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 401–500 of 1,000
Metabolome-wide Mendelian randomization for age at menarche and age at natural menopause
Yazdanpanah, M., Yazdanpanah, N., Gamache, I., Ong, K. K., Perry, J. R. B., & Manousaki, D. (2024) · Genome Medicine · doi:10.1186/s13073-024-01322-7 · Cited by 13
“…R 2 , where n is the size of the cohort, k is the number of SNP-IVs, and R 2 is the proportion of the variance of each exposure explained by the SNP-IVs [18] (according to the formula R 2 ≈ 2 β 2 f × 1 − f where β and f denote the effect estimate and the effect allele frequency of the allele [19]).”
BackgroundKang, J., Wu, X., Li, Y., Zhao, S., Wang, S., & Yu, D. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1425610 · Cited by 14
“…the following: (1) relevance: showing a robust association with the risk factor under study; (2) independence: showing no correlation with known or unknown confounders; and (3) exclusion restriction: in fl uencing the outcome solely through the risk factor, with no other direct causal pathways (30).”
Chen, G., Jin, Y., Chu, C., Zheng, Y., Chen, Y., & Zhu, X. (2024) · Frontiers in Microbiology · doi:10.3389/fmicb.2024.1414977 · Cited by 12
Fan, J., Lü, Y., Gan, J., & Lu, H. (2024) · International Journal of Colorectal Disease · doi:10.1007/s00384-024-04744-2 · Cited by 13
Gut microbiota and epigenetic age acceleration: a bi-directional Mendelian randomization study
Han, X., Li, O., Kim, D., Bao, Z., & Yang, F. (2024) · Aging Clinical and Experimental Research · doi:10.1007/s40520-024-02877-6 · Cited by 13
Yi, G., Li, Z., Sun, Y., Ma, X., Wang, Z., Chen, J., Cai, D., Zhang, Z., Chen, Z., Wu, F., et al. (2024) · Journal of Translational Medicine · doi:10.1186/s12967-024-05856-7 · Cited by 13
Yu, F., Qiu, C., Xu, C., Tian, Q., Zhao, L., Wu, L., Deng, H., & Shen, H. (2020) · Frontiers in Genetics · doi:10.3389/fgene.2020.00060 · Cited by 11
“February 2020 | Volume 11 | Article 60 MR analysis, which can offset the low power problem induced by small sample size (Palmer et al., 2012) and allow for a causal estimate of greater precision than the estimate from any of the individual variants (Pierce et al., 2011).”
BackgroundWhat is creating the height premium? New evidence from a Mendelian randomization analysis in China
Wang, J., Chen, Q., Chen, G., Li, Y., Kong, G., & Zhu, C. (2020) · PLoS ONE · doi:10.1371/journal.pone.0230555 · Cited by 12
“Mathematically, PGS_Heighti is calculated as the sum of genotyped or imputed allele j dosages carried by a respondent i (SNPj,i) multiplied by the estimated effect size (βj) reported by Wood et al. [47] (We use the Affymetrix WeGene V1 Arrays to assay common SNP variation in the genome of all participants, and then im…”
BackgroundInfluentialZou, X., Wang, L., Xiao, L., Xu, Z., Yao, T., Shen, M., Zeng, Y., & Zhang, L. (2021) · Frontiers in Endocrinology · doi:10.3389/fendo.2021.750999 · Cited by 12
“When F ≤ 10, the selected SNPs were viewed as weak instrument biases, and thus they could not explain the observed exposure associations well (44).”
BackgroundFeng, X., Yang, W., Huang, L., Cheng, H., Ge, X., Zan, G., Tan, Y., Xiao, L., Liu, C., Chen, X., et al. (2022) · Phenomics · doi:10.1007/s43657-022-00052-3 · Cited by 11
Hou, T., Li, M., Lin, H., Zhao, Z., Lu, J., Wang, T., Xu, Y., Wang, W., Bi, Y., Ning, G., et al. (2022) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgac354 · Cited by 11
Zhang, Q., Zhang, X., Zhang, J., Wang, B., Tian, Q., Meng, X., Zhang, J., Jiang, M., Zhang, Y., Zheng, D., et al. (2022) · Thrombosis Journal · doi:10.1186/s12959-022-00427-6 · Cited by 13
“N means the number of individuals of the GWAS- exposure [43].”
