The DOI matches its Crossref record; 75 of the 76 references it cites were found in a registry or an index.
Using multiple genetic variants as instrumental variables for modifiable risk factors
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
The cited source doesn’t support the claim as written.
In the citing paper
“All three of these SNPs have previously been shown to be strong instruments for MR analysis as measured by F-statistics > 10 [8,18]”
From Associations of genetically determined iron status across the phenome: A mendelian randomization study (2019) · cites this paper as [18]
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredIn the citing paper
“Interpretation of results from MR studies relies on four conditions.12,24”
From Mendelian randomization (2022) · cites this paper as [24]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
(2001) · RePEc: Research Papers in Economics · Cited by 27,577
Specification Tests in Econometrics
Hausman, J. A. (1978) · Econometrica · doi:10.2307/1913827 · Cited by 18,820
Statistical Analysis With Missing Data
Lahiff, M., Little, R. J. A., & Rubin, D. B. (1989) · Journal of the American Statistical Association · doi:10.2307/2289883 · Cited by 17,385
Large Sample Properties of Generalized Method of Moments Estimators
Hansen, L. P. (1982) · Econometrica · doi:10.2307/1912775 · Cited by 13,467
Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls
The Wellcome Trust Case Control Consortium, Management Committee, Burton, P. R., Clayton, D. G., Cardon, L. R., Craddock, N., Deloukas, P., Duncanson, A., Kwiatkowski, D. P., McCarthy, M. I., et al. (2007) · Nature · doi:10.1038/nature05911 · Cited by 9,442
Self-citationStatistical Analysis with Missing Data
Little, R. J. A., & Rubin, D. B. (2002) · Wiley Series in Probability and Statistics · doi:10.1002/9781119013563 · Cited by 8,473
Genetics of Food Intake Self-Regulation in Childhood: Literature Review and Research Opportunities
Faith, M. S., Carnell, S., & Kral, T. V. E. (2013) · Human Heredity · doi:10.1159/000353879 · Cited by 7,633
Instrumental Variables Regression with Weak Instruments
Staiger, D., & Stock, J. H. (1997) · Econometrica · doi:10.2307/2171753 · Cited by 7,081
Lippa, N. C., & Sanderson, S. C. (2013) · Human Heredity · doi:10.1159/000353712 · Cited by 6,095
Davey Smith, G., & Ebrahim, S. (2003) · International Journal of Epidemiology · doi:10.1093/ije/dyg070 · Cited by 5,882
Flagged first, then by citations
1 of the 76 references couldn’t be matched to a known paper.
Research works printed but not linked: 3
- Youngman LD, 2000, Circulation, 102, 31
- Pierce BL, 2010, Int J Epidemiol
- Davey Smith G, 2010, Genes Nutr
Cited by
Sorted by citations
Items 201–300 of 1,000
Xu, L., Lin, S. L., & Schooling, C. M. (2017) · Scientific Reports · doi:10.1038/srep42691 · Cited by 33
Gao, X., Jia, Z.-M., Zhao, F., An, D., Wang, B., Cheng, E., Chen, Y., Gong, J., Liu, D., Huang, Y., et al. (2020) · Aging · doi:10.18632/aging.102725 · Cited by 34
“com 4083 AGING observational studies [25].”
Mazidi, M., Shekoohi, N., Covic, A. C., Mikhailidis, D. P., & Banach, M. (2020) · Nutrients · doi:10.3390/nu12082216 · Cited by 33
“Instruments have F statistics higher than threshold, so that significant bias due to the use of weak instruments is unlikely [42].”
BackgroundRetinol and Retinol Binding Protein 4 Levels and Cardiometabolic Disease Risk
Schiborn, C., Weber, D., Grune, T., Biemann, R., Jäger, S., Neu, N., von Blumencron, M. M., Fritsche, A., Weikert, C., Schulze, M. B., et al. (2022) · Circulation Research · doi:10.1161/circresaha.122.321295 · Cited by 34
Bonilla, C., Lewis, S. J., Rowlands, M., Gaunt, T. R., Smith, G. D., Gunnell, D., Palmer, T., Donovan, J., Hamdy, F. C., Neal, D. E., et al. (2016) · International Journal of Cancer · doi:10.1002/ijc.30206 · Cited by 31
Self-citationViinikainen, J., Bryson, A., Böckerman, P., Elovainio, M. J., Pitkänen, N., Pulkki-Råbäck, L., Lehtimäki, T. J., Raitakari, O. T., & Pehkonen, J. (2018) · Preventive Medicine · doi:10.1016/j.ypmed.2018.08.026 · Cited by 34
“Second, the GRS reduces the risk that any individual SNP would bias the IV estimates via an alternative biological pathway (pleiotropy) (Palmer et al., 2012).”
