Cited by 1,289Genetic Associations and EpidemiologyAdvanced Causal Inference TechniquesGenetics and Physical Performance

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Using multiple genetic variants as instrumental variables for modifiable risk factors

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Palmer, Tom M, Lawlor, Debbie A, Harbord, Roger M, Sheehan, Nuala A, Tobias, Jon H, Timpson, Nicholas J, Smith, George Davey, Sterne, Jonathan AC·2012·Statistical Methods in Medical Research

DOI 10.1177/0962280210394459PMC PMC3917707

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Abstract

Mendelian randomisation analyses use genetic variants as instrumental variables (IVs) to estimate causal effects of modifiable risk factors on disease outcomes. Genetic variants typically explain a small proportion of the variability in risk factors; hence Mendelian randomisation analyses can require large sample sizes. However, an increasing number of genetic variants have been found to be robustly associated with disease-related outcomes in genome-wide association studies. Use of multiple instruments can improve the precision of IV estimates, and also permit examination of underlying IV assumptions. We discuss the use of multiple genetic variants in Mendelian randomisation analyses with continuous outcome variables where all relationships are assumed to be linear. We describe possible violations of IV assumptions, and how multiple instrument analyses can be used to identify them. We present an example using four adiposity-associated genetic variants as IVs for the causal effect of fat mass on bone density, using data on 5509 children enrolled in the ALSPAC birth cohort study. We also use simulation studies to examine the effect of different sets of IVs on precision and bias. When each instrument independently explains variability in the risk factor, use of multiple instruments increases the precision of IV estimates. However, inclusion of weak instruments could increase finite sample bias. Missing data on multiple genetic variants can diminish the available sample size, compared with single instrument analyses. In simulations with additive genotype-risk factor effects, IV estimates using a weighted allele score had similar properties to estimates using multiple instruments. Under the correct conditions, multiple instrument analyses are a promising approach for Mendelian randomisation studies. Further research is required into multiple imputation methods to address missing data issues in IV estimation.

