Factorial Mendelian randomization: using genetic variants to assess interactions

AbstractBackgroundFactorial Mendelian randomization is the use of genetic variants to answer questions about interactions. Although the approach has been used in applied investigations, little methodological advice is available on how to design or perform a factorial Mendelian randomization analysis. Previous analyses have employed a 2 × 2 approach, using dichotomized genetic scores to divide the population into 4 subgroups as in a factorial randomized trial.MethodsWe describe two distinct contexts for factorial Mendelian randomization: investigating interactions between risk factors, and investigating interactions between pharmacological interventions on risk factors. We propose two-stage least squares methods using all available genetic variants and their interactions as instrumental variables, and using continuous genetic scores as instrumental variables rather than dichotomized scores. We illustrate our methods using data from UK Biobank to investigate the interaction between body mass index and alcohol consumption on systolic blood pressure.ResultsSimulated and real data show that efficiency is maximized using the full set of interactions between genetic variants as instruments. In the applied example, between four- and ten-fold improvement in efficiency is demonstrated over the 2 × 2 approach. Analyses using continuous genetic scores are more efficient than those using dichotomized scores. Efficiency is improved by finding genetic variants that divide the population at a natural break in the distribution of the risk factor, or else divide the population into more equal sized groups.ConclusionsPrevious factorial Mendelian randomization analyses may have been under-powered. Efficiency can be improved by using all genetic variants and their interactions as instrumental variables, rather than the 2 × 2 approach.Key messagesFactorial Mendelian randomization is an extension of the Mendelian randomization paradigm to answer questions about interactions.There are two contexts in which factorial Mendelian randomization can be used: for investigating interactions between risk factors, and interactions between pharmacological interventions on risk factors.While most applications of factorial Mendelian randomization have dichotomized the population as in a 2 × 2 factorial randomized trial, this approach is generally inefficient for detecting statistical interactions.In the first context, efficiency is maximized by including all genetic variants and their cross-terms as instrumental variables for the two risk factors and their product term.In the second context, efficiency is maximized by using continuous genetic scores rather than dichotomized scores.

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Factorial Mendelian randomization: using genetic variants to assess interactions

International Journal of Epidemiology ◽

10.1093/ije/dyz161 ◽

2019 ◽

Vol 49 (4) ◽

pp. 1147-1158 ◽

Cited By ~ 6

Author(s):

Jessica M B Rees ◽

Christopher N Foley ◽

Stephen Burgess

Keyword(s):

Risk Factors ◽

Instrumental Variables ◽

Genetic Variants ◽

Mendelian Randomization ◽

Real Data ◽

Uk Biobank ◽

Pharmacological Interventions ◽

Natural Break ◽

Using Data ◽

Randomization Analysis

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Pleiotropy-robust Mendelian Randomization

10.1101/072603 ◽

2016 ◽

Cited By ~ 3

Author(s):

Hans van Kippersluis ◽

Cornelius A Rietveld

Keyword(s):

Sensitivity Analysis ◽

Instrumental Variables ◽

Genetic Variants ◽

Large Scale ◽

Mendelian Randomization ◽

Causal Effect ◽

Pleiotropic Effects ◽

List Type ◽

Exclusion Restriction ◽

The Uk

AbstractBackgroundThe potential of Mendelian Randomization studies is rapidly expanding due to (i) the growing power of GWAS meta-analyses to detect genetic variants associated with several exposures, and (ii) the increasing availability of these genetic variants in large-scale surveys. However, without a proper biological understanding of the pleiotropic working of genetic variants, a fundamental assumption of Mendelian Randomization (the exclusion restriction) can always be contested.MethodsWe build upon and synthesize recent advances in the econometric literature on instrumental variables (IV) estimation that test and relax the exclusion restriction. Our Pleiotropy-robust Mendelian Randomization (PRMR) method first estimates the degree of pleiotropy, and in turn corrects for it. If a sample exists for which the genetic variants do not affect the exposure, and pleiotropic effects are homogenous, PRMR obtains unbiased estimates of causal effects in case of pleiotropy.ResultsSimulations show that existing MR methods produce biased estimators for realistic forms of pleiotropy. Under the aforementioned assumptions, PRMR produces unbiased estimators. We illustrate the practical use of PRMR by estimating the causal effect of (i) cigarettes smoked per day on Body Mass Index (BMI); (ii) prostate cancer on self-reported health, and (iii) educational attainment on BMI in the UK Biobank data.ConclusionsPRMR allows for instrumental variables that violate the exclusion restriction due to pleiotropy, and corrects for pleiotropy in the estimation of the causal effect. If the degree of pleiotropy is unknown, PRMR can still be used as a sensitivity analysis.Key messagesIf genetic variants have pleiotropic effects, causal estimates of Mendelian Randomization studies will be biased.Pleiotropy-robust Mendelian Randomization (PRMR) produces unbiased causal estimates in case (i) a subsample can be identified for which the genetic variants do not affect the exposure, and (ii) pleiotropic effects are homogenous.If such a subsample does not exist, PRMR can still routinely be reported as a sensitivity analysis in any MR analysis.If pleiotropic effects are not homogenous, PRMR can be used as an informal test to gauge the exclusion restriction.

