearly unbiased or/and less biased estimates of causal effects compared to alternative methods and can achieve higher efficiency than comparably robust estimators. Application of MRMix to publicly available datasets leads to notable observations, including identification of causal effects of BMI and age-at-menarche on the risk of breast cancer; no causal effect of HDL and triglycerides on the risk of coronary artery disease; a strong detrimental effect of BMI on the risk of major depressive disorder.

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Fig. 1 Overview of MRMix approach. a Four components of the Mendelian randomization mixture (MRMix) model: (1) Direct effect on X and an indirect effect on Y only through X; (2) direct effects on both X and Y; (3) direct effect on Y but no relationship with X; (4) related to neither X nor Y. Direct effects are denoted by ux and uy and the causal effect is denoted by θ. Parameters π1, π2, π3, π4 are the mixing probabilities associated with components (1), (2), (3), and (4), respectively; within each component, we assume ux and uy to either be 0 or follow normal distributions and σx²,σy²,σxy are the variance-covariance parameters. b Schematic of the MRMix estimation algorithm. The line corresponding to the true causal effect (0.2) maximizes the number of points “close” to the line. Here the regions that are covered by the 95% probability band under the null distribution (shaded area, expressed as ∣β^y-θβ^x∣≤1.96√(sy²+θ²sx²)) are highlighted. We plot the line β^y=θβ^x corresponding to three values θ = −0.3, 0.2, 0.48; π^0 is the estimated proportion of valid IVs. Source data are provided as a Source Data file
Fig. 1 Overview of MRMix approach. a Four components of the Mendelian randomization mixture (MRMix) model: (1) Direct effect on X and an indirect effect on Y only through X; (2) direct effects on both X and Y; (3) direct effect on Y but no relationship with X; (4) related to neither X nor Y. Direct effects are denoted by ux and uy and the causal effect is denoted by θ. Parameters π1, π2, π3, π4 are the mixing probabilities associated with components (1), (2), (3), and (4), respectively; within each component, we assume ux and uy to either be 0 or follow normal distributions and σx²,σy²,σxy are the variance-covariance parameters. b Schematic of the MRMix estimation algorithm. The line corresponding to the true causal effect (0.2) maximizes the number of points “close” to the line. Here the regions that are covered by the 95% probability band under the null distribution (shaded area, expressed as ∣β^y-θβ^x∣≤1.96√(sy²+θ²sx²)) are highlighted. We plot the line β^y=θβ^x corresponding to three values θ = −0.3, 0.2, 0.48; π^0 is the estimated proportion of valid IVs. Source data are provided as a Source Data fileCC BY · PubMed Central
Fig. 2 Simulation results when genetic correlation due to causal and pleiotropic effects are in the same direction. Mean and standard deviation of causal estimates are reported over 100 simulations. The true causal effect θ is 0.2. Estimates of association coefficient for SNPs across two traits are simulated assuming an underlying four-component model for effect-size distribution (Scenario A, see Methods), where SNPs could have direct effects on neither traits, only on X, only on Y, or on both with the effects being correlated. The proportion of valid instruments, i.e., the SNPs which have only direct effects on X, as a proportion of the total number of SNPs which are associated with X, are fixed at 50% or 25%. nx = N: sample size of the study associated with X; ny: sample size of the study associated with Y. Standard error bars higher than 60 are truncated and marked with *true-value. The average number of IVs, defined as the SNPs which reach genome-wide significance (z-test p < 5 × 10−8) in the study associated with X, is 14, 105, 399, 1135, and 1780 for N = 50 k, 100 k, 200 k, 500 k, and 1000 k, respectively. Source data are provided as a Source Data file
Fig. 2 Simulation results when genetic correlation due to causal and pleiotropic effects are in the same direction. Mean and standard deviation of causal estimates are reported over 100 simulations. The true causal effect θ is 0.2. Estimates of association coefficient for SNPs across two traits are simulated assuming an underlying four-component model for effect-size distribution (Scenario A, see Methods), where SNPs could have direct effects on neither traits, only on X, only on Y, or on both with the effects being correlated. The proportion of valid instruments, i.e., the SNPs which have only direct effects on X, as a proportion of the total number of SNPs which are associated with X, are fixed at 50% or 25%. nx = N: sample size of the study associated with X; ny: sample size of the study associated with Y. Standard error bars higher than 60 are truncated and marked with *true-value. The average number of IVs, defined as the SNPs which reach genome-wide significance (z-test p < 5 × 10−8) in the study associated with X, is 14, 105, 399, 1135, and 1780 for N = 50 k, 100 k, 200 k, 500 k, and 1000 k, respectively. Source data are provided as a Source Data fileCC BY · PubMed Central
Fig. 3 Simulation results when genetic correlation due to causal and pleiotropic effects are in opposite directions. Mean and standard deviation of causal estimates are reported over 100 simulations. The true causal effect θ = −0.2. Estimates of association coefficient for SNPs across two traits are simulated assuming an underlying four-component model for effect-size distribution (Scenario A, see Methods), where SNPs could have direct effects on neither traits, only on X, only on Y, or on both with the effects being correlated. The proportion of valid instruments, i.e. the SNPs which have only direct effects on X as a proportion of the total number of SNPs which are associated with X, are fixed at 50% or 25%. nx = N: sample size of the study associated with X; ny: sample size of the study associated with Y. Standard error bars higher than 60 are truncated and marked with *true-value. The average number of IVs, defined as the SNPs which reach genome-wide significance (z-test p < 5 × 10−8) in the study associated with X, is 14, 105, 399, 1135, and 1780 for N = 50 k, 100 k, 200 k, 500 k and 1000 k, respectively. Source data are provided as a Source Data file
Fig. 3 Simulation results when genetic correlation due to causal and pleiotropic effects are in opposite directions. Mean and standard deviation of causal estimates are reported over 100 simulations. The true causal effect θ = −0.2. Estimates of association coefficient for SNPs across two traits are simulated assuming an underlying four-component model for effect-size distribution (Scenario A, see Methods), where SNPs could have direct effects on neither traits, only on X, only on Y, or on both with the effects being correlated. The proportion of valid instruments, i.e. the SNPs which have only direct effects on X as a proportion of the total number of SNPs which are associated with X, are fixed at 50% or 25%. nx = N: sample size of the study associated with X; ny: sample size of the study associated with Y. Standard error bars higher than 60 are truncated and marked with *true-value. The average number of IVs, defined as the SNPs which reach genome-wide significance (z-test p < 5 × 10−8) in the study associated with X, is 14, 105, 399, 1135, and 1780 for N = 50 k, 100 k, 200 k, 500 k and 1000 k, respectively. Source data are provided as a Source Data fileCC BY · PubMed Central