BackgroundXing, W., Lv, Q., Li, Y., Wang, C., Mao, Z., Li, Y., Li, J., Yang, T., & Li, L. (2023) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2023.01.011 · Cited by 12
Zhu, J., Lian, J., Wang, X., Wang, R., Pang, X., Xu, B., Wang, X., Li, C., Ji, S., & Lu, H. (2023) · Frontiers in Pharmacology · doi:10.3389/fphar.2023.1185850 · Cited by 12
“29, suggesting that weak instrumental bias may not have been substantial in our study (Palmer et al., 2012).”
BackgroundLiu, X., Li, X., Xie, M., Guo, J.-Y., Zheng, X., Shi, S., Cui, Q., Zhang, D., Zhang, Z., & Wang, Z. (2023) · Journal of Stomatology Oral and Maxillofacial Surgery · doi:10.1016/j.jormas.2023.101736 · Cited by 12
Genetic Analysis of Leukocyte Type-I Interferon Production and Risk of Coronary Artery Disease
Nelson, C. P., Schunkert, H., Samani, N. J., & Erridge, C. (2015) · Arteriosclerosis Thrombosis and Vascular Biology · doi:10.1161/atvbaha.114.304925 · Cited by 12
“The use of a combination of SNPs, rather than a single SNP, as an instrument for MR has also been argued to increase the power and specificity of the analysis.(35) Finally, although we noted modest pleiotropy of rs3131379 in terms of blood cholesterol and triglycerides, analyses conducted with omission of this SNP yie…”
ResultHsu, L., Chou, H., Teng, M., Wu, S., & Ko, Y. (2021) · Atherosclerosis · doi:10.1016/j.atherosclerosis.2021.01.014 · Cited by 12
Edwards, C. H., Bjørngaard, J. H., & Kinge, J. M. (2021) · Health Economics · doi:10.1002/hec.4285 · Cited by 13
Mendelian Randomization Methods for Causal Inference: Estimands, Identification and Inference
Yao, M., Wang, A., Li, X., & Liu, Z. (2026) · Statistics in Medicine · doi:10.1002/sim.70394 · Cited by 12
Ghanbari, F., Otomo, N., Gamache, I., Iwami, T., Koike, Y., Khanshour, A. M., Ikegawa, S., Wise, C. A., Terao, C. C., & Manousaki, D. (2023) · JBMR Plus · doi:10.1002/jbm4.10830 · Cited by 12
“[34] The variance explained of each exposure by its respective genetic instruments ( R 2 ) was the addition of the variance explained by each SNP, which we calculated using the following formula: R 2 ≈ 2 β 2 ƒ (1 – ƒ ), where β and ƒ denote respectively the effect estimate and the effect allele…”
MethodYu, J., Fu, L., Zhang, Z., Ding, L., Li, H., Gao, F., Jin, J., Feng, W., Fu, J., Hong, P., et al. (2023) · Clinical and Experimental Medicine · doi:10.1007/s10238-023-01221-y · Cited by 11
“Thirdly, F-statistics analyses were employed to evaluate the instrument strength linked to exposure traits [28, 29].”
Wang, P., Tao, W., Zhang, Z., Xu, C., Qiu, Y., & Xiao, W. (2024) · European journal of medical research · doi:10.1186/s40001-023-01614-5 · Cited by 12
“In MR analysis, an F statistic of ≥ 10 is typically considered indicative of a relatively low risk of weak instrument bias [30].”