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Bias in two-sample Mendelian randomization when using heritable covariable-adjusted summary associations

10.1101/816363 ◽

2019 ◽

Cited By ~ 5

Author(s):

Fernando Pires Hartwig ◽

Kate Tilling ◽

George Davey Smith ◽

Deborah A Lawlor ◽

Maria Carolina Borges

Keyword(s):

Waist Circumference ◽

Simulation Study ◽

Genetic Variants ◽

Mendelian Randomization ◽

Real Data ◽

Effect Estimate ◽

List Type ◽

Genome Wide Association Studies ◽

Genome Wide ◽

Residual Confounding

AbstractBackgroundTwo-sample Mendelian randomization (MR) allows the use of freely accessible summary association results from genome-wide association studies (GWAS) to estimate causal effects of modifiable exposures on outcomes. Some GWAS adjust for heritable covariables in an attempt to estimate direct effects of genetic variants on the trait of interest. One, both or neither of the exposure GWAS and outcome GWAS may have been adjusted for covariables.MethodsWe performed a simulation study comprising different scenarios that could motivate covariable adjustment in a GWAS and analysed real data to assess the influence of using covariable-adjusted summary association results in two-sample MR.ResultsIn the absence of residual confounding between exposure and covariable, between exposure and outcome, and between covariable and outcome, using covariable-adjusted summary associations for two-sample MR eliminated bias due to horizontal pleiotropy. However, covariable adjustment led to bias in the presence of residual confounding (especially between the covariable and the outcome), even in the absence of horizontal pleiotropy (when the genetic variants would be valid instruments without covariable adjustment). In an analysis using real data from the Genetic Investigation of ANthropometric Traits (GIANT) consortium and UK Biobank, the causal effect estimate of waist circumference on blood pressure changed direction upon adjustment of waist circumference for body mass index.ConclusionsOur findings indicate that using covariable-adjusted summary associations in MR should generally be avoided. When that is not possible, careful consideration of the causal relationships underlying the data (including potentially unmeasured confounders) is required to direct sensitivity analyses and interpret results with appropriate caution.Key messagesSummary genetic associations from large genome-wide associations studies (GWAS) have been increasingly used in two-sample Mendelian randomization (MR) analyses.Many GWAS adjust for heritable covariates in an attempt to estimate direct genetic effects on the trait of interest.In an extensive simulation study, we demonstrate that using covariable-adjusted summary associations may bias MR analyses.The bias largely depends on the underlying causal structure, specially the presence of unmeasured common causes between the covariable and the outcome.Our findings indicate that using covariable-adjusted summary associations in MR should generally be avoided.

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P–374 Investigating causality of risk factors for miscarriage – a Mendelian randomization analysis

Human Reproduction ◽

10.1093/humrep/deab130.373 ◽

2021 ◽

Vol 36 (Supplement_1) ◽

Author(s):

J Painter ◽

T Laisk ◽

C Lindgren ◽

S Medland

Keyword(s):

