Powerful three-sample genome-wide design and robust statistical inference in summary-data Mendelian randomization.
Abstract
BACKGROUND: Summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to use genetic instruments that are only weakly associated with the exposure. DEVELOPMENT: We propose a three-sample genome-wide design where typically 1000 independent genetic instruments across the whole genome are used. We develop an empirical partially Bayes statistical analysis approach where instruments are weighted according to their strength; thus weak instruments bring less variation to the estimator. The estimator is highly efficient with many weak genetic instruments and is robust to balanced and/or sparse pleiotropy. APPLICATION: We apply our method to estimate the causal effect of body mass index (BMI) and major blood lipids on cardiovascular disease outcomes, and obtain substantially shorter confidence intervals (CIs). In particular, the estimated causal odds ratio of BMI on ischaemic stroke is 1.19 (95% CI: 1.07-1.32, P-value <0.001); the estimated causal odds ratio of high-density lipoprotein cholesterol (HDL-C) on coronary artery disease (CAD) is 0.78 (95% CI: 0.73-0.84, P-value <0.001). However, the estimated effect of HDL-C attenuates and become statistically non-significant when we only use strong instruments. CONCLUSIONS: A genome-wide design can greatly improve the statistical power of MR studies. Robust statistical methods may alleviate but not solve the problem of horizontal pleiotropy. Our empirical results suggest that the relationship between HDL-C and CAD is heterogeneous, and it may be too soon to completely dismiss the HDL hypothesis.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Various statistical methods have been proposed to reduce weak instrument bias due to sample overlap and bias due to winner's curse.
“Various statistical methods have been proposed to reduce weak instrument bias due to sample overlap and bias due to winner’s curse (see Section 3) 43– 45 .”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [44]
Cites
PLINK: a tool set for whole-genome association and population-based linkage analyses.
Purcell, S., Neale, B., Todd-Brown, K., Thomas, L., Ferreira, M. A. R., Bender, D., Maller, J., Sklar, P., de Bakker, P. I. W., Daly, M. J., et al. (2007) · The American Journal of Human Genetics · doi:10.1086/519795 · Cited by 34,089 · see citing works
Bowden, J., Davey Smith, G., & Burgess, S. (2015) · International Journal of Epidemiology · doi:10.1093/ije/dyv080 · Cited by 9,816 · see citing works
Bowden, J., Davey Smith, G., Haycock, P. C., & Burgess, S. (2016) · Genetic Epidemiology · doi:10.1002/gepi.21965 · Cited by 8,922 · see citing works
Verbanck, M., Chen, C.-Y., Neale, B., & Do, R. (2018) · Nature Genetics · doi:10.1038/s41588-018-0099-7 · Cited by 8,591 · see citing works
OLSSON, A. G., McMurray, J. J. V., Thorgeirsson, G., Spaulding, C. M., Slattery, J., Pyörälà, K., Færgeman, O., Wright, R. S., Berg, K. M., Wilhelmsen, L., et al. (1994) · The Lancet · Cited by 8,467 · see citing works
The MR-Base platform supports systematic causal inference across the human phenome
Hemani, G., Zheng, J., Elsworth, B., Wade, K. H., Haberland, V., Baird, D., Laurin, C., Burgess, S., Bowden, J., Langdon, R., et al. (2018) · eLife · doi:10.7554/elife.34408 · Cited by 7,959 · see citing works
Mendelian Randomization Analysis With Multiple Genetic Variants Using Summarized Data