BackgroundPlasma metabolites and risk of myocardial infarction: a bidirectional Mendelian randomization study
Dong-Hua, L. I., Wu, Q., Jing-Sheng, L. A. N., Chen, S., HUANG, Y.-Y., Lan-Jin, W. U., Zhi-Qing, Q. I. N., Huang, Y., HUANG, W.-Z., Zeng, T., et al. (2024) · 老年心脏病学杂志：英文版 · doi:10.26599/1671-5411.2024.02.002 · Cited by 12
Li, L., Li, D., Geng, Z., Huo, Z., Kang, Y., Guo, X., Yuan, B., Xu, B., & Wang, T. (2024) · BMC Musculoskeletal Disorders · doi:10.1186/s12891-024-07631-7 · Cited by 11
Kang, T., Zhou, Y., Fan, C., Zhang, Y., Yu, Y., & Jiang, J. C. (2024) · The EPMA Journal · doi:10.1007/s13167-024-00373-5 · Cited by 11
“To ensure the selected SNPs are independent and reliable (with an r 2 threshold of 0.001 and a distance threshold of 10,000 kb), we calculated the F-statistic for each SNP (F = β 2 /se 2 ); F statistic > 20 indicates the absence of weak instrument bias [44].”
InfluentialRui, L., & Chen, R. (2024) · Renal Failure · doi:10.1080/0886022x.2024.2385065 · Cited by 11
“…prevalence of diabetic nephropathy (DN), with approximately 24.3% of individuals with diabetes mellitus also suffering from chronic kidney disease (CKD), contributing to the global burden of DN, which affects an estimated 850 million people, predominantly due to the rising prevalence of DM. [2,3].”
BackgroundInfluentialHow does gut microbiota affect the vaginitis axis? The mediating role of plasma metabolites
Li, M., Zhang, Q., Wu, T., Ma, L., Hu, D., Yuan, Z., Wang, S., Luo, A., & Zhang, J. (2024) · Microbiology Spectrum · doi:10.1128/spectrum.02263-24 · Cited by 11
“The F statistics of the IVs were all above 10, ranging from 12.8 to 155.5 (median, 57.34, Table S3), ensuring no weak instrument bias existed.”
InfluentialWang, B., Wu, J., Li, H., Jin, X., Sui, C., & Yu, Z. (2022) · Frontiers in Public Health · doi:10.3389/fpubh.2022.941067 · Cited by 12
“The equation R2 = 2Beta2EAF(1-EAF)/(2Beta2EAF(1EAF)+2SE2SampleSizeEAF(1-EAF), F= R2(SampleSize2)/(1 – R2) was used to calculate the F-statistic for all selected instrument SNPs separately and synthetically to reject the weak instruments with an F-statistic lower than 10 (19).”
MethodThe effect of systemic iron status on osteoarthritis: A mendelian randomization study
Ruan, G., Ying, Y., Lu, S., Zhu, Z., Chen, S., Zeng, M., Lu, M., Xue, S., Zhu, J., Cao, P., et al. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2023.1122955 · Cited by 11
“The strength of the instruments was evaluated by the F statistic using the formula F = R(2)(N-2)/(1-R(2)) (Palmer et al., 2012), where R(2) is the proportion of the variance of the four clinical iron biomarkers explained by the genetic variant and N is the sample size of the gene-each of the iron biomarker association.”
MethodXie, N., Xie, J., Wang, Z., Shu, Q., Shi, H., Wang, J., Liu, N., Xu, F., & Wu, J. (2022) · Nutrients · doi:10.3390/nu14235109 · Cited by 12
“R2 and N refer to the cumulative explained variance of selected SNPs and sample size separately [25].”
