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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.
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“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]
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“Interpretation of results from MR studies relies on four conditions.12,24”
From Mendelian randomization (2022) · cites this paper as [24]
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“Where, R2 is the percentage of the variability in handgrip strength explained by the selected SNPs and N represents the sample size of the GWAS (14).”
BackgroundChen, C., Lan, Y., Wang, Z., Yan, W., Yan, X., & Han, J. (2023) · Journal of Endocrinological Investigation · doi:10.1007/s40618-023-02176-3 · Cited by 19
“To avoid bias caused by weak IVs, we calculated R 2 that could explain the degree of exposure based on β-exposure, effect allele frequency of expose-related SNPs and sample size of the exposure variable [31].”
Fetuin-A and its genetic association with cardiometabolic disease
Ali, L. A., van de Vegte, Y. J., Said, M. A., Groot, H. E., Hendriks, T., Yeung, M. W., Lipšic, E., & van der Harst, P. (2023) · Scientific Reports · doi:10.1038/s41598-023-48600-9 · Cited by 20
“Here, n is the sample size used to obtain the fetuin-A estimates and R 2 is the amount of variance in fetuin-A explained by the genetic variant 24 .”
MethodWang, K., Zhang, Q., Zhang, P. Y., Yang, Q., Pan, F., & Zha, B. (2024) · Science Advances · doi:10.1126/sciadv.adi8646 · Cited by 19
Ong, J., Derks, E. M., Eriksson, M., An, J., Hwang, L., Easton, D. F., Pharoah, P. D. P., Berchuck, A., Kelemen, L. E., Matsuo, K., et al. (2020) · International Journal of Cancer · doi:10.1002/ijc.33308 · Cited by 19
“A Mendelian randomization (MR) study, using genetic variants associated with alcohol consumption as an instrument for alcohol consumption, offers a way to test hypotheses of causality, since the genetic variants are less likely to be associated with other known or unknown confounders, and they are not influenced by (p…”
BackgroundYe, C., Niu, J., Zhao, Z., Li, M., Xu, Y., Lu, J., Chen, Y., Wang, W., Ning, G., Bi, Y., et al. (2021) · Journal of Diabetes Investigation · doi:10.1111/jdi.13577 · Cited by 20
Ganel, L., Chen, L., Christ, R., Vangipurapu, J., Young, E. P., Das, I., Kanchi, K., Larson, D. E., Regier, A., Abel, H., et al. (2021) · Human Genomics · doi:10.1186/s40246-021-00335-2 · Cited by 20
“The goal of the MR approach was to use a large number of common variants to build a genetic instrument Z that satisfies the three assumptions of MR [76] (see Supplementary Methods - Additional File 3).”
Gurung, R. L., Zheng, H., Lee, B. T. K., Liu, S., Liu, J., Chan, C., Ang, K., Subramaniam, T., Sum, C. F., Coffman, T. M., et al. (2024) · Diabetes Research and Clinical Practice · doi:10.1016/j.diabres.2024.111790 · Cited by 18
Wang, T., Cheng, J., & Wang, Y. (2022) · Genes & Nutrition · doi:10.1186/s12263-022-00708-9 · Cited by 19
“MR– Egger, weighted median, simple mode, and weighted mode produced directionally consistent effects as the IVW estimates.”
MethodInfluentialXia, J., Zhang, L., Li, J., Yuan, C., Zhu, X.-W., Qian, Y., Khederzadeh, S., Gu, J.-X., Xu, L., Gao, J.-H., et al. (2022) · BMC Medicine · doi:10.1186/s12916-022-02531-w · Cited by 17
“Furthermore, we evaluated the strength of the abovementioned instrument variables using two parameters: the proportion of variance explained (R2) [21], which was calculated from the formula ∑β2 × 2 × MAF × (1 − MAF), where the β was the estimated effect, MAF was the minor allele frequency, and the F statistic, which w…”
MethodConsidering strategies for SNP selection in genetic and polygenic risk scores
St.-Pierre, J., Zhang, X., Lu, T., Jiang, L., Loffree, X., Wang, L., Bhatnagar, S., Greenwood, C. M. T., & CANSSI team on Improving Robust High-Dimensional Causal Inference and Prediction Modelling (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.900595 · Cited by 18
“Genetic scores are also being considered as tools for inferring causal relationships in the context of Mendelian randomization (MR) studies (Palmer et al., 2012; Burgess and Thompson, 2013; Davies et al., 2018).”