BackgroundLi, H., Zhang, Q., Shen, W., Li, B., Lv, W., Xiao, H., & Deng, H. (2020) · Aging · doi:10.18632/aging.102815 · Cited by 34
Ni, J., Wang, P., Yin, K.-J., Huang, J.-X., Tian, T., Cen, H., Sui, C., Xu, Z., & Pan, H. (2022) · Seminars in Arthritis and Rheumatism · doi:10.1016/j.semarthrit.2022.152013 · Cited by 34
Zhao, L., Zhao, W., Anttila, V., Artto, V., Belin, A. C., Bjornsdottir, A., Björnsdóttir, G., Boomsma, D. I., Børte, S., Chalmer, M. A., et al. (2023) · The Journal of Headache and Pain · doi:10.1186/s10194-023-01550-z · Cited by 31
“In addition, fewer significant SNP IVs in the forward MR analysis may be accompanied by low power due to a limited explained proportion for total variation.”
BackgroundInfluentialAge at menopause and lung function: a Mendelian randomisation study
van der Plaat, D. A., Pereira, M., Pesce, G., Potts, J. F., Amaral, A. F. S., Dharmage, S. C., García‐Aymerich, J., Thompson, J. R., Real, F. G., Jarvis, D., et al. (2019) · European Respiratory Journal · doi:10.1183/13993003.02421-2018 · Cited by 29
Ye, C., Kong, L., Zhao, Z., Li, M., Wang, S., Lin, H., Xu, Y., Lu, J., Chen, Y., Xu, Y., et al. (2021) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgab633 · Cited by 34
Blood copper and risk of cardiometabolic diseases: a Mendelian randomization study
Jäger, S., Cabral, M., Kopp, J. F., Hoffmann, P., Ng, E., Whitfield, J. B., Morris, A. P., Lind, L., Schwerdtle, T., & Schulze, M. B. (2021) · Human Molecular Genetics · doi:10.1093/hmg/ddab275 · Cited by 32
“We obtained the F-statistic as indicator of instrument strength (58).”
MethodXiong, A., Yao, Q. Z., He, J., Fu, W., Yu, J., & Zhang, Z. (2015) · Osteoporosis International · doi:10.1007/s00198-015-3341-5 · Cited by 31
“Mendelian randomization analyses use genetic variants as instrumental variables for causal inferences about the effect of modifiable exposures on health- and disease-related outcomes in the presence of unobserved confounding variables in the relationship of interest [15].”
BackgroundFeng, Y., Liu, X., & Tan, H. (2023) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2022.1042938 · Cited by 32
“Instrument strength was then assessed by the F-statistic which reflects the exposure variance explained by the instrument variables (23).”
MethodIL6 genetic perturbation mimicking IL-6 inhibition is associated with lower cardiometabolic risk
Zhang, L., Omarov, M., Xu, L., deGoma, E. M., Natarajan, P., & Georgakis, M. K. (2025) · Nature Cardiovascular Research · doi:10.1038/s44161-025-00700-7 · Cited by 32
“We calculated the F statistic as a proxy of instrument strength and the variance in CRP levels explained for each selected variant ( R 2 ) using formulas applied on summary statistics 79,80 .”
Iron and hepcidin as risk factors in atherosclerosis: what do the genes say?
Galesloot, T. E., Janss, L., Burgess, S., Kiemeney, L. A. L. M., den Heijer, M., Graaf, J. D., Holewijn, S., Benyamin, B., Whitfield, J. B., Swinkels, D. W., et al. (2015) · BMC Genetics · doi:10.1186/s12863-015-0246-4 · Cited by 30
“One would expect similar results for these two SNPs [43], thus the MR approach provides contradicting evidence for a causal role of ferritin in atherosclerosis.”
D’Urso, S., Wang, G., Hwang, L., Moen, G.-H., Warrington, N. M., & Evans, D. M. (2020) · Journal of Developmental Origins of Health and Disease · doi:10.1017/s2040174420001105 · Cited by 31
Morris, D., Jones, G. T., Holmes, M. V., Bown, M. J., Bulbulia, R. A., Singh, T. P., & Golledge, J. (2021) · European Journal of Vascular and Endovascular Surgery · doi:10.1016/j.ejvs.2021.10.038 · Cited by 33
Ren, Q., Luo, F., Ge, S., & Chen, P. (2022) · Cancer Medicine · doi:10.1002/cam4.5043 · Cited by 29
Thyroid Function and Metabolic Syndrome: A Two-Sample Bidirectional Mendelian Randomization Study
Pleić, N., Gunjača, I., Leko, M. B., & Zemunik, T. (2023) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgad371 · Cited by 31
Mendelian randomisation, lipids, and cardiovascular disease
Harrison, S. C., Holmes, M. V., & Humphries, S. E. (2012) · The Lancet · doi:10.1016/s0140-6736(12)60481-4 · Cited by 31
Age at Menarche and Time Spent in Education: A Mendelian Randomization Study
Gill, D., Fabiola Del Greco, M., Rawson, T. M., Sivakumaran, P., Brown, A., Sheehan, N. A., & Minelli, C. (2017) · Behavior Genetics · doi:10.1007/s10519-017-9862-2 · Cited by 32
“We measure the strength of the instruments using the F statistic, which is a function of the magnitude and precision of their genetic effects (Li and Martin 2002; Palmer et al. 2012).”