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BackgroundMethod
Relationship between low molecular weight heparin calcium therapy and prognosis in severe acute kidney injury in sepsis: Mendelian randomized analysis and retrospective study
Li, J., Huang, S.-T., Feng, F., Wang, L., Chen, T., Li, M., & Liu, L. (2024) · Frontiers in Pharmacology · doi:10.3389/fphar.2024.1389354 · Cited by 4
Genetic evidence for a causal link between gut microbiota and arterial embolism and thrombosis: a two-sample Mendelian randomization study
Shi, Y.-B., Dong, H., Chang, W.-K., Zhao, Y. P., Jin, H., Li, J.-K., & Yan, S. (2024) · Frontiers in Microbiology · doi:10.3389/fmicb.2024.1396699 · Cited by 4
A causal link between circulating leukocytes and three major urologic cancers: a mendelian randomization investigation
Zhi-gang, Y., & Handong, W. (2024) · Frontiers in Genetics · doi:10.3389/fgene.2024.1424119 · Cited by 4
Artificial sweetener and respiratory system cancer: A Mendelian randomization analysis
Zhang, J., Fan, R., Mao, C., Zhou, X., Zhang, Q., Li, S., & Zhuang, Z. (2024) · Clinical Nutrition ESPEN · doi:10.1016/j.clnesp.2024.06.008 · Cited by 5
Bidirectional two-sample Mendelian randomization analysis identifies causal associations between oxidative stress and Parkinson’s disease
Lv, L., Long, Z., Tan, X., Qin, L., Yan, W., Zhang, H., Ren, F., & Wang, C. (2024) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2024.1423773 · Cited by 4
Genetically predicted 1091 blood metabolites and 309 metabolite ratios in relation to risk of type 2 diabetes: a Mendelian randomization study
Li, J., Wang, W., Liu, F., Qiu, L., Ren, Y., Li, M., Li, W., Gao, F., & Zhang, J. (2024) · Frontiers in Genetics · doi:10.3389/fgene.2024.1356696 · Cited by 5
Genetic prediction of asthma increases multiple sepsis risks: A Mendelian randomization study
Luo, J., Liu, P., & Luo, Y. (2024) · World Allergy Organization Journal · doi:10.1016/j.waojou.2024.100937 · Cited by 4
“18 Here, R2 represents the proportion of exposure variance explained by the selected IVs, n is the sample size, and k is the number of IVs.”
Background
Hospital-Treated Infectious Diseases, Infection Burden, and Risk of Lung Cancer
Zheng, J., Huang, J., Yang, Q., Zhou, R., Huang, Y., Wu, X., & Tang, S. (2024) · CHEST Journal · doi:10.1016/j.chest.2024.06.3811 · Cited by 4
Causal relationship between air pollution and infections: a two-sample Mendelian randomization study
Yang, S., Tong, T., Wang, H., Li, Z., Wang, M., & Ni, K. (2024) · Frontiers in Public Health · doi:10.3389/fpubh.2024.1409640 · Cited by 4
Causal Relationship between Chronic Hepatitis B and Stroke in East Asians: A Mendelian Randomization Study
Zhang, Q., Shen, C., Zhang, L., & Wang, M. (2024) · Journal of Cardiovascular Development and Disease · doi:10.3390/jcdd11080247 · Cited by 4
“To avoid weak instrument bias, the strength of each IV was assessed by the F-statistic using the formula F = (R 2 × (N − 2))/(1 − R 2 ), where R 2 referred to the variance explained by the SNP and N was the sample size of exposure data [23].”
Method
Breast cancer and neoplasms of the thyroid gland: a bidirectional two-sample Mendelian randomization study
Sun, Y., Wan, B., Liu, X., Dong, J., Yin, S., & Wu, Y. (2024) · Frontiers in Oncology · doi:10.3389/fonc.2024.1422009 · Cited by 4
Uric acid is associated with increased risk of myocardial infarction: results from NHANES 2009-2018 and bidirectional two-sample Mendelian randomization analysis
Deng, T., & Liu, X. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1424070 · Cited by 4
Investigating the causal association between serum uric acid levels and gastric cancer risk: a Mendelian randomization study
Zhao, X., & Ding, N. (2024) · Scientific Reports · doi:10.1038/s41598-024-77788-7 · Cited by 4
“Furthermore, research indicates that SUA levels are associated with the risk of various cancers—including colorectal, pancreatic, and gallbladder cancers—in a gender-specific manner 47,50 .”
Background
Causal links of human serum metabolites on the risk of prostate cancer: insights from genome-wide Mendelian randomization, single-cell RNA sequencing, and metabolic pathway analysis
Pan, R., Liu, J., Xiao, M., Sun, C., Zhu, J., Wan, L., & Xue, B. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1443330 · Cited by 4
“R 2 ), where R 2 represents the proportion of variance in the trait illuminated by the SNP, and N denotes the sample size of GWAS involving SNPs with the trait (23).”