Risk Factors ◽

Body Mass Index ◽

Risk Factor ◽

Instrumental Variables ◽

Genetic Variants ◽

Odds Ratio ◽

Mendelian Randomization ◽

Recurrent Miscarriage ◽

Coffee Consumption ◽

Smoking Initiation

Abstract Study question Do modifiable risk factors such as smoking, alcohol or coffee consumption, and adiposity causally increase the risk of sporadic or recurrent miscarriage? Summary answer We found evidence for a causal relationship between smoking initiation and sporadic miscarriage, but not for any other risk factor tested. What is known already Miscarriage is estimated to end between 10–25% of clinically confirmed pregnancies, and many observational studies have suggested numerous lifestyle factors, such as coffee and alcohol consumption, smoking and increased adiposity, may increase miscarriage risk. However, results are not always consistent across studies, and definitive causal relationships between various risk factors and miscarriage have not yet been demonstrated. Mendelian randomization utilizes genetic variants significantly associated with heritable risk factors (i.e. at P-values <5x10–8 in large genome-wide association studies) as instrumental variables to investigate causality of risk factors in population health outcomes. Study design, size, duration We conducted two-sample Mendelian randomization analyses to investigate causality of smoking (initiation and quantity), alcohol and coffee consumption (quantity), and adiposity (body mass index and waist-hip ratio) in sporadic and recurrent miscarriage. Data included in this study were taken from previously published summary genetic association statistics (betas, standard errors and P-values) from large-scale genome-wide association studies (GWAS) for each risk factor, and from our recently published GWAS of sporadic and recurrent miscarriage. Participants/materials, setting, methods Instrumental variables were constructed using 5–306 genetic variants significantly associated with the listed risk factors in published GWAS (minimum N = 178,000 individuals). Two instrumental variables were constructed per risk factor using data from different GWAS. Associations of the instrumental variables with miscarriage were investigated using summary association data from women of European ancestry included in our miscarriage GWAS, including 49,996 sporadic miscarriage cases and 174,109 female controls, and 750 recurrent miscarriage cases and 150,215 female controls. Main results and the role of chance We found a significant association between sporadic miscarriage and the instrumental variables for two smoking measures: smoking initiation (inverse variance weighted Odds Ratio = 1.17, 95% confidence intervals = 1.10–1.24, P = 2.7 x 10–07) and lifetime smoking (inverse variance weighted Odds Ratio = 1.22, 95% confidence intervals 1.11–1.35, P = 4.2x10–5). No other risk factors (smoking quantity, coffee or alcohol consumption, or BMI or waist-hip ratio) were associated with either sporadic or recurrent miscarriage. A priori power calculations considering the amount of phenotypic variance in each risk factor explained by the associated SNPs suggested our analysis to have at least 75% power to detect an association with Odds Ratio of 1.2 with sporadic miscarriage for analyses of body mass index, waist hip ratio and smoking initiation, quantity and the lifetime smoking measure, but that the alcohol and coffee consumption analyses were underpowered (4.9% and 48%, respectively). All analyses were underpowered for recurrent miscarriage given the small case sample size (N = 750). Limitations, reasons for caution While data utilised here come from large-scale GWAS including 1000s of individuals, genetic variants significantly associated with each risk factor currently explain small percentages (0.02–6%) of the variance in each trait. Larger GWAS for specific risk factors, and for sporadic and recurrent miscarriage, are required to clarify some published associations. Wider implications of the findings: We find no evidence of a causal link between adiposity and miscarriage, indicating that observational findings of increased miscarriage risk with increasing body mass index require further explanation. Significant associations between measures of ever-smoking and sporadic miscarriage highlights that no amount of smoking is safe in regards to miscarriage risk. Trial registration number Not applicable

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Bias in two-sample Mendelian randomization when using heritable covariable-adjusted summary associations

International Journal of Epidemiology ◽

10.1093/ije/dyaa266 ◽

2021 ◽

Author(s):

Fernando Pires Hartwig ◽

Kate Tilling ◽

George Davey Smith ◽

Deborah A Lawlor ◽

Maria Carolina Borges

Keyword(s):