MethodLipids and amyotrophic lateral sclerosis: A two‐sample Mendelian randomization study
Xia, K., Klose, V., Högel, J., Huang, T., Zhang, L., Dorst, J., Fan, D., & Ludolph, A. C. (2023) · European Journal of Neurology · doi:10.1111/ene.15810 · Cited by 27
“The phenotypic variance explanation (R2, R2 = 2 × beta2 × [1− EAF] × EAF/SD2, EAF = effect allele frequency, beta = effect of each SNP on exposures) [33] and F- statistics (F = R2 × [N−2]/[1−R2]) [34] of each IV were calculated to assess their strength.”
MethodCausal associations between human gut microbiota and cholelithiasis: a mendelian randomization study
Li, W., Ren, A., Qin, Q., Zhao, L., Peng, Q., Ma, R., & Luo, S. (2023) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2023.1169119 · Cited by 30
“Using the following formula, we calculated the F and R(2) values of each SNP to analyze its impact on gut microbiota: F = [R(2) × (N-2)]/(1-R(2)), R(2) =[2 × b(2) × EAF × (1-EAF)]/[2 × b(2) × EAF × (1-EAF) + 2 × SE(2) × N × EAF × (1-EAF)] (Burgess and Thompson, 2011; Palmer et al., 2012; Levin et al., 2020).”
BackgroundMethodLi, J., Wang, W., Yang, Z., Qiu, L., Ren, Y., Wang, D., Li, M., Li, W., Gao, F., & Zhang, J. (2024) · Lipids in Health and Disease · doi:10.1186/s12944-024-02042-y · Cited by 34
“The formula is as follows [42]: where MAF = minor allele frequency; β = effect size; SE = standard error; n = sample size; and k = number of instrumental variables.”
BackgroundRukh, G., Dang, J., Olivo, G., Ciuculete, D. M., Rask‐Andersen, M., & Schiöth, H. B. (2020) · Translational Psychiatry · doi:10.1038/s41398-020-0691-3 · Cited by 32
Fang, X., Wang, X., Song, Z., Han, D., Yin, X., Liu, B., Chen, L., Zhang, R., Lian, F., & Sui, X. (2021) · International Journal of Cancer · doi:10.1002/ijc.33691 · Cited by 29
“The following equation was used: F = (R(2)/k)/([1 R(2)]/ [n k 1]), where R(2) is the proportion of the variability accounted for by the SNP, k is the number of instruments used in the model and n is the sample size.(12) To minimize weak instrument bias, only SNPs with an F statistic >10 were included in subsequent ana…”
MethodXia, K., Wang, Y., Zhang, L., Tang, L., Zhang, G., Huang, T., Huang, N., & Fan, D. (2022) · Nutrients · doi:10.3390/nu14050920 · Cited by 30
“We similarly calculated F statistics for individual SNPs to indicate the strength of IVs (F = R2 × (N − 2)/((1 − R2))) [44].”
Xu, M., Bi, Y., Huang, Y. F., Xie, L., Hao, M., Zhao, Z., Xu, Y., Lu, J., Chen, Y., Sun, Y., et al. (2016) · EBioMedicine · doi:10.1016/j.ebiom.2016.02.032 · Cited by 29
“…reduce the statistical errors with multi-testing, we created a T2D genetic risk score (GRS) by using 34 T2D associated common variants that were identified in East Asians and represented the comprehensive genetic susceptibility of T2D, to be used as the IV (Palmer et al., 2012; Liu and Song, 2010).”
MethodMendelian randomization provides support for obesity as a risk factor for meningioma
Takahashi, H., Cornish, A. J., Sud, A., Law, P., Disney–Hogg, L., Calvocoressi, L., Lu, L., Hansen, H. M., Smirnov, I. V., Walsh, K. M., et al. (2019) · Scientific Reports · doi:10.1038/s41598-018-36186-6 · Cited by 28
Causal Associations between Serum Urea and Cancer: A Mendelian Randomization Study
Sun, Y., Li, J., Qu, Z., Yang, Z. R., Jia, X., Lin, Y., He, Q., Zhang, L., & Luo, Y. (2021) · Genes · doi:10.3390/genes12040498 · Cited by 28
“More importantly, MR analyses take advantage of the single nucleotide polymorphism (SNP), which in conjunction with external elements can avoid confounding factors and other potential complications [24,25].”
