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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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“F-statistic was performed to assess the strength of the instrument (17).”
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“Weak IVs, defined as having an F statistic less than 10, were excluded to avoid bias (16).”
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“An F statistic >10 was identified as sufficient enough to avert deviation from the causal IV strength evaluate (24).”
BackgroundLi, M., Xiao, L., Cai, J., Jiang, K., Li, Y., Li, S., Wang, Q., Wang, W., Shi, K., & Liu, H. (2024) · Journal of Global Health · doi:10.7189/jogh.14.05001 · Cited by 7
“Lastly, we estimated the F-statistic to assess instrument strength, where F 10 indicates weaker strength [24–26].”
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Serum albumin levels and risk of atrial fibrillation: a Mendelian randomization study
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“F-statistics were calculated following established formulas in previous studies [20].”
Αikepa, D., He, Y., Chen, W., Liang, M., Du, Y., Chen, X., Du, M., Zhu, Y., Wang, J., & Sun, Y. (2025) · Diabetes Metabolic Syndrome and Obesity · doi:10.2147/dmso.s510384 · Cited by 7
“26 When the F-statistic’s threshold was more than 10, it was deemed statistically significant, meaning that weak instrumental bias had no impact on the causal relationship.”
Xiong, Z., Zhao, L., Liu, G., Qiu, D., Mei, Y., Li, X., Guo, Z., Zhang, P., Zhang, M., Gao, T., et al. (2025) · The Journal of Headache and Pain · doi:10.1186/s10194-025-02119-8 · Cited by 7
“To reduce bias from weak instruments, only SNPs with F-statistics > 10 were retained [19, 20].”
Li, S., Hu, S., Zheng, X., Ku, X., Zou, J., Wang, L., Nie, G., Liu, Y., Tian, C., Ran, J., et al. (2025) · Clinical Interventions in Aging · doi:10.2147/cia.s547803 · Cited by 7
“To evaluate instrument strength and rule out weak instrument bias, the F-statistic was calculated for each SNP, 19 with values above 10 indicating sufficient strength.”
Yan, W., Luo, Q., Nie, Q., Wang, H., & Wu, J. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e14110 · Cited by 7
Chen, Y., Lou, L., Zhang, X., Jin, L., Chen, Y., Chen, L., Li, Z., Zhang, F., Fu, T., Hu, S., et al. (2023) · Frontiers in Immunology · doi:10.3389/fimmu.2023.1041591 · Cited by 7
“The proportions of variance in respective leukocyte counts explained by the selected SNPs were estimated (Supplementary Table S2), and F-statistics were calculated as measures of instrument strength (24).”
MethodShi, Z., Zhao, Z., Puyan, Z., An, C., & Zhang, K. (2023) · Journal of Dairy Science · doi:10.3168/jds.2022-22392 · Cited by 7
“of the selected instruments (Palmer et al., 2012), was also calculated as described in Supplemental Table S1 (https: / / doi .”
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Jin, Y., Zhou, H., Xiaoli, J., & Wang, J. (2024) · Lipids in Health and Disease · doi:10.1186/s12944-024-02191-0 · Cited by 7
“Furthermore, we calculated the F-statistics for each SNP to exclude weak IVs, setting a minimum threshold of 10 to ensure robustness [14].”
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Shared genetic architecture between type 2 diabetes and COVID-19 severity
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“A threshold of F statistic over 10 indicated lower risk of weak instrument bias [22].”
BackgroundMethodType 2 diabetes and the risk of synovitis-tenosynovitis: a two-sample Mendelian randomization study
Guo, J., Peng, C., He, Q., & Li, Y. (2023) · Frontiers in Public Health · doi:10.3389/fpubh.2023.1142416 · Cited by 7
“We used the F-statistic to assess weak instrumental variable effects (27).”
MethodChen, Y., Liu, S., Gong, W., Guo, P., Xue, F., Zhou, X., Wang, S., & Yuan, Z. (2023) · Human Genetics · doi:10.1007/s00439-023-02627-0 · Cited by 8
“Thus, we assessed the strength of IVs by the F statistic and removed the weak IVs with the F-statistic less than 10 (Bottigliengo et al. 2022; Burgess et al. 2011; Palmer et al. 2012; Wang et al. 2021).”
Causal Inference and Structure Learning of Genotype–Phenotype Networks Using Genetic Variation
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“The F statistic in MR analysis measured instrument strength based on R 2 , sample size (N), as well as the number of instruments (K), which could be calculated by: 2 R 1 R 2 (cid:28) [33].”
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“23 Furthermore, we employed the LDLink-LDTrait approach to exclude SNPs related to confounding factors such as body mass index, body weight, smoking, alcohol consumption, and nicotine intake.”