Causal Relationships Between Gut Microbiota, Immune Cell and Pancreatic Cancer: A Two-Step, Two-Sample Mendelian Randomization Study
Wang, S. M., Zhang, M. F., Pan, Q. H., Yu, T., Lei, R. L., & Li, Q. (2024) · World Journal of Oncology · doi:10.14740/wjon1960 · Cited by 4
Assessment of relationships between epigenetic age acceleration and multiple sclerosis: a bidirectional mendelian randomization study
Liu, H., Zhang, H., Yin, Z., & Hou, M. (2025) · Epigenetics & Chromatin · doi:10.1186/s13072-025-00567-9 · Cited by 4
A Bayesian approach to Mendelian randomisation with dependent instruments
Shapland, C. Y., Thompson, J. R., & Sheehan, N. A. (2018) · Statistics in Medicine · doi:10.1002/sim.8029 · Cited by 4
“The assumptions of Mendelian randomisation ought to be validated by biological knowledge [8, 54] and in a Bayesian approach this same knowledge could be incorporated into the priors.”
Background
Health endowment and later-life outcomes in the labour market: Evidence using genetic risk scores and reduced-form models
Pehkonen, J., Viinikainen, J., Böckerman, P., Pitkänen, N., Lehtimäki, T. J., & Raitakari, O. T. (2019) · SSM - Population Health · doi:10.1016/j.ssmph.2019.100379 · Cited by 4
Non-Causal Effects of Asthma on COVID-19 Susceptibility and Severity
Qiu, L., Yin, K.-J., Pan, G., Ni, J., & Wang, B. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2021.762697 · Cited by 4
“Meanwhile, in order to quantitatively verify instrument strength, F-statistics for each instrumental variables individually and cumulatively were calculated via the formula F-statistic R(2) × (SampleSize-2)/(1R(2)) (Palmer et al., 2012).”
Method
Illuminating the potential causality of serum level of matrix metalloproteinases and the occurrence of cardiovascular and cerebrovascular diseases: a Mendelian randomization study
Zou, X., Wang, L., Zeng, Y., & Zhang, L. (2023) · Journal of Human Genetics · doi:10.1038/s10038-023-01154-0 · Cited by 4
“In addition, we detected the differences between the various instrumental variables to reduce differences between groups by Cochran’s Q statistics [25].”
Method
Exploring Causal Relationships between Leukocyte Telomere Length, Sex Hormone‐Binding Globulin Levels, and Osteoporosis Using Univariable and Multivariable Mendelian Randomization
Sun, K., Li, M., Wu, Y., Wu, Y., Zeng, Y., Zhou, S., Peng, L., & Shen, B. (2023) · Orthopaedic Surgery · doi:10.1111/os.13947 · Cited by 5
Causal relationship between lipid profile and muscle atrophy: A bi‐directional Mendelian randomization study
Chen, K., Gao, P., Fang, X., Tang, K., Ouyang, P., Li, Z., Li, L., & Deng, Z. (2023) · Animal Models and Experimental Medicine · doi:10.1002/ame2.12373 · Cited by 4
“27 In this study, the F sta - tistics of all IVs that were ultimately included were greater than 10.”
Targeting ERBB2 and PIK3R1 as a therapeutic strategy for dilated cardiomyopathy: A single-cell sequencing and mendelian randomization analysis
He, B., Quan, L.-P., Li, C., Yan, W., Zhang, Z., Zhou, L., Wei, Q., Li, Z., Mo, J., Zhang, Z., et al. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e25572 · Cited by 4
“The F-test statistic ], N: sample size; K: number of IVs) was used to assess whether these selected SNPs were affected by weak instrumental variables (F > 10) [32].”
Method
Genetic correlation between circulating metabolites and chalazion: a two-sample Mendelian randomization study
Zhang, X., Cai, Y., Jiang, Y., Du, W., An, W., Fu, Q.-Q., & Chen, Y. (2024) · Frontiers in Molecular Biosciences · doi:10.3389/fmolb.2024.1368669 · Cited by 4
The genetic relationship between systemic lupus erythematosus and risk of primary ovarian failure from a mendelian randomization study
Wang, X., Mao, R., Wang, M., Zhu, L., & Jin, L. (2024) · Scientific Reports · doi:10.1038/s41598-024-59726-9 · Cited by 5
“The following equation was used: by each IV; N is the number of samples in GWAS;and K represents the number of SNPs for analysis) 17 .”
Method
Fetal/Maternal-Determined Birth Weight and Adulthood Type 2 Diabetes and Its Subtypes: A Mendelian Randomization Study
Wang, W., Xiao, W., Song, Z., Zhuang, Z., Huang, N., Zhao, Y., & Huang, T. (2024) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgae455 · Cited by 4
Causal relationship between mitochondrial-associated proteins and cerebral aneurysms: a Mendelian randomization study
Wang, S., Wang, J., Niu, Z., Zhang, K., Yang, T., Hou, S., & Lin, N. (2024) · Frontiers in Neurology · doi:10.3389/fneur.2024.1405086 · Cited by 4
MR-PheWAS for the causal effects of serum magnesium on multiple disease outcomes in Caucasian descent