BackgroundThe Effect of Weight on Labor Market Outcomes: an Application of Genetic Instrumental Variables
Böckerman, P., Cawley, J., Viinikainen, J., Lehtimäki, T. J., Rovio, S., Seppälä, I., Pehkonen, J., & Raitakari, O. T. (2016) · National Bureau of Economic Research · doi:10.3386/w22200 · Cited by 11
A Mendelian randomization study on causal effects of 25(OH) vitamin D levels on diabetic nephropathy
He, M., Yang, T., Zhou, P., Bu, P., Yang, X., Zou, Y., & Zhong, A. (2023) · BMC Nephrology · doi:10.1186/s12882-023-03186-2 · Cited by 12
Wang, Y., Wang, J., Yan, Z., Liu, S., & Xu, W. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1240517 · Cited by 11
“…our results the primary MR analysis. i) Weak instrument bias: We calculated the F statistics (32) and the proportion of variance explained (PVE) (33) of the SNPs in our investigation, and the SNPs for the top fi ndings showed that all the SNPs were strong instruments with F statistics >10, and…”
MethodInfluentialZhao, X., Xu, W., Gu, Y., Li, Z., & Sun, G. (2023) · BMC Pulmonary Medicine · doi:10.1186/s12890-023-02720-0 · Cited by 11
“An F-sta-tistic<10 indicates a low risk of weak instrument bias in MR analyses [23].”
BackgroundMethodYazdanpanah, N., Jumentier, B., Yazdanpanah, M., Ong, K. K., Perry, J. R. B., & Manousaki, D. (2024) · Communications Biology · doi:10.1038/s42003-023-05737-7 · Cited by 10
“ANXA2 (annexin A2) has also been involved in the regulation of lipoproteins, while its cis -pQTL (rs36032232) is in LD with a cis - pQTL in the harbor Related Orphan Receptor A (rs3743266) which has been associated with timing of menarche (57).”
BackgroundMethodLiu, J., Li, J., Yuan, G., Cao, T., & He, X. (2024) · Scientific Reports · doi:10.1038/s41598-024-65512-4 · Cited by 10
Liu, M., Long, X., Fu, S., Zhang, Y., Liu, Z., Xu, X., & Wu, M. (2024) · Journal of Translational Autoimmunity · doi:10.1016/j.jtauto.2024.100251 · Cited by 10
“Second, to eliminate the bias caused by poor quality IVs, we calculated the R2 and F-statistics for each SNP (the formulas are shown in Table S3) [19,20].”
MethodLiu, Q., Chen, J., Liu, Y., Zhang, S., Feng, H., Wan, T., Zhang, S., Zhang, N., & Yang, Z. (2024) · Gene · doi:10.1016/j.gene.2024.149064 · Cited by 10
Salenius, K., Väljä, N., Thusberg, S., Iris, F., Ladd‐Acosta, C., Roos, C., Nykter, M., Fasano, A., Autio, R., Lin, J., et al. (2024) · BMC Psychiatry · doi:10.1186/s12888-024-06392-w · Cited by 11
Ge, Y., Yang, H., Fu, Y., Zhou, J., Cheng, Z., Fan, X., & Yang, Y. (2025) · European Spine Journal · doi:10.1007/s00586-025-08795-z · Cited by 10
Causal Effects of Blood Lipid Traits on Inflammatory Bowel Diseases: A Mendelian Randomization Study
Yao, Z., Jiang, F., Luo, H., Zhou, J., Shi, W., Xu, S., Zhang, Y., Dai, F., Li, X., Liu, Z., et al. (2023) · Metabolites · doi:10.3390/metabo13060730 · Cited by 10
“F < 10 indicates the presence of weak instrumental bias [25].”
BackgroundInstrumental variable model average with applications in Mendelian randomization
Seng, L. L., Liu, C., Wang, J., & Li, J. (2023) · Statistics in Medicine · doi:10.1002/sim.9819 · Cited by 10
Chen, X., Zheng, C., Xu, J., Zhao, Z., & Jiang, Q. (2023) · BMC Oral Health · doi:10.1186/s12903-023-03179-5 · Cited by 10
“At last, we calculated R2 and F-statistics as described before to estimate the strength of instrumental variables [28].”