Burgess, S., Butterworth, A., & Thompson, S. G. (2013) · Genetic Epidemiology · doi:10.1002/gepi.21758 · Cited by 6,050 · see citing works
Davey Smith, G., & Ebrahim, S. (2003) · International Journal of Epidemiology · doi:10.1093/ije/dyg070 · Cited by 5,882 · see citing works
LD Score regression distinguishes confounding from polygenicity in genome-wide association studies
Schizophrenia Working Group of the Psychiatric Genomics Consortium, Bulik-Sullivan, B. K., Loh, P.-R., Finucane, H. K., Ripke, S., Yang, J., Patterson, N., Daly, M. J., Price, A. L., & Neale, B. M. (2015) · Nature Genetics · doi:10.1038/ng.3211 · Cited by 5,559 · see citing works
Mendelian randomization: genetic anchors for causal inference in epidemiological studies
Davey Smith, G., & Hemani, G. (2014) · Human Molecular Genetics · doi:10.1093/hmg/ddu328 · Cited by 4,677 · see citing works
An atlas of genetic correlations across human diseases and traits
ReproGen Consortium, Bulik-Sullivan, B., Psychiatric Genomics Consortium, Genetic Consortium for Anorexia Nervosa of the Wellcome Trust Case Control Consortium 3, Finucane, H. K., Anttila, V., Gusev, A., Day, F. R., Loh, P.-R., Duncan, L., et al. (2015) · Nature Genetics · doi:10.1038/ng.3406 · Cited by 4,255 · see citing works
A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments
Stock, J. H., Wright, J. H., & Yogo, M. (2002) · Journal of Business and Economic Statistics · doi:10.1198/073500102288618658 · Cited by 4,151 · see citing works
Avoiding bias from weak instruments in Mendelian randomization studies
Burgess, S., Thompson, S. G., & CRP CHD Genetics Collaboration (2011) · International Journal of Epidemiology · doi:10.1093/ije/dyr036 · Cited by 3,952 · see citing works
Biological, clinical and population relevance of 95 loci for blood lipids
Teslovich, T. M., Musunuru, K., Smith, A. V., Edmondson, A. C., Stylianou, I. M., Koseki, M., Pirruccello, J. P., Ripatti, S., Chasman, D. I., Willer, C. J., et al. (2010) · Nature · doi:10.1038/nature09270 · Cited by 3,487 · see citing works
Self-citationEffects of torcetrapib in patients at high risk for coronary events
Barter, P. J., Caulfield, M., Eriksson, M., Grundy, S. M., Kastelein, J. J. P., Komajda, M., Lopez-Sendon, J., Mosca, L., Tardif, J.-C., Waters, D. D., et al. (2007) · New England Journal of Medicine · doi:10.1056/nejmoa0706628 · Cited by 3,139 · see citing works
Pedersen, T. R. (2004) · Atherosclerosis Supplements · doi:10.1016/j.atherosclerosissup.2004.08.027 · Cited by 3,098 · see citing works
Willer (2013) · doi:10.1038/ng.2797 · Cited by 2,983 · see citing works
Variable Selection via Gibbs Sampling
George, E. I., & McCulloch, R. E. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476353 · Cited by 2,828 · see citing works
Major lipids, apolipoproteins, and risk of vascular disease
The Emerging Risk Factors Collaboration* (2009) · JAMA · doi:10.1001/jama.2009.1619 · Cited by 2,731 · see citing works
Consistent Estimates Based on Partially Consistent Observations
Neyman, J., & Scott, E. L. (1948) · Econometrica · doi:10.2307/1914288 · Cited by 2,691 · see citing works
PLASMA-HIGH-DENSITY-LIPOPROTEIN CONCENTRATION AND DEVELOPMENT OF ISCHÆMIC HEART-DISEASE
Miller, G. J., & Miller, N. E. (1975) · The Lancet · doi:10.1016/s0140-6736(75)92376-4 · Cited by 2,621 · see citing works
Does Compulsory School Attendance Affect Schooling and Earnings?