BackgroundHuang, Y., Zhang, W.-M., Wei, Z.-S., Huang, H., Mo, Q., Shi, D.-L., Han, L., Han, Y.-Y., Nong, S.-K., & Lin, G. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1136169 · Cited by 18
“If the F statistic was ≥ 10, it implied a low probability of instrument bias in MR analysis (45).”
BackgroundWang, Y., Kong, L., Ye, C., Dou, C., Zheng, J., Xu, M., Xu, Y., Li, M., Zhao, Z., Lu, J., et al. (2023) · Liver International · doi:10.1111/liv.15669 · Cited by 18
Association Between Autoimmune Diseases and Sarcopenia: A Two-Sample Mendelian Randomization Study
Su, Q., Jin, C., Yang, Y., Wang, J., Wang, J., Zeng, H., Chen, Y., Zhou, J., & Wang, Y. (2023) · Clinical Epidemiology · doi:10.2147/clep.s416778 · Cited by 19
“The former can make robust inferences when weak IVs are included, and the latter yields valid estimates of causal effects when less than half of SNPs are invalid instruments.25,26 MR-Egger regression was used for assessment of pleiotropy.27 MR-Pleiotropy RESidual Sum and Clinical Epidemiology 2023:15 https://doi.org/1…”
MethodInfluentialZhang, F., Xian, D., Feng, J., Ning, L.-N., Jiang, T., Xu, W., Liu, Y., Zhao, Q., & Peng, M. (2023) · Aging · doi:10.18632/aging.205013 · Cited by 17
“In this equation, R(2) is the cumulative explained variance of the selected SNPs during exposure, MAF is the minor allele frequency, β is the effect value, SE is the standard error, K is the number of SNPs used for the final analysis, and N is the sample size [31].”
BackgroundPsychiatric disorders and cardiovascular diseases: A mendelian randomization study
Sui, X., Liu, T., Liang, Y., & Zhang, B. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e20754 · Cited by 17
“At the same time, a query was conducted in the Phenosanner database to determine whether the included SNPs were not related to known confounding factors.”
BackgroundInfluentialSun, J., Xiang, J., An, Y., Xu, J., Xiong, Y., Wang, S., & Xia, Q. (2023) · Cancers · doi:10.3390/cancers15215147 · Cited by 18
Yang, Q., Yang, Q., Wu, X., Zheng, R., Lin, H., Wang, S., Joseph, J., Sun, Y. V., Li, M., Wang, T., et al. (2024) · Cell Reports Medicine · doi:10.1016/j.xcrm.2023.101382 · Cited by 18
“…confounding in the outcome, 25 and the utilization of only lead cis -eQTLs for target genes in each tissue limited the detection of potential bias, 24,26 we should note that this study focused exclusively on homogeneous ethnic populations of Euro-peans, which avoid bias due to population admixture.”
BackgroundPreliminary study of the effect of gut microbiota on the development of prostatitis
Shen, C., Chen, Z., Zhang, W., Chen, X., Zheng, B., & Shi, C. (2024) · BMC Medical Genomics · doi:10.1186/s12920-024-01812-y · Cited by 17
Sun, X., Ye, D., Du, L., Qian, Y., Jiang, X., & Mao, Y. (2020) · International Journal of Cancer · doi:10.1002/ijc.33221 · Cited by 18
“The F-statistic for cytokines ranged from 24 to 797, satisfying the threshold of >10.(21) Among them, the strongest instrument was for IL-13 (median F-statistics = 292.”
BackgroundChen, G., Wang, Q., Xue, R., Liu, X., & Yu, H. (2021) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2021.753224 · Cited by 17
“To reduce the potential for weak instrument bias in the MR, we removed SNPs with F-statistics < 10 (25).”
MethodMbutiwi, F. I. N., Dessy, T., & Sylvestre, M. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.803238 · Cited by 17
“Further, weighted GRS with independently-derived weights lead to MR studies with similar statistical power than those using multiple independent IVs (Palmer et al., 2012).”