MethodGiratallah, H., Chenoweth, M. J., Pouget, J. G., El‐Boraie, A., Alsaafin, A., Lerman, C. E., Knight, J., & Tyndale, R. F. (2023) · Human Molecular Genetics · doi:10.1093/hmg/ddad172 · Cited by 10
“We used six CYP2A6 variants in our wGRS and only one was weak; thus, our MR analyses were unlikely to suffer from weak instrument bias [45, 46].”
MethodHuang, Q., Guo, J., Zhao, H., Zheng, Y., & Zhang, Y. (2023) · PLoS ONE · doi:10.1371/journal.pone.0292881 · Cited by 10
Jia, H., Liu, Y., & Liu, D. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1221228 · Cited by 14
Liu, Y., Lin, Y., Lin, M., Wu, C., & Wang, T. (2024) · Annals of Human Genetics · doi:10.1111/ahg.12545 · Cited by 10
“This can reflect the magnitude and precision of the SNP’s effect on the exposure trait (Palmer et al., 2012).”
BackgroundZhong, X., Wang, L., Xu, L., Lian, J., Chen, J., Gong, X., & Shao, Y. (2023) · Brain and Behavior · doi:10.1002/brb3.3238 · Cited by 9
Karhunen, V., Gill, D., Malik, R., Ponsford, M., Ahola‐Olli, A., Papadopoulou, A., Palaniswamy, S., Mutt, S. J., Sebert, S. P., Männikkö, M., et al. (2020) · medRxiv · doi:10.1101/2020.10.26.20219477 · Cited by 10
Yazdanpanah, M., Yazdanpanah, N., Chardoli, M., & Dehghan, A. (2024) · International Journal of Cardiology · doi:10.1016/j.ijcard.2024.131964 · Cited by 9
Zhang, Z., Kutty, S., Peng, W., Zeng, G., Luo, H., Xiao, Z., Liu, Q., & Xiao, Y. (2024) · Journal of Affective Disorders · doi:10.1016/j.jad.2024.01.276 · Cited by 10
Li, B., Li, M., Qi, X., Tong, T., & zhang, G. (2024) · Human Genomics · doi:10.1186/s40246-024-00608-6 · Cited by 9
“The calculation of the F value and R 2 adhered to the formula utilized in previous studies [29, 30].”
MethodIron status and sarcopenia-related traits: a bi-directional Mendelian randomization study
Chen, H., Zhang, Z., Wang, Y., Ma, A., Li, L., & Zhao, G. (2024) · Scientific Reports · doi:10.1038/s41598-024-60059-w · Cited by 9
Lu, Y., Pei, Y., Gao, Y., Zhao, F., Wang, L., & Zhang, Y. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1344917 · Cited by 9
Wang, S., Yin, F., Sun, W., Li, R., Guo, Z., Wang, Y., Zhang, Y., Sun, C., & Sun, D. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1304973 · Cited by 9
Xu, T., Chen, G., Li, J., & Zhang, Y. (2024) · JOR Spine · doi:10.1002/jsp2.1349 · Cited by 9
“20,21 In this study, we used MR analysis to investigate the causal relationship between inflammatory cytokines and IVDD, aiming to offer evidence for alleviating and delaying the development of IVDD.”
MethodZhou, P., Jiang, X. M., & Wang, D. (2024) · Skin Research and Technology · doi:10.1111/srt.13853 · Cited by 8
RetractedGut microbiota and risk of ankylosing spondylitis
Jiang, X., Wang, M., Liu, B., Yang, H., Ren, J., Chen, S., Ye, D., Yang, S., & Mao, Y. (2024) · Clinical Rheumatology · doi:10.1007/s10067-024-07102-3 · Cited by 10
“The equation for calculating F -statistics was as follows: F represented the variance explained by the SNPs for each trait, “ n ” meant the sample size of exposures, and “ k ” was the number of IVs employed [26].”