BackgroundCoagulation Factors and the Risk of Ischemic Heart Disease
Zhao, J. V., & Schooling, C. M. (2018) · Circulation Genomic and Precision Medicine · doi:10.1161/circgen.117.001956 · Cited by 27
Lee, S., & Lee, W. (2025) · Journal of Obesity & Metabolic Syndrome · doi:10.7570/jomes24031 · Cited by 28
Husemoen, L. L. N., Skaaby, T., Martinussen, T., Jørgensen, T., Thuesen, B. H., Kistorp, C., Jeppesen, J., Thyssen, J. P., Meldgaard, M., Szecsi, P. B., et al. (2013) · European Journal of Clinical Nutrition · doi:10.1038/ejcn.2013.233 · Cited by 27
Bucur, I. G., Claassen, T., & Heskes, T. (2019) · Statistical Methods in Medical Research · doi:10.1177/0962280219851817 · Cited by 30
“What’s more, the use of multiple genetic instruments provides opportunities to test for violations of the IV assumptions.(20) Genetic variants are typically selected based on the size of the genetic effect on the exposure of interest and the specificity of the association.”
BackgroundMiao, L., Yan, M., Qi, B., Zhu, C.-M., Chen, J.-H., Deng, G., Wang, Y., Li, J., & Li, R. (2021) · BMC Nephrology · doi:10.1186/s12882-020-02228-3 · Cited by 27
Huang, S.-J., Li, R., Xu, S., Liu, Y., Li, S., & Duan, S. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2023.1124638 · Cited by 28
“Fourth, the F-statistic = R(2) × (N-2)/(1-R(2)) was calculated for each IV used for cytokines as a measure of instrumental strength, where R(2) is the phenotypic variation explained by each genetic variant in the exposure and N is the sample size (Palmer et al., 2012).”
MethodQin, J., Zhang, L., Ke, B., Liu, T., Kong, C., & Jin, C. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1248325 · Cited by 28
A Decade of Genetic and Metabolomic Contributions to Type 2 Diabetes Risk Prediction
Merino, J., Udler, M. S., Leong, A., & Meigs, J. B. (2017) · Current Diabetes Reports · doi:10.1007/s11892-017-0958-0 · Cited by 28
Shi, X., Yuan, W., Cao, Q., & Cui, W. (2022) · Addiction · doi:10.1111/add.16019 · Cited by 27
Association of modifiable risk factors with obstructive sleep apnea: a Mendelian randomization study
Li, Y., Miao, Y., Tan, J., & Zhang, Q. (2023) · Aging · doi:10.18632/aging.205288 · Cited by 27
Genetically Predicted Blood Pressure and Risk of Atrial Fibrillation
Hyman, M. C., Levin, M. G., Gill, D., Walker, V. M., Georgakis, M. K., Davies, N. M., Marchlinski, F. E., & Damrauer, S. M. (2021) · Hypertension · doi:10.1161/hypertensionaha.120.16191 · Cited by 27
Tuberculosis Exposure With Risk of Behçet Disease Among Patients With Uveitis
Zhong, Z., Su, G., Zhou, Q., Meguro, A., Takeuchi, M., Mizuki, N., Ohno, S., Liao, W., Feng, X., Ding, J., et al. (2021) · JAMA Ophthalmology · doi:10.1001/jamaophthalmol.2020.6985 · Cited by 26
Mazidi, M., Shekoohi, N., Katsiki, N., & Banach, M. (2021) · Archives of Medical Science · doi:10.5114/aoms/136070 · Cited by 30
“Arch Med Sci 2, 1st March / 2022 473 have F-statistics ranging from 263 to 324, making significant bias from use of weak instruments unlikely [42].”
BackgroundCampos‐Obando, N., Bosman, A., Kavousi, M., Medina‐Gómez, C., van der Eerden, B. C. J., Bos, D., Franco, O. H., Uitterlinden, A. G., & Zillikens, M. C. (2022) · Journal of the American Heart Association · doi:10.1161/jaha.121.023024 · Cited by 26
Xiao, Z., Wang, Z., Zhang, T., Liu, Y., & Si, M. (2023) · Journal of Translational Medicine · doi:10.1186/s12967-023-04612-7 · Cited by 26
“The strength of the association between SNP and the exposures are evaluated using the F statistic [29].”