Association between metabolic syndrome and low back pain: a two-sample Mendelian randomization study
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“R 2 ) for each IV, was employed to assess the strength of the instruments, with R 2 denoting the proportion of phenotypic variance explained by each genetic variant in the exposure, and N representing the sample size 31 .”
Yang, Q., Zhong, F., Liu, X., Hong, J., Chen, L. L., Lin, H., Fu, J., Zheng, X., & Jiang, J. (2025) · Medicine · doi:10.1097/md.0000000000042768 · Cited by 6
“[37] Furthermore, a causal estimate derived from multiple causal SNPs is generally more precise than 1 derived from a single SNP. [36,38] Therefore, we conducted a multi-SNP SMR as a sensitivity analysis in our study, [20] incorporating all independent cis-eQTLs with P 5E-8 within the cis-region…”
Jiang, Z., He, R., Wu, H., Yu, J., Zhu, K., Luo, Q., Liu, X., Pan, J., & Huang, H. (2023) · Frontiers in Genetics · doi:10.3389/fgene.2023.1098616 · Cited by 6
“Finally, to avoid weak instrument bias, we calculated the F-statistics of each genetic instrument (SNP) (Li and Martin, 2002; Palmer et al., 2012) and ensured strong effect sizes by selecting instruments with F-statistic values larger than 10 in our MR analysis.”
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“[19] We also performed reverse MR analysis between gut microbiota and sepsis to investigate whether sepsis affects gut microbiota.”
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“Third, the R 2 value of each SNP was used to calculate the proportion of variance in exposure, and the F statistic was used to estimate the instrumental strength to avoid weak instrumental bias (30, 31).”
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“Central focus of this study was the results of the IVW method, which showed the strongest ability to test for causal relationships in MR analyses (26).”
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“The limitations of the present study are as follows: (i) Since the number of IVs fulfilling the strict threshold ( p 5 × 10 − 8 ) was extremely small, a more relaxed threshold ( p 1 × 10 − 5 ) was adopted Forest plot for the causal effects of Phosphatidylcholine (18:1_18:1) on epilepsy mediated by TNFSF12.”
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Exploring the shared genetic basis of major depressive disorder and frailty
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“[17] MR analysis included previously published GWAS summary statistics.”
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“…insensitive to different instruments (sets), then this would support the generalizability of the results to other groups, as well as the validity of the instruments and the IV approach (Wehby, Ohsfeldt, and Murray 2008; Davey Smith 2011; Palmer et al. 2011; von Hinke Kessler Scholder et al. 2010).”
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“The instruments have F-statistics higher than threshold, making significant bias from use of weak instruments unlikely [42].”
BackgroundEdwards, C. H., Vie, G. Å., & Kinge, J. M. (2022) · BMC Health Services Research · doi:10.1186/s12913-022-07597-z · Cited by 6
“Combining genetic variants into a GRS, as we have done in this study, leads to a higher first-stage F-statistic, and reduced bias [51].”
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“27”
BackgroundMethodInfluentialZhao, S., Zhang, J., Ding, F., & Sun, S. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1293170 · Cited by 7
“Subsequently, we computed the F statistic for each SNP to detect any weak IV bias (19).”
MethodWang, B.-R., Wang, J., Tian, T., Zhang, S., Zhao, Y.-Q., Meng, S., Wu, Z.-Y., Huang, F., Zeng, J., & Ni, J. (2023) · Journal of Affective Disorders · doi:10.1016/j.jad.2023.12.042 · Cited by 6
Caffeinated beverages intake and risk of deep vein thrombosis: A Mendelian randomization study
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She, Y., He, Y., Wu, J., & Liu, N. (2024) · Archives of Gerontology and Geriatrics · doi:10.1016/j.archger.2024.105374 · Cited by 6
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“The proportion of variance in exposures was calculated with R2 values for each SNP and instrument strength was assessed using the F -statistic ( F > 10) to avoid weak instrument bias [19].”
Wu, S., Yi, J., & Wu, B. (2024) · Frontiers in Endocrinology · doi:10.3389/fendo.2024.1376139 · Cited by 6
“R 2 ), to evaluate the signi fi cant association of the genetic instruments with the exposure (24, 25).”
Que, H., Zhang, Q., Xu, S., Chu, T., Xu, L., & Wang, Y. (2024) · Journal of Oral Rehabilitation · doi:10.1111/joor.13771 · Cited by 6
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“…IV analysis, comparable to those for typical Mendelian randomization studies using genetic variants as an IV, e.g. ALDH2 variants for alcohol consumption (F-statistic = 75 and R2 of 0.03) (Au Yeung et al., 2013) or FTO variants for adult BMI (F-statistic = 45 and R2 of 0.01) (Palmer et al., 2012).”