A Mendelian randomization study of the association between serum uric acid and osteoporosis risk
Wu, H., Li, H., Dai, X., Dai, Y., Liu, H., Xu, S., Huang, J., Chi, H., & Wang, S. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1434602 · Cited by 10
Liu, L., Huang, P., Wang, C., Liu, Y., Gao, Y., & Yu, K. (2024) · Clinical Epidemiology · doi:10.2147/clep.s487118 · Cited by 10
“33,34 A strong instrumental variable is indicated by an F-statistic greater than 10.”
BackgroundUnraveling the causal associations between systemic cytokines and six inflammatory skin diseases
Liu, W., Zhang, X., & Chen, X. (2024) · Cytokine · doi:10.1016/j.cyto.2024.156810 · Cited by 9
Ren, Q., Liang, J., Su, Y., Tian, R., Wu, J., Ge, S., & Chen, P. (2025) · Journal of Cachexia Sarcopenia and Muscle · doi:10.1002/jcsm.13778 · Cited by 9
“Using the formula as stated, we computed the F - statistic to evaluate the strength of each IVs [22].”
InfluentialXu, S., Wang, X., Xu, J., Tang, X., Hao, W., Xiang, C., Lei, X., Wang, M. Y., & Yang, X. K. (2025) · Eye · doi:10.1038/s41433-025-03841-y · Cited by 9
Mendelian randomization on the association of obesity with vitamin D: Guangzhou Biobank Cohort Study
Huang, Y. Y., Zhang, W. S., Jiang, C. Q., Zhu, F., Jin, Y. L., Cheng, K. K., Lam, T., & Xu, L. (2022) · European Journal of Clinical Nutrition · doi:10.1038/s41430-022-01234-y · Cited by 9
“The strengths of our study included the use of genetic allele score, which helps to minimize the risk of pleiotropic effects, and increase the variance explained by the IV and statistical power [48].”
MethodWang, M., Zhang, Z., Liu, D., Karhunen, V., Georgakis, M. K., Ren, Y., Ye, D., Gill, D., & Liu, M. (2023) · Journal of Stroke and Cerebrovascular Diseases · doi:10.1016/j.jstrokecerebrovasdis.2023.107136 · Cited by 7
Cho, J. M., Koh, J. H., Kim, S. G., Lee, S., Kim, Y., Cho, S., Kim, K., Kim, Y. C., Han, S. S., Lee, H., et al. (2023) · Communications Biology · doi:10.1038/s42003-023-05091-8 · Cited by 10
“In addition, the F-statistic and r 2 for each genetic variant based on the circulating protein concentration were calculated as a measure of the strength of the instrument 40,53 – 55 .”
Zou, X., Zhang, L., Wang, L., Wang, S., & Zeng, Y. (2023) · Molecular Neurobiology · doi:10.1007/s12035-023-03517-2 · Cited by 9
“Finally, we pooled there was no weak instrument bias [33].”
MethodChen, M., Wang, Z., Xu, H., Li, W., Teng, P., & Ma, L. (2023) · Journal of Affective Disorders · doi:10.1016/j.jad.2023.11.052 · Cited by 10
Liu, X., Han, Y., Yan, G., Xu, B., Sun, M., & Feng, M. (2023) · European Journal of Nutrition · doi:10.1007/s00394-023-03281-y · Cited by 11
“Finally, to evaluate the strength of SNPs, the F-statistics were calculated by the following equation: where R is the portion of exposure variance explained by SNPs, and N is the sample size, K is the number of SNPs[50].”
Zhang, W., Lei, X., Tu, Y., Ma, T., Wen, T., Yang, T., Xue, L., Ji, J., & Xue, H. (2024) · Frontiers in Genetics · doi:10.3389/fgene.2024.1340044 · Cited by 11
Sun, W., Jian, X., Zhang, J., Meng, X., Wang, H., Zheng, D., Wu, L., & Wang, Y. (2024) · Molecules · doi:10.3390/molecules29061281 · Cited by 9
“If the value was below 10, it was considered a weak IV [57].”