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Metadata

Authors
Qi, G., & Chatterjee, N.
Affiliations
Johns Hopkins University (US)
Corresponding author
Chatterjee, Nilanjan
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2019-04-26
Volume
10
Issue
1
Pages
1941-1941
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-019-09432-2
PMC
PMC6486646
OpenAlex
W2941271956
Cited by
207
References
60
Citations by year
2026: 22 · 2025: 34 · 2024: 52 · 2023: 28 · 2022: 26 · 2021: 20 · 2020: 19 · 2019: 6
FWCI
10.66
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • Johns Hopkins University
  • Genome Canada (C1287/A16563, U19 CA148065)
  • Government of Canada (C1287/A10710, U19 CA148065, 634935, PSR-SIIRI-701, C1287/A10118, HEALTH-F2-2009-223175, C1287/A16563, 633784)
  • Cancer Research UK (223175, U19 CA148065, C1287/A10118, C1287/A16563, C1287/A10710, C1287‐A10118, HEALTHF2-2009-223175, A10118, C1287, 633784, 634935, A16563, C1287-A10710, PSRSIIRI-701, A10710, C1287‐A16563)
  • European Commission (PSRSIIRI-701, U19 CA148065, 633784, C1287/A10118, C1287/A10710, 634935, H2020, C1287/A16563, 223175)
  • National Institutes of Health (634935, 223175, 633784, PSR-SIIRI-701, C1287/A16563, C1287/A10118, C1287/A10710, HEALTH-F2-2009-223175, X01HG007492, H2020, CA148065, U19 CA148065, X01HG007492, U24OD023382)
  • Horizon 2020 Framework Programme (633784, U19 CA148065, 634935, PSR-SIIRI-701, C1287/A10118, C1287/A10710, C1287/A16563, HEALTH-F2-2009-223175, 223175)
  • Canadian Institutes of Health Research (C1287/A10710, X01HG007492, C1287/A10118, C1287/A16563, PSR-SIIRI-701, 634935, HEALTH-F2-2009-223175, 633784, U19 CA148065, 223175)
  • National Human Genome Research Institute (X01HG007492)
  • National Cancer Institute (U19CA148065)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
Keywords
Mendelian randomization, horizontal pleiotropy, spike detection, normal mixture models, causal effect estimation, genetic instruments, effect size distribution, body mass index, age at menarche, breast cancer risk, coronary artery disease, HDL cholesterol, triglycerides, major depressive disorder
MeSH terms
Age Factors, Algorithms, Breast Neoplasms, Coronary Artery Disease, Major Depressive Disorder, Female, Humans, Cholesterol, HDL, Menarche, Risk Factors, Triglycerides, Genome, Human, Body Mass Index, Quantitative Trait, Heritable, Genome-Wide Association Study, Mendelian Randomization Analysis, Datasets as Topic

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