MethodPlasma fetuin-A concentration, genetic variation in the AHSG gene and risk of colorectal cancer
Nimptsch, K., Aleksandrova, K., Boeing, H., Janke, J., Lee, Y., Jenab, M., Kong, S. Y., Tsilidis, K. K., Weiderpass, E., Bueno-de-Mesquita, H. B., et al. (2015) · International Journal of Cancer · doi:10.1002/ijc.29448 · Cited by 26
“Instrumental variable estimates can be biased when both the variance explained by the instruments and the sample size are small.(29) However, the selected polymorphisms in the AHSG gene were strong predictors of fetuin-A concentrations, explaining a good proportion of interindividual variation.”
BackgroundGMM with Multiple Missing Variables
Chaudhuri, S., & Guilkey, D. K. (2015) · Journal of Applied Econometrics · doi:10.1002/jae.2444 · Cited by 26
“…genetic markers as IVs (see, for example, Lawlor et al. (2008), Ding et al. (2009), Scholder et al. (2010), Scholder et al. (2011), Burgess et al. (2011), Palmer et al. (2012), Berry et al. (2012), etc. and the references therein), missing IVs is likely to become more common in empirical work.”
BackgroundMethodClarke, P. S., Palmer, T., & Windmeijer, F. A. G. (2015) · Statistical Science · doi:10.1214/14-sts503 · Cited by 27
“Both the 2SGMM and joint-GMM estimators use saturated logistic models for β as in (20) All of the estimators are virtually unbiased and the means of the estimated standard errors are close to Monte Carlo standard errors.”
Self-citationWang, J., Li, A. M., Lam, H. S., Leung, G. M., & Schooling, C. M. (2019) · Obesity · doi:10.1002/oby.22469 · Cited by 26
“The F statistic reflects the magnitude and precision of the genetic effect and indicates the strength of the instrument (35,36).”
BackgroundAge of puberty and Sleep duration: Observational and Mendelian randomization study
Wang, J., Kwok, M. K., Yeung, S. L. A., Zhao, J. V., Li, A. M., Lam, H. S., Leung, G. M., & Schooling, C. M. (2020) · Scientific Reports · doi:10.1038/s41598-020-59811-9 · Cited by 26
Howell, A., Robinson, J. W., Wootton, R. E., McAleenan, A., Tsavachidis, S., Ostrom, Q. T., Bondy, M. L., Armstrong, G., Relton, C. L., Haycock, P., et al. (2020) · BMC Cancer · doi:10.1186/s12885-020-06967-2 · Cited by 24
“Polygenic risk scores (PRS) can be used to assess putative causal associations [28, 62] (see Additional file Figure 3).”
BackgroundHigh Level of Uromodulin Increases the Risk of Hypertension: A Mendelian Randomization Study
You, R., Chen, L., Xu, L., Zhang, D., Li, H., Shi, X., Zheng, Y.-L., & Chen, L. (2021) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2021.736001 · Cited by 25
“When R2 is not available, we use the formula R2 = 2×MAF× (1–MAF)× beta2 (where beta represents the effect value of the genetic variant in the exposure andMAF represents the effect allele frequency) (28).”
MethodWang, Y., Yan, S., Li, X., Huang, Q. Y., Luo, L.-S., Wang, Y., Huang, J., Jin, Y., & Zeng, X. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2021.792396 · Cited by 26
“We used an F-statistic to estimate the strength of each chosen SNP (Palmer et al., 2012) and calculate the variance explained by each IV in the exposure.”
MethodLin, Y., Wang, G., Li, Y., Yang, H., Zhao, Y., Liu, J., & Mu, L. (2023) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgad376 · Cited by 26
Hatcher, C., Richenberg, G., Waterson, S., Nguyen, L. H., Joshi, A. D., Carreras‐Torres, R., Moreno, V. R., Chan, A. T., Gunter, M. J., Lin, Y., et al. (2023) · Scientific Reports · doi:10.1038/s41598-023-31840-0 · Cited by 26
Lewis, S. J., Relton, C. L., Zammit, S., & Smith, G. D. (2013) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.12127 · Cited by 26
Causal Inference Methods to Integrate Omics and Complex TraitsPreprint
Porcu, E., Sjaarda, J., Lepik, K., Carmeli, C., Darrous, L., Sulc, J., Mounier, N., & Kutalik, Z. (2020) · Cold Spring Harbor Perspectives in Medicine · doi:10.1101/cshperspect.a040493 · Cited by 23
“…factors that are not directly linked to the DNA sequence (e.g., not related to chromatin properties, gene expression, protein, or methylation levels), multiple genetic variants across the genome can be used as instruments to look for a homogenous effect across all instruments (Palmer et al. 2012).”