BackgroundYe, D., Zhu, Z., Huang, H., Sun, X., Liu, B., Xu, X., He, Z., Li, S., Wen, C., & Mao, Y. (2021) · Journal of Nutrition · doi:10.1093/jn/nxab015 · Cited by 11
Yu, Z., Zhang, F., Xu, C., & Wang, Y.-G. (2022) · BioMed Research International · doi:10.1155/2022/4012603 · Cited by 10
“F statistic above 10 suggests that the possibility of weak instrument bias is small [42].”
A Bidirectional Mendelian Randomization Study of Selenium Levels and Ischemic Stroke
Fang, H., Liu, W., Zhang, L., Pei, L., Gao, Y., Zhao, L., Zhang, R., Yang, J., Song, B., & Xu, Y. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.782691 · Cited by 9
“In addition, the benefit of effective medication for IS (i.e., alteplase) is time-dependent, which limits the wide application of alteplase practice (Phipps and Cronin, 2020).”
BackgroundWan, A., Zhao, W., & Tao, J. (2022) · Frontiers in Oncology · doi:10.3389/fonc.2022.930243 · Cited by 7
“Furthermore, we then derived the R(2) of each SNP and summed them up to the computer F-statistic to test for weak instrument bias with the following equation: F-statistic =R2×(SampleSize−2)/(1 −R2) (21).”
MethodLi, X., Fu, Z., Xu, H., Zou, J., Zhu, H., Li, Z., Su, K., Huai, D., Yi, H., Guan, J., et al. (2020) · Nutrition & Metabolism · doi:10.1186/s12986-020-00501-8 · Cited by 9
Diabetes mellitus, glycemic traits, and cerebrovascular disease: a Mendelian randomization studyPreprint
Georgakis, M. K., Harshfield, E. L., Malik, R., Franceschini, N., Langenberg, C., Wareham, N. J., Markus, H. S., & Dichgans, M. (2019) · medRxiv · doi:10.1101/2019.12.27.19015834 · Cited by 9
Trichia, E., Malden, D. E., Jin, D., Wright, N., Taylor, H., Karpe, F., Sherliker, P., Murgia, F., Hopewell, J. C., Lacey, B., et al. (2023) · International Journal of Epidemiology · doi:10.1093/ije/dyad143 · Cited by 8
Associations of 10 dietary habits with breast cancer: a Mendelian randomization study
Wang, X., Chen, L., Cao, R., Ma, R., Liu, Y., Zhao, Q., & Du, Y. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1215220 · Cited by 8
Qiao, T., Tian, H., Shan, S., Shan, L., Peng, Z., Ke, J., Li, M., Wu, Y., & Han, Y. (2024) · Brain and Behavior · doi:10.1002/brb3.3399 · Cited by 8
“IVs of exposure must satisfy three following assumptions: (1) IVs are significantly associated with exposure ( p < 5e − 08) (Palmer et al., 2012); (2) the IVs should not be related to other confounding factors; (3) IVs are expected to affect the outcome exclusively through the exposure.”
Unveiling challenges in Mendelian randomization for gene–environment interaction
Gorfine, M., Qu, C., Peters, U., & Hsu, L. (2024) · Genetic Epidemiology · doi:10.1002/gepi.22552 · Cited by 8
Wu, Y., Ma, W., Cheng, Z., Zhang, Q., Li, Z., Weng, P., Li, B., Huang, Z., & Fu, C. (2024) · PLoS ONE · doi:10.1371/journal.pone.0298610 · Cited by 9
Yao, J., Duan, R., Li, Q., Mo, R., Zheng, P., & Feng, T. (2024) · Frontiers in Oncology · doi:10.3389/fonc.2024.1346809 · Cited by 9
Zhao, J., Sun, B., Huang, S., Chen, Y., & Yan, J. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1432041 · Cited by 8
Qi, S., Ma, A., Lin, H. Y., Peng, L., & Deng, E. (2024) · Archives of Dermatological Research · doi:10.1007/s00403-024-03303-7 · Cited by 8
Shi, Y., Bao, L., Li, Y., Ou, D., Li, J., Liu, X., Deng, N., Deng, C.-Q., Huang, X., Zhang, W., et al. (2024) · Journal of Affective Disorders · doi:10.1016/j.jad.2024.08.182 · Cited by 9
Lan, W., Lu, Q., Ma, W., Jiang, Z. S., Chen, Y., Wang, Z., Yao, X., & Tang, F. (2025) · Journal of Translational Medicine · doi:10.1186/s12967-025-06206-x · Cited by 10
Chen, J., Zhu, L., Wang, F., Zhu, Y., Chen, J., Liang, C., Liu, B., Pang, A., & Yang, X. (2025) · Molecular Neurobiology · doi:10.1007/s12035-025-04765-0 · Cited by 9
“Weak IVs pose a risk of bias in MR results [18].”