Li, L., Yang, W., Huang, L., Feng, X., Cheng, H., Ge, X., Zan, G., Tan, Y., Xiao, L., Liu, C., et al. (2021) · iScience · doi:10.1016/j.isci.2021.103191 · Cited by 4
Re: "Credible Mendelian Randomization Studies: Approaches For Evaluating The Instrumental Variable Assumptions"
Palmer, T., Ramsahai, R. R., Lawlor, D. A., Sheehan, N. A., & Didelez, V. (2012) · American Journal of Epidemiology · doi:10.1093/aje/kws250 · Cited by 4
Self-citation
Does Smoking Protect Against Developing Osteoarthritis? Evidence From a Genetically Informed PerspectivePreprint
Ni, J., Wang, P., Yin, K.-J., Huang, J.-X., Tian, T., Cen, H., Sui, C., Xu, Z., & Pan, H. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4045943 · Cited by 4
The relationship between BMI and COVID-19: exploring misclassification and selection bias in a two-sample Mendelian randomisation studyPreprint
Clayton, G., Soares, A. G., Goulding, N., Borges, M. C., Holmes, M. V., Smith, G. D., Tilling, K. M., Lawlor, D. A., & Carter, A. R. (2022) · medRxiv · doi:10.1101/2022.03.03.22271836 · Cited by 4
Neuroticism and posttraumatic stress disorder: A Mendelian randomization analysis
You, Z., Chen, S., & Tang, J. (2024) · Brain and Behavior · doi:10.1002/brb3.70041 · Cited by 4
“Subsequently, the F statistic was calculated to evaluate the strength of the instruments with F > 10 avoiding weak IV bias (Sanderson & Windmeijer, 2016), utilizing the formula ( F = beta 2 /se 2 ) for exposures (Palmer et al., 2012), of which beta is the effect size of single SNP.”
Method
The causal relationship between type 2 diabetes mellitus and isolated REM sleep behavior disorder: results from multivariable and network Mendelian randomization analysis
Zhang, R.-Y., Li, J.-Y., Liu, Y.-N., Zhang, Z.-X., Zhao, J., & Li, F.-J. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1408053 · Cited by 3
“The instrument strength was estimated using the F-statistic: F k , where N represents the sample size and k is the number of instrumental variables (37).”
Causal roles of dietary structure and types on prostate cancer risk: A mendelian randomization study
Li, C., Jing, Z., Guo, Q., Zheng, Z., Zhao, X., Yuan, W., Xi, Y., & Wang, J. (2024) · BMC Cancer · doi:10.1186/s12885-024-13252-z · Cited by 3
“In addition, the P of the SNP and the outcome cannot be less than 1 × 10–5 to ensure that the SNP is not directly related to the outcome [17].”
Gut-disc axis: A Mendelian randomization study on the relationship between gut microbiota and cervical spondylosis
Zhang, J., Wang, B., Du, P., Song, H., Yang, L., & Zhou, Y. J. (2025) · Medicine · doi:10.1097/md.0000000000041536 · Cited by 4
“F -value is calculated by the formula Here, R 2 is the proportion of variance explained by all SNPs, N is the total sample size, and k is the number of SNPs. [17]”
Proximity extension assay reveals serum inflammatory biomarkers in two amyotrophic lateral sclerosis cohorts
Chen, Y., Sun, S., Gao, N., Bai, Z., Yu, W., Zhao, B. Q., Yun, Y., Sun, X., Lin, P., Li, W., et al. (2025) · Neurobiology of Disease · doi:10.1016/j.nbd.2025.106933 · Cited by 3
“We selected genetic variants with a genome-wide significant p -value ( p 5 × 10 8 ) and F-statistic greater than 10 (Palmer et al., 2011), which satisfies the first assumption, whose violation might introduce so-called “ weak instrument bias ” (Burgess and Thompson, 2011).”
Circulating Cytokines Mediate the Protective Effect of Physical Activity on Cardiovascular Diseases: A Mendelian Randomization Mediation Analysis
Sun, Y., & Liu, Y. (2025) · International Journal of Molecular Sciences · doi:10.3390/ijms26104615 · Cited by 4
“This approach is based on three core assumptions: (i) the genetic instruments are strongly linked with the exposure, (ii) these instruments are free from confounding factors, and (iii) they affect CVD outcomes solely through physical activity, without involving other pathways [26–28].”
Identification of Potential Therapeutic Targets for Coronary Atherosclerosis from an Inflammatory Perspective Through Integrated Proteomics and Single-Cell Omics
Wang, H., Xie, F., Wang, M., Ji, J., Song, Y., Dai, Y., Wang, L., Zheng, K., & Cao, L. (2025) · International Journal of Molecular Sciences · doi:10.3390/ijms26136201 · Cited by 3
“…gene region to eliminate pleiotropy; (iii) linkage disequilibrium (LD) clumping (r 2 < 0.001) was used to ensure the independence of genetic associations and remove horizontal pleiotropy [49]; (iv) the instrument strength (F-statistic) must be greater than 10 to ensure strong correlation [57].”
Influential