BackgroundConstrained instruments and their application to Mendelian randomization with pleiotropy
Jiang, L., Oualkacha, K., Didelez, V., Ciampi, A., Rosa‐Neto, P., Benedet, A. L., Mathotaarachchi, S., Richards, J. B., Greenwood, C. M. T., & Initiative, A. F. T. A. D. N. (2019) · Genetic Epidemiology · doi:10.1002/gepi.22184 · Cited by 23
“However, weighted scores usually also reduce the power (sensitivity) of MR studies (Pierce et al., 2010; Palmer et al., 2012) and require all instruments to be valid.”
C‐Reactive Protein Level as a Novel Serum Biomarker in Sarcopenia
Lin, S., Chen, X., Cheng, Y., Huang, H., Yang, F., Bao, Z., & Fan, Y. (2024) · Mediators of Inflammation · doi:10.1155/2024/3362336 · Cited by 24
“The formula for calculating the F-statistic can be expressed as follows: where the sample size of the CRP level GWAS study is denoted by n, the number of IVs is represented by k, and R 2 indicates the extent to which the selected IVs account for the variation in exposure [15].”
MethodQing, J., Li, Y., Soliman, K., & Cheungpasitporn, W. (2025) · Renal Failure · doi:10.1080/0886022x.2024.2445763 · Cited by 23
“IVs, typically single nucleotide polymorphisms (SNPs), must meet three fundamental criteria to be considered robust: they must be strongly associated with the exposure of interest, must not be associated with confounding factors, and must influence the outcome solely through the exposure [44].”
Mazidi, M., Katsiki, N., Shekoohi, N., & Banach, M. (2020) · Frontiers in Nutrition · doi:10.3389/fnut.2020.00123 · Cited by 23
“The instruments have F-statistics higher than threshold, making significant bias from the use of weak instruments unlikely (29).”
BackgroundChiu, P.-C., Chattopadhyay, A. S., Wu, M.-C., Hsiao, T., Lin, C., & Lu, T. (2021) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2021.743075 · Cited by 24
“Fstatistics were evaluated by a Gaussian regression model of the genetic components and the exposure trait after adjusting for all confounders (30).”
MethodGhanbari, F., Yazdanpanah, N., Yazdanpanah, M., Richards, J. B., & Manousaki, D. (2022) · Diabetes · doi:10.2337/db21-1046 · Cited by 23
(GICC), T. G. I. C.-C. S., Zhang, C., Ostrom, Q. T., Semmes, E. C., Ramaswamy, V., Hansen, H. M., Morimoto, L. M., de Smith, A. J., Pekmezci, M., Vaksman, Z., et al. (2020) · Acta Neuropathologica Communications · doi:10.1186/s40478-020-01038-w · Cited by 23
“Polygenic score analyses test genetic propensity for a phenotype, rather than a single variant, and have improved power over both single-SNP analyses and MR approaches [42, 43, 45].”
BackgroundNonparametric Bounds for the Causal Effect in a Binary Instrumental-Variable Model
Palmer, T., Ramsahai, R. R., Didelez, V., & Sheehan, N. A. (2011) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1101100302 · Cited by 23
Self-citationZou, M., Zhang, W., Shen, L., Xu, Y., & Zhu, Y. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1203707 · Cited by 21
“Given the low significance threshold, we calculated the F statistics to assess the bias of the weak instrumental variables (22).”
MethodA General Approach to Sensitivity Analysis for Mendelian Randomization
Zhang, W., & Ghosh, D. (2020) · Statistics in Biosciences · doi:10.1007/s12561-020-09280-5 · Cited by 22
Fruit Intake, Genetic Risk and Type 2 Diabetes: A Population Based Gene-Diet Interaction Analysis
Xu, J. Y., Zhu, W., Deng, C., Wang, T., Hou, Y., Xuan, L., Dai, H., Li, M., Zhao, Z., Lu, J., et al. (2019) · European Journal of Nutrition · doi:10.1007/s00394-020-02449-0 · Cited by 22
Chu, S., Wu, Z., Wu, Z., Wu, J. H., & Qian, Y. (2021) · Pharmacogenomics and Personalized Medicine · doi:10.2147/pgpm.s305780 · Cited by 22
“Mendelian randomization (MR), which utilizes genetic variants associated with exposure variables as genetic instruments to infer the causality, can be a useful tool for assessing the role of insomnia in migraine occurrence.(11) The MR design is rarely affected by confounding bias and reverse causation due to the rando…”
BackgroundMendelian randomization of circulating proteome identifies actionable targets in heart failure
Moncla, L.-H. M., Mathieu, S., Sylla, M. S., Bossé, Y., Thériault, S., Arsenault, B. J., & Mathieu, P. (2022) · BMC Genomics · doi:10.1186/s12864-022-08811-2 · Cited by 22
Hsu, L., Teng, M., Wu, S., Chou, H., & Ko, Y. (2022) · International Journal of Molecular Sciences · doi:10.3390/ijms231810418 · Cited by 21
“An F statistic of >10 indicates a relatively low risk of weak instrumental bias in MR analyses [52].”