Angrist, J. D., & Krueger, A. B. (1991) · The Quarterly Journal of Economics · doi:10.2307/2937954 · Cited by 2,565 · see citing works
A comprehensive 1000 Genomes–based genome-wide association meta-analysis of coronary artery disease
the CARDIoGRAMplusC4D Consortium (2015) · Nature Genetics · doi:10.1038/ng.3396 · Cited by 2,447 · see citing works
Effects of dalcetrapib in patients with a recent acute coronary syndrome
Schwartz, G. G., Olsson, A. G., Abt, M., Ballantyne, C. M., Barter, P. J., Brumm, J., Chaitman, B. R., Holme, I. M., Kallend, D., Leiter, L. A., et al. (2012) · New England Journal of Medicine · doi:10.1056/nejmoa1206797 · Cited by 2,022 · see citing works
A framework for the investigation of pleiotropy in two‐sample summary data Mendelian randomization
Bowden, J., Del Greco M, F., Minelli, C., Davey Smith, G., Sheehan, N., & Thompson, J. (2017) · Statistics in Medicine · doi:10.1002/sim.7221 · Cited by 1,887 · see citing works
EPIC- InterAct Consortium, Burgess, S., Scott, R. A., Timpson, N. J., Davey Smith, G., & Thompson, S. G. (2015) · European Journal of Epidemiology · doi:10.1007/s10654-015-0011-z · Cited by 1,803 · see citing works
Burgess, S., & Thompson, S. G. (2015) · American Journal of Epidemiology · doi:10.1093/aje/kwu283 · Cited by 1,605 · see citing works
Bowden, J., Fabiola Del Greco, M., Minelli, C., Smith, G. D., Sheehan, N. A., & Thompson, J. R. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw220 · Cited by 1,572 · see citing works
Bayesian Variable Selection in Linear Regression
Mitchell, T. J., & Beauchamp, J. J. (1988) · Journal of the American Statistical Association · doi:10.1080/01621459.1988.10478694 · Cited by 1,427 · see citing works
HDL cholesterol efflux capacity and incident cardiovascular events
Rohatgi, A., Khera, A., Berry, J. D., Givens, E. G., Ayers, C. R., Wedin, K. E., Neeland, I. J., Yuhanna, I. S., Rader, D. R., de Lemos, J. A., et al. (2014) · New England Journal of Medicine · doi:10.1056/nejmoa1409065 · Cited by 1,390 · see citing works
Pleiotropy in complex traits: challenges and strategies
Solovieff, N., Cotsapas, C., Lee, P. H., Purcell, S. M., & Smoller, J. W. (2013) · Nature Reviews Genetics · doi:10.1038/nrg3461 · Cited by 1,085 · see citing works
Bowden, J., Del Greco M, F., Minelli, C., Zhao, Q., Lawlor, D. A., Sheehan, N. A., Thompson, J., & Davey Smith, G. (2019) · International Journal of Epidemiology · doi:10.1093/ije/dyy258 · Cited by 995 · see citing works
Self-citationInstruments for Causal Inference: An Epidemiologist's Dream?
Hernán, M. A., & Robins, J. M. (2006) · Epidemiology · doi:10.1097/01.ede.0000222409.00878.37 · Cited by 961 · see citing works
Burgess, S., Dudbridge, F., & Thompson, S. G. (2015) · American Journal of Epidemiology · doi:10.1093/aje/kwv017 · Cited by 945 · see citing works
Mendelian randomization as an instrumental variable approach to causal inference
Didelez, V., & Sheehan, N. (2007) · Statistical Methods in Medical Research · doi:10.1177/0962280206077743 · Cited by 923 · see citing works
Bowden, J., Spiller, W., Del Greco M, F., Sheehan, N., Thompson, J., Minelli, C., & Davey Smith, G. (2018) · International Journal of Epidemiology · doi:10.1093/ije/dyy101 · Cited by 880 · see citing works
HDL and cardiovascular disease
Rader, D. J., & Hovingh, G. K. (2014) · The Lancet · doi:10.1016/s0140-6736(14)61217-4 · Cited by 870 · see citing works
Zhao, Q., Wang, J., Hemani, G., Bowden, J., & Small, D. S. (2020) · The Annals of Statistics · doi:10.1214/19-aos1866 · Cited by 854 · see citing works
Self-citationEvacetrapib and cardiovascular outcomes in high-risk vascular disease
Lincoff, A. M., Nicholls, S. J., Riesmeyer, J. S., Barter, P. J., Brewer, H. B., Fox, K. A. A., Gibson, C. M., Granger, C., Menon, V., Montalescot, G., et al. (2017) · New England Journal of Medicine · doi:10.1056/nejmoa1609581 · Cited by 801 · see citing works