Vitamin D and heart failure: A two-sample mendelian randomization study
Luo, Q., Yan, W., Nie, Q., & Wang, H. (2022) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2022.08.003 · Cited by 17
Genetic predisposition to smoking in relation to the risk of frailty in ageing
Liu, W., Yang, H., Lv, L., Song, J., Jiang, Y., Sun, X., Ye, D., & Mao, Y. (2023) · Scientific Reports · doi:10.1038/s41598-023-28780-0 · Cited by 17
Causal effects of fatty acids on atopic dermatitis: A Mendelian randomization study
Lin, J.-Y., Ma, L.-J., Yuan, J.-P., Yu, P., & Bai, B. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1083455 · Cited by 17
“Above-mentioned R2 is the proportion of exposure accounted for the genetic variant, and N means the sample size of exposure to assess the strength of the extracted instruments (25).”
BackgroundWang, H., Li, C., Chen, L., Zhang, M., Ren, T., & Zhang, S. (2023) · Reproductive BioMedicine Online · doi:10.1016/j.rbmo.2023.103584 · Cited by 18
Causal Associations Between Gut Microbiota and Cerebrovascular Diseases
Zhang, H., Jiang, X., Li, A., & Wang, X. (2024) · World Neurosurgery · doi:10.1016/j.wneu.2023.12.150 · Cited by 17
Song, Z., Li, X., Xie, J., Han, F., Wang, N., Hou, Y., & Yao, J. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1327879 · Cited by 18
Zheng, T., Liu, C., Wang, Y., Zhou, H., Zhou, R., Zhu, X., Zhu, Z., Tan, Y., Li, Z., Huang, X., et al. (2024) · BMC Oral Health · doi:10.1186/s12903-024-04104-0 · Cited by 17
“Furthermore, each SNP’s R 2 value was utilized to measure the variance in exposure, and the strength of these instruments was evaluated using the F-statistic, where SNPs with an F-value > 10 were considered effective instruments [33].”
MethodWang, W., Huang, M., Ge, W., Feng, J., Zhang, X., Li, C., & Wang, L. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1300457 · Cited by 17
Genetically Predicted Cigarette Smoking in Relation to Risk of Polycystic Ovary Syndrome
Tao, Y., Liu, B., Chen, Y., Hu, Y., Zhu, R., Ding, Y., Mao, Y., & Sun, X. (2021) · Clinical Epidemiology · doi:10.2147/clep.s311785 · Cited by 17
“Moreover, the F-statistics for the IVs were all satisfying the threshold of F-statistics >10, indicating that the analysis was unlikely to be affected by weak instrument bias.(33)”
BackgroundMissing Data Methods in Mendelian Randomization Studies With Multiple Instruments
Burgess, S., Seaman, S. R., Lawlor, D. A., Casas, J. P., & Thompson, S. G. (2011) · American Journal of Epidemiology · doi:10.1093/aje/kwr235 · Cited by 17
“…Health Study; CRP, C- reactive protein; CHD, coronary heart disease; CI, confidence interval; IV, instrumen- tal variable; LD, linkage disequilibrium; MAR, missing at random; MCAR, missing completely at random; MNAR, missing not at random; SE, standard error; SNP, single nucleotide polymorphism.”
Genetic Evidence for the Association between Schizophrenia and Breast Cancer
Shi, J., Wu, L., Zheng, W., Wen, W., Wang, S., Shu, X., Long, J., Shen, C., Wu, P., Saloustros, E. S., et al. (2018) · Journal of Psychiatry and Brain Science · doi:10.20900/jpbs.20180007 · Cited by 18
“…multiple genetic variants associated with complex human traits or diseases including SCZ [6,7] and breast cancer [8–10] , which enable MR analysis by using such genetic variants as IVs with an increased statistical power to detect potential causal associations of exposure with an outcome [11–13] .”
Guo, H., Zhao, X., Han, K. Q., & Wang, Y. (2025) · Brain Research Bulletin · doi:10.1016/j.brainresbull.2025.111402 · Cited by 17
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“An F statistic of >10 indicates a relatively low risk of weak instrumental bias in MR analyses [60].”