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Daytime sleepiness and risk of stroke: A Mendelian randomization analysis
Ma, Y., Wang, M., Chen, X., Ruan, W., Yao, J., & Lian, X. (2021) · Clinical Neurology and Neurosurgery · doi:10.1016/j.clineuro.2021.106857 · Cited by 6
Gene-Based Association Tests Using New Polygenic Risk Scores and Incorporating Gene Expression Data
Yan, S., Sha, Q., & Zhang, S. (2022) · Genes · doi:10.3390/genes13071120 · Cited by 6
“Studies show that PRS not only can be applied to predict disease [6], but can also be used in gene-based association tests [7].”
Qin, H., Zeng, W., & Lou, Y.-F. (2022) · Medicine · doi:10.1097/md.0000000000029879 · Cited by 6
“[15] F-statistic is a common method for evaluating instrument strength, and only SNPs with an F-statistic > 10 were used in our study to avoid potential weak instrumental bias.[16] Because the linkage disequilibrium between the 2 loci (rs1800562 and rs1799945) within the HFE gene was low (r2 < 0.”
MethodShi, D., & Tong, X. (2020) · Sociological Methods & Research · doi:10.1177/0049124120914920 · Cited by 6
Liang, X., Mounier, N., Apfel, N., Khalid, S., Frayling, T. M., & Bowden, J. (2023) · medRxiv · doi:10.1101/2023.03.18.23287164 · Cited by 6
Toikumo, S., Davis, C. N., Jinwala, Z., Khan, Y., Jennings, M. V., Davis, L. K., Sanchez‐Roige, S., Kember, R. L., & Kranzler, H. R. (2025) · Research Square · doi:10.1101/2025.02.28.25323112 · Cited by 6
Han, D., Yu, F., & Zheng, L. (2024) · Epidemiology and Health · doi:10.4178/epih.e2024046 · Cited by 5
“The primary method used for this analysis was the random-effect inverse-variance weighting (IVW) method [20].”
MethodInflammatory cytokines and carpal tunnel syndrome: A causal relationship revealed
Yang, C.-F., Pu, Y., Li, L., Guo, M.-G., & Feng, Z. (2024) · Cytokine · doi:10.1016/j.cyto.2024.156777 · Cited by 6
Tai, Y., Wang, H., Dai, Y., & Liang, Y. (2024) · Nature and Science of Sleep · doi:10.2147/nss.s480491 · Cited by 6
Zhang, J., Hu, Y., Xu, J., Shao, H., Zhu, Q., & Si, H. (2024) · Frontiers in Microbiology · doi:10.3389/fmicb.2024.1442506 · Cited by 7
Unveiling the Causal Relationship between Thyroid and Kidney Function
Tsao, H., Shao, Y. J., Chang, Y., Chou, Y., Wu, V., Lin, S., Chen, Y., & Lai, T. (2025) · Clinical Journal of the American Society of Nephrology · doi:10.2215/cjn.0000000722 · Cited by 6
Wang, H., Wang, C., Qin, R., He, J., Zhang, X., Ma, C., Shi, L., Fan, L., Wang, L., & Cao, L. (2025) · Biomedicines · doi:10.3390/biomedicines13061380 · Cited by 5
Mendelian randomization: estimation of inpatient hospital costs attributable to obesity
Dick, K. J., Schneider, J. E., Briggs, A. H., Lecomte, P., Régnier, S. A., & Lean, M. E. J. (2021) · Health Economics Review · doi:10.1186/s13561-021-00314-2 · Cited by 5
“This can be tested by linear regression of the instrument on each covariate [22, 29, 33].”
Dong, W., Li, Q., Chen, L., Tang, H., Tu, K., Luo, L., Jiang, L., & Huang, Y. (2024) · Renal Failure · doi:10.1080/0886022x.2024.2357746 · Cited by 5
“We gauged the strength of the IVs by calculating the F statistic, expressed as representing the number of participants, EAF denoting the effect allele frequency, and β indicating the estimated effect of the SNPs to assess their ability to uniquely predict the outcome [22–24].”
MethodLiao, Q., Wang, F., Zhou, W., Liao, G., Zhang, H., Shu, Y., & Chen, Y. (2024) · Microorganisms · doi:10.3390/microorganisms12061170 · Cited by 5
“The strength of IVs was assessed using F -statistics, calculated using the formula [27]: where N represents the sample size, k indicates the number of IVs, and R 2 stands for the proportion of variance explained.”