BackgroundMethodTrajectories and Transitions in Childhood and Adolescent Obesity
Howe, L. D., Firestone, R., Tilling, K. M., & Lawlor, D. A. (2015) · Life course research and social policies · doi:10.1007/978-3-319-20484-0_2 · Cited by 22
“2012), as is utilising innovative methodological tools such as Mendelian Randomization (Davey Smith et al. 2009; Lawlor et al. 2008; Palmer et al. 2012), cross-cohort comparisons (Brion et al.”
MethodBeyond 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
Stature and long-term labor market outcomes: Evidence using Mendelian randomization
Böckerman, P., Viinikainen, J., Vainiomäki, J., Hintsanen, M., Pitkänen, N., Lehtimäki, T. J., Pehkonen, J., Rovio, S., & Raitakari, O. T. (2016) · Economics & Human Biology · doi:10.1016/j.ehb.2016.10.009 · Cited by 23
“Second, non-cognitive skills, such as social skills, may play a role in the height premium (Persico et al., 2004).”
BackgroundKar, S., Andrulis, I. L., Brenner, H., Burgess, S., Chang-Claude, J. C., Considine, D., Dörk, T., Evans, D. G., Gago-Domínguez, M., Giles, G. G., et al. (2019) · European Journal of Epidemiology · doi:10.1007/s10654-019-00485-7 · Cited by 21
“The strength of the 41-SNP and 59-SNP IVs was also evaluated using the F-statistic [48], with F < 10 considered as an indicator of a ‘weak’ instrument [49].”
MethodAlcohol consumption and risk of breast and ovarian cancer: A Mendelian randomization study
Zhu, J., Jiang, X., & Niu, Z. (2020) · Cancer Genetics · doi:10.1016/j.cancergen.2020.06.001 · Cited by 22
Mendelian randomisation approaches to the study of prenatal exposures: A systematic review
Diemer, E. W., Labrecque, J. A., Neumann, A., Tiemeier, H., & Swanson, S. A. (2021) · Paediatric and Perinatal Epidemiology · doi:10.1111/ppe.12691 · Cited by 21
Li, L., Zhang, Y., Liu, H., Wang, T., Li, J., & Wang, X. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1288517 · Cited by 23
Ren, Y., Zhang, Y., Cheng, Y., Qin, H., & Zhao, H. (2024) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2024.1348685 · Cited by 21
Thanassoulis, G. (2012) · Canadian Journal of Cardiology · doi:10.1016/j.cjca.2012.09.014 · Cited by 21
Xiao, J., Lv, J., Wang, S., Zhou, Y., Chen, L., Lu, J., Zhang, X., Wang, X., Gu, Y., & Lu, Q. (2021) · BMC Geriatrics · doi:10.1186/s12877-021-02307-6 · Cited by 20
“Although MR is a potentially powerful technique for strengthening causal inference, several issues could disturb instrumental variable assumptions; these include developmental changes compensating for genetic variation; linkage disequilibrium between genotype and other causal variables; pleiotropy, which refers to a s…”
Mendelian Randomization Focused Analysis of Vitamin D on the Secondary Prevention of Ischemic Stroke
Chan, Y.-H., Schooling, C. M., Zhao, J. V., Yeung, S. L. A., Hai, J. J., Thomas, G. N., Cheng, K.-K., Jiang, C.-Q., Wong, Y., Au, K.-W., et al. (2021) · Stroke · doi:10.1161/strokeaha.120.032634 · Cited by 21
Gao, Y., Mi, J., Liu, Z., & Song, Q. (2021) · Frontiers in Genetics · doi:10.3389/fgene.2021.763626 · Cited by 22
“The risk of weak instrument bias is relatively low with an F-statistic over 10 (Palmer et al., 2012).”
BackgroundZhou, H., Luo, Y., Zhang, W., Xie, F., Deng, C., Zheng, W., Zhu, S., & Wang, Q. (2023) · European Journal of Neurology · doi:10.1111/ene.15702 · Cited by 22
“For each SNP, the F statistic was calculated using the formula [ 41 ] where R 2 represents the proportion of variance in phenotypes which can be explained by SNPs and N is the sample size.”
Luo, F., Zhou, P., Xiong, R., Gu, M., & Zhou, S. (2023) · Scientific Reports · doi:10.1038/s41598-023-45545-x · Cited by 22
“To further evaluate the efficacy of the IVs, the F-statistic was calculated for each SNP using the following formula: where in R 2 is the amount of exposure variation that can be explained by each genetic variant and N is the number of people in each sample 19 .”