BackgroundWootton, R. E., Lawn, R. B., Magnus, M. C., Treur, J. L., Corfield, E. C., Njølstad, P. R., Andreassen, O. A., Lawlor, D. A., Munafo, M. R., Håberg, S. E., et al. (2023) · BMC Medicine · doi:10.1186/s12916-023-02831-9 · Cited by 18
Wang, J., Hu, Y., Zeng, J., Li, Q., He, L., Hao, W., Song, X., Yan, S., & Lv, C. (2023) · International Journal of Public Health · doi:10.3389/ijph.2023.1605548 · Cited by 16
Vitamin D and idiopathic pulmonary fibrosis: a two-sample mendelian randomization study
Lin, T., Zhou, F., Mao, H., Xie, Z., & Jin, Y. (2023) · BMC Pulmonary Medicine · doi:10.1186/s12890-023-02589-z · Cited by 16
“Third, we calculated the F-statistic (F = beta2/se2) [17], since the included IVs were susceptible to weak IVs [18].”
MethodWei, L., Li, G., Peng, D., Li, N., & Wang, W. (2023) · Scientific Reports · doi:10.1038/s41598-023-50055-x · Cited by 15
“In order to minimize the impact of weak IVs on the causal analysis, we calculated the F-statistic using the following equation: F = R 2 / (1 − R 2 ) * (N − k − 1)/k 24 .”
MethodHuang, Q., Huang, Y., Xu, S., Yuan, X., Liu, X., & Chen, Z. (2024) · Medicine · doi:10.1097/md.0000000000035060 · Cited by 19
“[27]”
Cai, S., Fu, Y., Chen, J., Tian, M., & Li, X. (2024) · Journal of the American Heart Association · doi:10.1161/jaha.123.032084 · Cited by 19
“29 Moreover, 2 meth-ods were used to evaluate pleiotropy in this study.”
MethodXie, S., Zhang, R., Tang, Y., & Dai, Q. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1373723 · Cited by 17
Ma, Y., Wang, M., Chen, X., Yao, J., Ding, Y., Gao, Q., Zhou, J., & Lian, X. (2024) · Stroke · doi:10.1161/strokeaha.123.045664 · Cited by 17
“27 The statistical power for our MR analysis was calculated using an online tool (shiny.cnsgenomics.com/mRnd/).”
MethodHuang, P., Liu, Q., Zhang, T., & Yang, J. (2024) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2024.1380998 · Cited by 16
Liang, W., Zhong, K., Lai, T., Zeng, Y., Huang, Z., Zhou, J., Huang, J., Shi, Z., Zhang, J., & Ding, F. (2024) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2024.1384003 · Cited by 17
Chen, J., Yuan, X., Zhou, X., Xu, J., Zhang, X., & Duan, X. (2024) · Clinical Epigenetics · doi:10.1186/s13148-024-01723-w · Cited by 17
“…F-statistics was calculated using the formula F = β 2 SE 2 , and the proportion of variance in the exposure explained by the genetic variants ( R 2 ) was calculated using the formula where β is the genetic association with exposure (SE, standard error for β ; MAF, minor allele frequency) [25, 26].”
MethodBurgess, S., & Thompson, S. G. (2012) · Statistical Methods in Medical Research · doi:10.1177/0962280212451882 · Cited by 17
“This is equivalent to the commonly used ratio of coefficients valid for a single IV, but can be used with multiple instruments.(36) Then, we present a Bayesian method similar to the two-stage method, which extends naturally to a meta-analysis model where studies are combined in a hierarchical model on the causal param…”
MethodGenetically determined selenium concentrations and risk for autoimmune diseases
Ding, Y., Sun, X., Guo, Y. Q., Shao, K., Qian, Y., Huang, H., Liu, B., Wen, C., & Mao, Y. (2021) · Nutrition · doi:10.1016/j.nut.2021.111391 · Cited by 17
Zhang, Q., Zhang, X., Zhang, J., Wang, B., Meng, X., Tian, Q., Zhang, J., Jiang, M., Zhang, Y., Zheng, D., et al. (2021) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2021.769198 · Cited by 16
“Since this study only used publicly available summary statistic from relevant genome-wide-association studies (GWAS) and did not use the individual data, ethical approval was not required.”