Mendelian randomization of blood lipids for coronary heart disease
Holmes, M. V., Asselbergs, F. W., Palmer, T. M., Drenos, F., Lanktree, M. B., Nelson, C. P., Dale, C. E., Padmanabhan, S., Finan, C., Swerdlow, D. I., et al. (2015) · European Heart Journal · doi:10.1093/eurheartj/eht571 · Cited by 748 · see citing works
Instrumental variable methods for causal inference
Baiocchi, M., Cheng, J., & Small, D. S. (2014) · Statistics in Medicine · doi:10.1002/sim.6128 · Cited by 687 · see citing works
Self-citationMendelian randomization in cardiometabolic disease: challenges in evaluating causality
Holmes, M. V., Ala-Korpela, M., & Smith, G. D. (2017) · Nature Reviews Cardiology · doi:10.1038/nrcardio.2017.78 · Cited by 679 · see citing works
The Coronary Artery Disease (C4D) Genetics Consortium (2011) · Nature Genetics · doi:10.1038/ng.782 · Cited by 674 · see citing works
C Reactive Protein Coronary Heart Disease Genetics Collaboration (CCGC) (2011) · BMJ · doi:10.1136/bmj.d548 · Cited by 642 · see citing works
Mendelian Randomization: New Applications in the Coming Age of Hypothesis-Free Causality
Evans, D. M., & Smith, G. D. (2015) · Annual Review of Genomics and Human Genetics · doi:10.1146/annurev-genom-090314-050016 · Cited by 524 · see citing works
Genome-wide association study identifies 112 new loci for body mass index in the Japanese population
Akiyama, M., Okada, Y., Kanai, M., Takahashi, A., Momozawa, Y., Ikeda, M., Iwata, N., Ikegawa, S., Hirata, M., Matsuda, K., et al. (2017) · Nature Genetics · doi:10.1038/ng.3951 · Cited by 455 · see citing works
Inactivating Mutations in <i>NPC1L1</i> and Protection from Coronary Heart Disease
The Myocardial Infarction Genetics Consortium Investigators (2014) · New England Journal of Medicine · doi:10.1056/nejmoa1405386 · Cited by 419 · see citing works
APOUPOPROTEIN E ISOFORMS, SERUM CHOLESTEROL, AND CANCER
Katan, M. (1986) · The Lancet · doi:10.1016/s0140-6736(86)92972-7 · Cited by 371 · see citing works
Dale, C. E., Fatemifar, G., Palmer, T. M., White, J., Prieto-Merino, D., Zabaneh, D., Engmann, J. E. L., Shah, T., Wong, A., Warren, H. R., et al. (2017) · Circulation · doi:10.1161/circulationaha.116.026560 · Cited by 345 · see citing works
Ference, B. A., Kastelein, J. J. P., Ginsberg, H. N., Chapman, M. J., Nicholls, S. J., Ray, K. K., Packard, C. J., Laufs, U., Brook, R. D., Oliver-Williams, C., et al. (2017) · JAMA · doi:10.1001/jama.2017.11467 · Cited by 304 · see citing works
Kang, H., Zhang, A., Cai, T. T., & Small, D. S. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2014.994705 · Cited by 265 · see citing works
Zhao, Q., Wang, J., Hemani, G., et al. (2018) · Bristol Research (University of Bristol) · doi:10.48550/arxiv.1801.09652 · Cited by 258 · see citing works
Self-citationEstimation With Many Instrumental Variables
Hansen, C., Hausman, J. A., & Newey, W. K. (2008) · Journal of Business and Economic Statistics · doi:10.1198/073500108000000024 · Cited by 247 · see citing works
VIRUS-INFECTION OF URINARY-TRACT
Brouwers, T. M., Fontein, D. L., & Value, N. (1974) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 236 · see citing works
Lyall, D. M., Celis-Morales, C., Ward, J., Iliodromiti, S., Anderson, J. J., Gill, J. M. R., Smith, D. J., Ntuk, U. E., Mackay, D. F., Holmes, M. V., et al. (2017) · JAMA Cardiology · doi:10.1001/jamacardio.2016.5804 · Cited by 235 · see citing works
Holmes, M. V., Lange, L. A., Palmer, T., Lanktree, M. B., North, K. E., Almoguera, B., Buxbaum, S., Chandrupatla, H. R., Elbers, C. C., Guo, Y., et al. (2014) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2013.12.014 · Cited by 216 · see citing works
Estimation with many instrumental variables
Hansen, C., Hausman, J. A., & Newey, W. K. (2017) · doi:10.1920/wp.cem.2006.1906 · Cited by 193 · see citing works