MethodFeng, W., Zhang, B., Duan, P., Bi, Y.-H., Jin, Z., Li, X., Zhao, X., & Zuo, K. (2024) · Frontiers in Public Health · doi:10.3389/fpubh.2024.1372758 · Cited by 7
“An F statistic ≥ 10 indicates that the risk of incorporating weak correlation instrument bias in the MR analysis is relatively low (33).”
BackgroundMethodMa, Y., Ji, J., Liu, X., Zheng, X., Xu, L., Zhou, Q., Li, Z., & Yang, L. (2024) · Kidney Diseases · doi:10.1159/000539689 · Cited by 8
“…bias, F statistics were calculated in the formula F R 2 × N − 2 ( ) In this estimation, N refers to total sample size of population in the selected exposure, while EAF represents effect allele frequency. β and SE, respectively, mean the effect size and the standard error in exposure GWAS [34 – 36].”
MethodInflammatory factors and the risk of urolithiasis: a bidirectional Mendelian randomization study
Huang, K., Peng, Z., Zha, C., Li, W., Deng, G., Chen, X., Luo, Y., Ji, Z., Wang, Q., & Jiang, K. (2024) · Frontiers in Medicine · doi:10.3389/fmed.2024.1432275 · Cited by 5
Chen, Q., Zhang, C., Wu, S., He, Y., Liu, Y., Zheng, L., Li, B., Liu, G., & Liu, L. (2024) · BMC Medical Genomics · doi:10.1186/s12920-024-01956-x · Cited by 5
“SNPs with an F statistic 10 were regarded as weak instruments and were subsequently excluded from the analysis [26].”
MethodAutoimmune diseases and COPD risk: A Mendelian randomization study
Ma, X., Sun, Y., Mou, H., & Zhang, W. (2024) · International Immunopharmacology · doi:10.1016/j.intimp.2024.112791 · Cited by 5
Immune thrombocytopenia increases the risk of thrombosis: A two-sample Mendelian randomization study
Yu, J., Fu, L., Jin, G., Gao, F., Ding, L., Hong, L., Lv, S., Jin, J., Tang, L., Feng, W., et al. (2024) · International Journal of Cardiology · doi:10.1016/j.ijcard.2024.132417 · Cited by 5
Long, K., Gong, A., Zheng, T., Liu, S., Ying, Z., & Cong, X. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1433219 · Cited by 5
Liang, X., Mounier, N., Apfel, N., Khalid, S., Frayling, T. M., & Bowden, J. (2024) · Genetic Epidemiology · doi:10.1002/gepi.22582 · Cited by 8
Chen, J., Yu, H., Liu, H.-H., Yu, H., Liang, S., Wu, Q., Zhang, X., Zeng, R., & Diao, L. (2024) · Scientific Reports · doi:10.1038/s41598-024-70370-1 · Cited by 5
Mendelian randomization analyses explore the effects of micronutrients on different kidney diseases
Shi, C., Cao, H., Zeng, G., Wu, H., & Wang, Y. (2024) · Frontiers in Nutrition · doi:10.3389/fnut.2024.1440800 · Cited by 5
“Mendel’s law of inheritance posits that genetic differences are predetermined and independent of postnatal conditions, significantly mitigating the impact of common confounding variables and the potential for reverse causation (10, 11).”
BackgroundLin, Y., Zhu, Z., Aodeng, S., Wang, X., Wang, L., Wang, W., & Lv, W. (2024) · Ecotoxicology and Environmental Safety · doi:10.1016/j.ecoenv.2024.117205 · Cited by 6
Ren, B.-W., Liu, Y., Wu, J., An, B., Liu, Q.-Z., Liu, C.-Y., Mao, K.-Y., & Liu, J.-H. (2024) · European Spine Journal · doi:10.1007/s00586-024-08551-9 · Cited by 5
“Utilizing genetic variants associated with exposure factors as instrumental variables (IVs), MR analysis investigates the likeliness of causal links between risk factors and outcomes [15].”
Liu, Y., Feng, H., Ma, H., Li, J., Yu, Y., Zhao, H., Wang, X., Li, Y., Zhang, J., & Liu, Q. (2024) · Discover Oncology · doi:10.1007/s12672-024-01644-3 · Cited by 5
Sun, L., Yan, K., Zhang, Q., Ma, J., Shi, B., Yang, X., & Li, L. (2025) · JOR Spine · doi:10.1002/jsp2.70034 · Cited by 5
Yuan, W., Xu, X. P., Zhang, X., Fan, W., Zhou, W., & Zhao, F. (2025) · Ophthalmic Epidemiology · doi:10.1080/09286586.2025.2458245 · Cited by 5
“16 Because genetic variation is randomly assigned, this study will be protected from potential confounding factors.”
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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