MethodInfluentialZheng, S., Liu, L., Liang, K., Yan, J., Meng, D., Liu, Z., Tian, S., & Shan, Y. (2024) · Communications Biology · doi:10.1038/s42003-024-06680-x · Cited by 15
Joint Associations of APOC3 and LDL-C–Lowering Variants With the Risk of Coronary Heart Disease
Wang, W., Li, R. P., Song, Z., Huang, N., Huang, T., Hua, X., & Tang, Y.-D. (2025) · JAMA Cardiology · doi:10.1001/jamacardio.2025.0195 · Cited by 16
Huang, Y., Chang, Y., Cheng, C., Wu, C.-M., Liao, W., & Tsai, F. (2020) · Genes · doi:10.3390/genes12010017 · Cited by 15
“The MR study makes 3 assumptions of the IV analysis to derive a valid interpretation [31,32].”
BackgroundHou, C., Hou, Q., Xie, X., Wang, H.-F., Chen, Y., Lu, T., Wu, Q., Liang, Y., Hu, Y., & Mao, Y. (2021) · Genes & Nutrition · doi:10.1186/s12263-021-00691-7 · Cited by 15
Zhang, Y., Li, Y., Dai, X., Lin, H., & Ma, L. (2023) · Diabetology & Metabolic Syndrome · doi:10.1186/s13098-023-01101-1 · Cited by 16
“Besides, the instrument strength was estimated using F-statistic, and weak instruments with F-statistic<10 were removed [20].”
MethodOtomo, N., Khanshour, A. M., Koido, M., Takeda, K., Momozawa, Y., Kubo, M., Kamatani, Y., Herring, J. A., Ogura, Y., Takahashi, Y., et al. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1089414 · Cited by 16
“R2 represents the proportion of variance explained by the exposure SNP-instruments, k represents the number of instruments, and N represents the exposure GWAS sample size (30, 31).”
BackgroundZhao, J. V., Wang, J., Xu, H., Hu, W., Shi, F., Fan, Z., Zhou, C., & Mu, H. (2023) · Calcified Tissue International · doi:10.1007/s00223-023-01165-1 · Cited by 16
“To further verify the strength of the selected IVs, we calculated the F-statistics of the selected IVs using an online tool (https:// sb452. shiny apps. io/ overl ap) [19].”
Zhou, H., Shen, B., Huang, Z., Zhu, S., Yang, W., Xie, F., Luo, Y., Yuan, F., Zhu, Z., Deng, C., et al. (2023) · npj Parkinson s Disease · doi:10.1038/s41531-023-00611-z · Cited by 15
“(1) 64 and eliminated SNPs with an F-statistic below 10 to prevent the inclusion of weak SNPs 65 .”
Proteomic Associations of Adverse Outcomes in Human Heart Failure
Dib, M., Levin, M. G., Zhao, L., Diab, A., Wang, Z., Ebert, C., Salman, O., Azzo, J. D., Gan, S., Zamani, P. L., et al. (2024) · Journal of the American Heart Association · doi:10.1161/jaha.123.031154 · Cited by 15
“29 We used a Wald ratio when 1 SNV was available for MR 30 and inverse variance–weighted MR when >1 SNV was available, 31 adjusting for correlation between genetic instruments in the analysis.”
Obstructive sleep apnea and 19 gastrointestinal diseases: a Mendelian randomization study
Yan, W., Zhou, J., Jiang, M., Kong, Y., Qin, H., Qi, Y., Wang, S., & Tai, J. (2024) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2024.1256116 · Cited by 16
“When the F-statistic is greater than 10, IV is considered to have good statistical performance (31, 32): In this context, R 2 denotes the fraction of variability in exposure that can be ascribed to genetic variants.”
BackgroundSun, H., Zeng, X., Gao, W. Q., & Lu, X. (2025) · Aging Clinical and Experimental Research · doi:10.1007/s40520-025-02963-3 · Cited by 17
“All IVs with F value > 10 were consid - ered of a sufficient strength of instrument [16].”