Le, N. N., Tran, T., McClure, J., Gill, D., & Padmanabhan, S. (2025) · European Heart Journal - Cardiovascular Pharmacotherapy · doi:10.1093/ehjcvp/pvaf015 · Cited by 9
Elevated high-density lipoprotein triglycerides increase atherosclerotic risk
Liu, W., Chen, S., Yang, C., Lei, F., Huang, X., Zhang, X., Sun, T., Lin, L., Wang, C., Cao, Y., et al. (2025) · Journal of Lipid Research · doi:10.1016/j.jlr.2025.100791 · Cited by 10
The continuing evolution of birth cohort studies: achievements and challenges
Lin, Y., Jiang, Y., Du, J., Ma, H., Shen, H., & Hu, Z. (2022) · Biology of Reproduction · doi:10.1093/biolre/ioac117 · Cited by 9
Dietrich, E., Jomard, A., & Osto, E. (2022) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2022.989428 · Cited by 9
“C levels also did not influence the risk score for myocardial infarction (1, 43).”
BackgroundYang, J., Nie, D., Chen, Y., Liu, Z., Li, M., Gong, C., & Liu, Q. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2022.1054132 · Cited by 8
Wu, H., Guo, J.-L., Yao, J.-J., Yu, J., Xia, R.-Y., Huang, W., Tang, X., & He, G.-M. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1162031 · Cited by 9
“We calculated F-statistic, an indicator of instrument strength measure, and the F-statistic above 10 reveals a low chance of weak instrument bias in our MR analysis (29).”
MethodZou, M., Zhang, W., Shen, L., Xu, Y., & Zhu, Y. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2023.1198476 · Cited by 8
“We calculated the R statistic [R(2) = 2 × EAF × (1-EAF) × beta(2), where EAF is the effect allele frequency and beta is the estimate of the effect of the SNP] for each SNP to detect the proportion of variation (Palmer et al., 2012).”
MethodPan, R., Xiao, M., Wu, Z., Liu, J., & Wan, L. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1276257 · Cited by 9
Relationship between bullous pemphigoid and malignancy: A Mendelian randomization study
He, M., Wang, Y., Ran, D.-L., Fu, D.-S., He, Q., Zhang, H., Mao, Y., Zhao, P., Yu, J., & Zhang, J. (2024) · The Journal of Dermatology · doi:10.1111/1346-8138.17100 · Cited by 7
Liao, O., Xie, S., Ye, J., Du, Q., & Lou, G. (2024) · World Journal of Psychiatry · doi:10.5498/wjp.v14.i1.15 · Cited by 8
Sun, T., Wang, J., Zheng, M., Cai, C., Yu, J., Fu, L., & Duan, L. (2024) · COPD Journal of Chronic Obstructive Pulmonary Disease · doi:10.1080/15412555.2024.2309236 · Cited by 9
“The formula for calculating the F value and R 2 is as follows (11).”
Zhang, J., Chen, X., Zhu, Y., Wan, S., Hu, S., & Yang, Y. (2024) · Nature and Science of Sleep · doi:10.2147/nss.s439274 · Cited by 8
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