Linsel‐Nitschke, P., Götz, A., Erdmann, J., Brænne, I., Braund, P. S., Hengstenberg, C., Stark, K. J., Fischer, M., Schreiber, S., Mokhtari, N. E. E., et al. (2008) · PLoS ONE · doi:10.1371/journal.pone.0002986 · Cited by 166 · see citing works
HDL and atherosclerotic cardiovascular disease: genetic insights into complex biology
Rosenson, R. S., Brewer, H. B., Barter, P. J., Björkegren, J., Chapman, M. J., Gaudet, D., Kim, D. S., Niesor, E. J., Rye, K., Sacks, F. M., et al. (2017) · Nature Reviews Cardiology · doi:10.1038/nrcardio.2017.115 · Cited by 148 · see citing works
Adiposity as a cause of cardiovascular disease: a Mendelian randomization study
Hägg, S., Fall, T., Ploner, A., Mägi, R., Fischer, K., Draisma, H. H. M., Kals, M., de Vries, P. S., Dehghan, A., Willems, S. M., et al. (2015) · International Journal of Epidemiology · doi:10.1093/ije/dyv094 · Cited by 142 · see citing works
Guo, Z., Kang, H., Cai, T., & Small, D. S. (2018) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12275 · Cited by 87 · see citing works
Self-citationMining the Human Phenome Using Allelic Scores That Index Biological Intermediates
Evans, D. M., Brion, M., Paternoster, L., Kemp, J. P., McMahon, G., Munafo, M. R., Whitfield, J. B., Medland, S. E., Montgomery, G. W., Timpson, N. J., et al. (2013) · PLoS Genetics · doi:10.1371/journal.pgen.1003919 · Cited by 73 · see citing works
Mendelian randomization to assess causal effects of blood lipids on coronary heart disease
Burgess, S., & Harshfield, E. L. (2016) · Current Opinion in Endocrinology Diabetes and Obesity · doi:10.1097/med.0000000000000230 · Cited by 58 · see citing works
Using Empirical Partially Bayes Inference for Increased Efficiency
Lindsay, B. G. (1985) · The Annals of Statistics · doi:10.1214/aos/1176349646 · Cited by 51 · see citing works
Beyond the Single SNP: Emerging Developments in Mendelian Randomization in the “Omics” Era
Brion, M., Benyamin, B., Visscher, P. M., & Smith, G. D. (2014) · Current Epidemiology Reports · doi:10.1007/s40471-014-0024-2 · Cited by 22 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Guidelines for performing Mendelian randomization investigations
Burgess, S., Davey Smith, G., Davies, N. M., Dudbridge, F., Gill, D., Glymour, M. M., Hartwig, F. P., Holmes, M. V., Minelli, C., Relton, C. L., et al. (2020) · Wellcome Open Research · doi:10.12688/wellcomeopenres.15555.2 · Cited by 1,273 · see citing works
Polimanti, R., Peterson, R. E., Ong, J.-S., MacGregor, S., Edwards, A. C., Clarke, T.-K., Frank, J., Gerring, Z., Gillespie, N. A., Lind, P. A., et al. (2019) · Psychological Medicine · doi:10.1017/s0033291719000667 · Cited by 108 · see citing works
Wang, Z., Wang, X., Zhao, X., Hu, Z., Sun, D., Wu, D., & Xing, Y. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.970933 · Cited by 10 · see citing works
- Authors
- Zhao, Q., Chen, Y., Wang, J., & Small, D. S.
- Affiliations
- University of Pennsylvania (US)
- University of Michigan (US)
- Corresponding author
- Zhao, Qingyuan
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2019-07-11
- Volume
- 48
- Issue
- 5
- Pages
- 1478-1492
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- OpenAlex
- W2956730167
- Cited by
- 188
- References
- 67
- Citations by year
- 2026: 10 · 2025: 26 · 2024: 35 · 2023: 51 · 2022: 33 · 2021: 20 · 2020: 9 · 2019: 4
- FWCI
- 9.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- pleiotropy, statistical power, body mass index, cardiovascular disease, ischemic stroke, HDL cholesterol, coronary artery disease, serum lipids, causal inference
- MeSH terms
- Bayes Theorem, Coronary Artery Disease, Humans, Lipids, Cholesterol, HDL, Cholesterol, LDL, Myocardial Infarction, Models, Statistical, Body Mass Index, Odds Ratio, Stroke, Genome-Wide Association Study, Mendelian Randomization Analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