Association Between Thyroid-Stimulating Hormone and Renal Function: a Mendelian Randomization Study
Chen, C., Xia, F., Chen, Y., Zhang, K., Cheng, J., Li, Q., Han, B., Zhao, L., Zhu, C., Wang, N., et al. (2018) · Kidney & Blood Pressure Research · doi:10.1159/000491808 · Cited by 16
Wang, K., Yang, F., Zhang, P., Yang, Y., & Li, J. (2022) · Frontiers in Nutrition · doi:10.3389/fnut.2022.964163 · Cited by 15
“Then we performed fixed-effect inverse-variance weighted (IVW) meta-analysis for all 3 instrument SNPs to derive the overall MR estimate (23).”
MethodChen, M., Wang, Z., Xu, H., Chen, X., Teng, P., & Ma, L. (2023) · BMC Medical Genomics · doi:10.1186/s12920-023-01496-w · Cited by 15
“An F statistic ≥ 10 indicates that the risk of weak instrument bias in MR analyses is relatively low [22].”
BackgroundThe role of adiposity, diet and inflammation on the discordance between LDL-C and apolipoprotein B
Webb, R. J., Mazidi, M., Lip, G. Y. H., Kengne, A. P., Banach, M., & Davies, I. G. (2021) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2021.12.004 · Cited by 14
Association between gut microbiota and endometriosis: a two-sample Mendelian randomization study
Ji, X., Yang, Q., Zhu, X.-L., Xu, L., Guo, J.-Y., Rong, Y., & Cai, Y. (2023) · Frontiers in Microbiology · doi:10.3389/fmicb.2023.1188458 · Cited by 15
“F statistical and R2 were calculated using the following equations (Palmer et al., 2012; Kamat et al., 2019).”
MethodDu, W., Yang, S., Zhou, H., Wu, Y., Cai, Y., Meng, H., Teng, H., & He, A. F. (2023) · Frontiers in Neuroscience · doi:10.3389/fnins.2023.1276032 · Cited by 17
Lin, D., Zhu, Y., Tian, Z., Tian, Y., Liang, C., Peng, X., Li, J., & Wu, X. (2023) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2023.1269414 · Cited by 14
Li, J., Zhang, C., Tang, J., He, M., He, C., Pu, G., Liu, L., & Sun, J. (2024) · BMC Pulmonary Medicine · doi:10.1186/s12890-024-02898-x · Cited by 13
“R 2 n − k − 1 The equation of the F statistic is , where R 2 represents the proportion of variance explained by SNPs, n is the sample size, and k is the number of included IVs [42].”
BackgroundFu, C., Zhao, Y., Zhou, X., Lv, J., Jin, S., Zhou, Y., Liu, F., & Feng, N. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1395580 · Cited by 14
Chen, W., Liu, K., Huang, L., Mao, Y., Wen, C., Ding, Y., & He, Z. (2022) · Frontiers in Nutrition · doi:10.3389/fnut.2022.923472 · Cited by 14
“Furthermore, to assess the strength of the IVs, the F-statistics were calculated by the formula of F = R2 × (N−k−1)/k× (1−R2) (34), where R2 is the total variance explained by the IVs, N represents the sample size and k indicates the number of included IVs.”
MethodChen, B., Han, Z., & Geng, L. (2022) · Frontiers in Immunology · doi:10.3389/fimmu.2022.911631 · Cited by 15
“IVs (F statistics < 10) were considered weak instruments, and the exposure would be excluded from MR analysis (16).”
MethodZgaga, L., Agakov, F. V., Τheodoratou, E., Farrington, S. M., Tenesa, A., Dunlop, M. G., McKeigue, P., & Campbell, H. (2013) · PLoS ONE · doi:10.1371/journal.pone.0063475 · Cited by 14
“Note that while highdimensional instruments may be integrated into our framework relatively easily, this is less easy in the classic non-Bayesian methods due to the problems with weak instruments and possible overfitting [23,24,26,53].”
BackgroundZhang, X., He, J., Fu, W., Liu, Y., & Zhang, Z. (2016) · Lifestyle Genomics · doi:10.1159/000452130 · Cited by 14
Body mass index and type 2 diabetes and breast cancer survival: a Mendelian randomization study.