Fang, J., Luo, C., Zhang, D., He, Q., & Liu, L. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1265711 · Cited by 23
Qin, S., Wang, J., Yuan, H., He, J., Luan, S., & Deng, Y. (2024) · Frontiers in Genetics · doi:10.3389/fgene.2023.1260352 · Cited by 24
Qiu, Y., Wei, X., Tao, Y., Song, B., Wang, M., Yin, Z., Xie, M., Duan, A., Chen, Z., & Wang, Z. (2024) · Frontiers in Public Health · doi:10.3389/fpubh.2024.1284594 · Cited by 22
M endelian R andomization — the K ey to U nderstanding A spects of P arkinson's D isease C ausation?
Noyce, A. J., & Nalls, M. A. (2015) · Movement Disorders · doi:10.1002/mds.26492 · Cited by 21
“Previously, use of multiple gene variants known to operate via the same intermediate phenotype (such as the example above from Pichler and colleagues(23)) and finding similar effect size estimates and absence of heterogeneity offered some evidence against pleiotropy.(25) Post-GWAS, increasingly, MR studies use multipl…”
BackgroundFang, M., Liu, W., Wang, Z., Li, J., Hu, S., Li, Z., Chen, W., & Zhang, N. (2024) · European Spine Journal · doi:10.1007/s00586-024-08131-x · Cited by 20
“The F statistic of each gut microbiota was calculated [27] ) to prevent weak IVs ( F 10) from violating the association assumption and reducing the power of the test.”
Instrumental Variables in Causal Inference and Machine Learning: A Survey
Wu, A., Kuang, K., Xiong, R., & Wu, F. Q. (2025) · ACM Computing Surveys · doi:10.1145/3735969 · Cited by 28
Kong, L., Ye, C., Wang, Y., Zheng, J., Zhao, Z., Li, M., Xu, Y., Lu, J., Chen, Y., Xu, M., et al. (2023) · Liver International · doi:10.1111/liv.15532 · Cited by 22
Yang, H., Song, J., Li, A., Lv, L., Sun, X., Mao, Y., & Ye, D. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1139799 · Cited by 20
“86 (Supplementary Table S3), satisfying the assumption of F >10 for MR analyses (17).”
BackgroundChen, C., Zhang, H., Lan, Y., Yan, W., Liu, S., Chen, Y., Xie, T., Ning, J., Yan, X., Shang, L., et al. (2024) · Journal of Translational Medicine · doi:10.1186/s12967-024-05097-8 · Cited by 20
“The R 2 (an indicator explaining the degree of exposure) [31] and F-sta-tistic were calculated to measure the strength of the IVs (the calculation method is described in the Additional file 1).”
MethodObstructive sleep apnea and mental disorders: a bidirectional mendelian randomization study
Liu, H., Wang, X., Hu, F., Zhou, S., Pan, J., Ouyang, C., & Hu, X. (2024) · BMC Psychiatry · doi:10.1186/s12888-024-05754-8 · Cited by 21
“The F-statistic of each IV we selected for OSA was greater than 10, indicating a low probability of weak instrument bias [39].”
BackgroundXu, W., Mesa‐Eguiagaray, I., Morris, D. M., Wang, C., Gray, C. D., Sjöström, S., Papanastasiou, G., Badr, S., Paccou, J., Wang, L., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-63395-1 · Cited by 22
Cao, Y., Rajan, S. S., & Wei, P. (2016) · Genetic Epidemiology · doi:10.1002/gepi.22013 · Cited by 20
“The GRS is widely accepted in current MR studies to increase IV strength by combining the effect of multiple SNPs (Holmes et al., 2014b; Palmer et al., 2012; Proitsi et al., 2014; Voight et al., 2012), where the weights used to construct the GRS are effect estimates from previous large-scale…”
MethodLiu, D., Dong, J., Zhang, J., Xu, X., Tian, Q., Meng, X., Wu, L., Zheng, D., Chu, X., Wang, W., et al. (2022) · The Journal of Immunology · doi:10.4049/jimmunol.2100080 · Cited by 19
He, Q., Bennett, A. N., Fan, B., Han, X., Liu, J., Wu, K. C. H., Huang, R., Chan, J. C. N., & Chan, K. H. K. (2022) · Genes · doi:10.3390/genes13060962 · Cited by 21
“An F value higher than 10 means a possible low risk of weak instrumental bias in MR analyses [34] which is important to prevent violation of the ‘NO Measurement Error’ assumption.”
BackgroundMethod
Metadata
- 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
- 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
- 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
- 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
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