Authors: Palmer, T. M., Lawlor, D. A., Harbord, R. M., Sheehan, N. A., Tobias, J. H., Timpson, N. J., Smith, G. D., & Sterne, J. A.
Affiliations: University of Bristol (GB)
University of Leicester (GB)
School of Clinical Sciences, University of Bristol, Bristol, UK
Corresponding author: Palmer, Tom M
ORCID: Palmer, Tom M
Lawlor, Debbie A
Harbord, Roger M
Sheehan, Nuala A
Timpson, Nicholas J
Smith, George Davey
Sterne, Jonathan AC
Venue: Statistical Methods in Medical Research
Publisher: SAGE Publications
Published: 2011-01-07
Volume: 21
Issue: 3
Pages: 223-242
ISSN: 0962-2802 (ISSN-L)
1477-0334
DOI: 10.1177/0962280210394459
PMC: PMC3917707
OpenAlex: W2151096860
Cited by: 1,289
References: 76
Citations by year: 2026: 92 · 2025: 240 · 2024: 394 · 2023: 164 · 2022: 83 · 2021: 67 · 2020: 44 · 2019: 33 · 2018: 22 · 2017: 20 · 2016: 27 · 2015: 44 · 2014: 20 · 2013: 19 · 2012: 14
FWCI: 11.61
Type: journal article
Language: en
Open access: green
www.ncbi.nlm.nih.gov
Licence: cc-by
journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations: Statistical Methods in Medical Research (publishedVersion)
Europe PMC (PubMed Central) (publishedVersion, cc-by)
PubMed Central (publishedVersion, cc-by)
PubMed (publishedVersion)
Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
Lancaster EPrints (Lancaster University) (submittedVersion)
Figshare (submittedVersion, cc-by)
Leicester Research Archive (University of Leicester) (submittedVersion, cc-by)
Bristol Research (University of Bristol) (submittedVersion, cc-by)
Funders: Wellcome Trust (G0600705, 092731)
University of Bristol (G0600705)
Medical Research Council (G0600705)
Economic and Social Research Council (ES/E00234X/1)
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 › Genetics and Physical Performance
Keywords: Mendelian randomization, modifiable risk factors, weak instruments, finite-sample bias, fat mass, bone mineral density, children, causal effect estimation, continuous outcomes
MeSH terms: Female, Genotype, Humans, Male, Risk Factors, Genetic Variation, Mendelian Randomization Analysis

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Using multiple genetic variants as instrumental variables for modifiable risk factors

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