Liu, Y.-S., Wu, P., Chou, W., Vikram, R., Chen, W.-T., Yang, S.-L., Bolla, M. K., Wang, Q., Dennis, J., Chan, T. L., et al. (2021) · PubMed Central · doi:10.17863/cam.73616 · Cited by 14
Type 2 Diabetes Prevention: Implications of Hemoglobin A1c Genetics
Leong, A., & Meigs, J. B. (2015) · The Review of Diabetic Studies · doi:10.1900/rds.2015.12.351 · Cited by 13
Iron status and mental disorders: A Mendelian randomization study
Qiu, J., Lian, F., & Fang, X. (2022) · Frontiers in Nutrition · doi:10.3389/fnut.2022.1084860 · Cited by 13
“F statistic of first-stage regression was employed to evaluate the strength of the instruments and was calculated using the following equation: F = (R2/k)/([1-R2]/[n-k-1]), where R2 is the proportion of the iron status variability accounted for by the SNP, k is the number of instruments used in the model and n is the…”
BackgroundMethodLu, K., Tan, J., Li, T., Yuan, J., Wang, H., & Wang, W. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1111950 · Cited by 13
“Therefore, we used these SNPs to investigate the correlation between genetically predicted serum 25OHD levels and the risk of COPD by using two-sample MR (14, 15).”
MethodGuo, Y. P., Li, D., & Hu, Y. (2023) · American Journal of Clinical Nutrition · doi:10.1016/j.ajcnut.2023.05.004 · Cited by 13
Wang, M., Jin, G., Cheng, Y., Guan, S., Zheng, J., & Zhang, S.-X. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2023.1242614 · Cited by 13
“To estimate the proportion of variance in exposure explained by each SNP and to avoid weak instrument bias, we calculated the R(2) value and F-statistic respectively (Palmer et al., 2012).”
MethodLiang, X., Shi, W., Zhang, X., Pang, R., Zhang, K., Xu, Q., Xu, C., Wan, X. H., Cui, W., Li, D., et al. (2023) · BMC Medical Genomics · doi:10.1186/s12920-023-01708-3 · Cited by 13
“In this study, we calculated the F values by which the intensity of the screened IVs was assessed [30].”
MethodThe impact of air pollution on atopic dermatitis: A transethnic Mendelian randomization study
Ni, Y., He, A., Ye, J., & Lv, W. (2023) · Journal of the European Academy of Dermatology and Venereology · doi:10.1111/jdv.19675 · Cited by 13
Dice, A. L. E., Lawn, R. B., Ratanatharathorn, A. D., Roberts, A. L., Denckla, C. A., Kim, A. H., de la Rosa, P. A., Zhu, Y., VanderWeele, T. J., & Koenen, K. C. (2024) · BMC Medicine · doi:10.1186/s12916-024-03360-9 · Cited by 14
Jiang, R., Sun, C., Yang, Y., Sun, Q., & Bai, X. (2024) · Heart & Lung · doi:10.1016/j.hrtlng.2024.04.007 · Cited by 12
Yeung, M. W., Said, M. A., van de Vegte, Y. J., Verweij, N., Dullaart, R. P. F., & van der Harst, P. (2024) · Atherosclerosis Plus · doi:10.1016/j.athplu.2024.07.001 · Cited by 13
“Weak instrument bias was tested using F-statistics [24], with F-statistics > 10 indicating low risk of weak instrument bias.”
Duan, K., Wang, J., Chen, S., Chen, T., Wang, J., Wang, S., & Chen, X. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1422626 · Cited by 13
Proteome-wide Mendelian randomization identified potential drug targets for migraine
Xiong, Z., Zhao, L., Mei, Y., Qiu, D., Li, X., Zhang, P., Zhang, M., Cao, J., & Wang, Y. (2024) · The Journal of Headache and Pain · doi:10.1186/s10194-024-01853-9 · Cited by 13
“To minimize weak instrument bias, only SNPs with an F value greater than 20 in the GWAS of exposure were considered as potential IVs [20, 21].”
BackgroundMendelian Randomization Studies in Atherosclerotic Cardiovascular Diseases
Ko, D. S., & Kim, Y. H. (2024) · Journal of Lipid and Atherosclerosis · doi:10.12997/jla.2024.13.3.280 · Cited by 13
“58 In particular, two-sample MR allows the use of summary data from different sources, enhancing the feasibility of MR analyses without the need for individual-level data.”
MethodMandaviya, P. R., Joehanes, R., Aïssi, D., Kühnel, B., Marioni, R. E., Trương, V., Stolk, L., Beekman, M., Bonder, M. J., Franke, L., et al. (2017) · PLoS ONE · doi:10.1371/journal.pone.0182472 · Cited by 13
“The use of genetic variants is less sensitive to confounding and bias as compared to classical epidemiological studies [32].”
ResultPredictors and consequences of health anxiety symptoms: a novel twin modeling study
López‐Solà, C., Bui, M., Hopper, J. L., Fontenelle, L. F., Davey, C. G., Pantelis, C., Alonso, P., van den Heuvel, O. A., & Harrison, B. J. (2018) · Acta Psychiatrica Scandinavica · doi:10.1111/acps.12850 · Cited by 13
“ICE FALCON is similar to the Mendelian randomization approach to making inference on causation (36) which makes use of genetic risk scores as ‘instrumental variables’.”
MethodYe, D., Liu, B., He, Z., Huang, L. C., Qian, Y., Shao, K., Wen, C., & Mao, Y. (2021) · Clinical Epidemiology · doi:10.2147/clep.s305024 · Cited by 15
“We calculated F-statistics to quantify the strength of the selected instruments.(24) The variance explained by the three SNPs was estimated according to minor allele frequency (MAF) and beta value (β), using the equation of 2 × MAF × (1-MAF) ×β The smallest effect detected by the sample size to provide >80% statistica…”
MethodCausal Genetic Inference Using Haplotypes as Instrumental Variables
Wang, F., Meyer, N. J., Walley, K. R., Russell, J. A., & Feng, R. (2015) · Genetic Epidemiology · doi:10.1002/gepi.21940 · Cited by 13
“To improve the strength of IV, multiple SNPs can be used as IVs [Palmer et al., 2012], though there might be a noticeable percentage of subjects with at least one SNP missing.”
MethodInfluentialUsing Mendelian randomization to assess and develop clinical interventions: limitations and benefits
Burgess, S., & Mälarstig, A. (2013) · Journal of Comparative Effectiveness Research · doi:10.2217/cer.13.14 · Cited by 13
Qiu, J., Hu, P., Li, F., Huang, Y., Yang, Y., Sun, F., Wu, P., Lai, Y., Wang, Y., He, X., et al. (2025) · BMC Medicine · doi:10.1186/s12916-025-04061-7 · Cited by 12
“For each variant incorporated into the genetic instruments, F-statistics were subsequently computed according to literature and an F-statistic below 10 implies the presence of weak instrument bias [30, 31].”
Inflammatory cytokines and two subtypes of breast cancer: A two-sample mendelian randomization study
Zhou, H., Cai, Z., Yang, Q., Yang, X., Chen, J., & Huang, T. C. (2023) · PLoS ONE · doi:10.1371/journal.pone.0293230 · Cited by 12
Causal association between dietary factors and esophageal diseases: A Mendelian randomization study
Zou, M., Liang, Q., Zhang, W., Zhu, Y., & Xu, Y. (2023) · PLoS ONE · doi:10.1371/journal.pone.0292113 · Cited by 13
Feng, Z., Zhang, Y., Lai, Y., Jia, C., Wu, F., & Chen, D. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1277554 · Cited by 11
Association of Lipoprotein(a) with arterial stiffness: A Mendelian randomization study
Simistiras, A., Georgiopoulos, G. A., Delialis, D., Mavraganis, G., Oikonomou, E., Maneta, E., Loutos, C., Εvangelou, Ε., & Stamatelopoulos, K. S. (2024) · European Journal of Clinical Investigation · doi:10.1111/eci.14168 · Cited by 12
“22 The fraction of the exposure variance explained by each IV was calculated via the R 2 metric, 37 and a total of 67% of the explained variance of Lp(a) was attributed to the selected IVs.”
MethodLou, Y., Liu, B., Jiang, Z., Wen, X., Song, S., Xie, Z., Mao, Y., & Shao, T. (2024) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2024.01.021 · Cited by 13
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
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