Waist Circumference ◽

Genetic Variants ◽

Mendelian Randomization ◽

Causal Effect ◽

Association Studies ◽

Real Data ◽

Sensitivity Analyses ◽

Effect Estimate ◽

Genome Wide Association Studies ◽

Residual Confounding

Abstract Background Two-sample Mendelian randomization (MR) allows the use of freely accessible summary association results from genome-wide association studies (GWAS) to estimate causal effects of modifiable exposures on outcomes. Some GWAS adjust for heritable covariables in an attempt to estimate direct effects of genetic variants on the trait of interest. One, both or neither of the exposure GWAS and outcome GWAS may have been adjusted for covariables. Methods We performed a simulation study comprising different scenarios that could motivate covariable adjustment in a GWAS and analysed real data to assess the influence of using covariable-adjusted summary association results in two-sample MR. Results In the absence of residual confounding between exposure and covariable, between exposure and outcome, and between covariable and outcome, using covariable-adjusted summary associations for two-sample MR eliminated bias due to horizontal pleiotropy. However, covariable adjustment led to bias in the presence of residual confounding (especially between the covariable and the outcome), even in the absence of horizontal pleiotropy (when the genetic variants would be valid instruments without covariable adjustment). In an analysis using real data from the Genetic Investigation of ANthropometric Traits (GIANT) consortium and UK Biobank, the causal effect estimate of waist circumference on blood pressure changed direction upon adjustment of waist circumference for body mass index. Conclusions Our findings indicate that using covariable-adjusted summary associations in MR should generally be avoided. When that is not possible, careful consideration of the causal relationships underlying the data (including potentially unmeasured confounders) is required to direct sensitivity analyses and interpret results with appropriate caution.

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MR-LDP: a two-sample Mendelian randomization for GWAS summary statistics accounting for linkage disequilibrium and horizontal pleiotropy

NAR Genomics and Bioinformatics ◽

10.1093/nargab/lqaa028 ◽

2020 ◽

Vol 2 (2) ◽

Cited By ~ 2

Author(s):

Qing Cheng ◽

Yi Yang ◽

Xingjie Shi ◽

Kar-Fu Yeung ◽

Can Yang ◽

...

Keyword(s):

Risk Factors ◽

Linkage Disequilibrium ◽

Genetic Variants ◽

Mendelian Randomization ◽

Association Studies ◽

Alternative Methods ◽

Genome Wide Association Studies ◽

Summary Statistics ◽

Causal Relationships ◽

Disease Outcomes

Abstract The proliferation of genome-wide association studies (GWAS) has prompted the use of two-sample Mendelian randomization (MR) with genetic variants as instrumental variables (IVs) for drawing reliable causal relationships between health risk factors and disease outcomes. However, the unique features of GWAS demand that MR methods account for both linkage disequilibrium (LD) and ubiquitously existing horizontal pleiotropy among complex traits, which is the phenomenon wherein a variant affects the outcome through mechanisms other than exclusively through the exposure. Therefore, statistical methods that fail to consider LD and horizontal pleiotropy can lead to biased estimates and false-positive causal relationships. To overcome these limitations, we proposed a probabilistic model for MR analysis in identifying the causal effects between risk factors and disease outcomes using GWAS summary statistics in the presence of LD and to properly account for horizontal pleiotropy among genetic variants (MR-LDP) and develop a computationally efficient algorithm to make the causal inference. We then conducted comprehensive simulation studies to demonstrate the advantages of MR-LDP over the existing methods. Moreover, we used two real exposure–outcome pairs to validate the results from MR-LDP compared with alternative methods, showing that our method is more efficient in using all-instrumental variants in LD. By further applying MR-LDP to lipid traits and body mass index (BMI) as risk factors for complex diseases, we identified multiple pairs of significant causal relationships, including a protective effect of high-density lipoprotein cholesterol on peripheral vascular disease and a positive causal effect of BMI on hemorrhoids.

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Exploring and mitigating potential bias when genetic instrumental variables are associated with multiple non-exposure traits in Mendelian randomization

10.1101/19009605 ◽

2019 ◽

Cited By ~ 5

Author(s):

Qian Yang ◽

Eleanor Sanderson ◽

Kate Tilling ◽

M Carolina Borges ◽

Deborah A Lawlor

Keyword(s):

Population Structure ◽

Instrumental Variables ◽

Population Stratification ◽

Mendelian Randomization ◽

Mr Studies ◽

Sensitivity Analyses ◽

List Type ◽

Genome Wide Association Studies ◽

Inverse Association ◽

Genome Wide

AbstractBackgroundOur aim is to produce guidance on exploring and mitigating possible bias when genetic instrumental variables (IVs) associate with traits other than the exposure of interest in Mendelian randomization (MR) studies.MethodsWe use causal diagrams to illustrate scenarios that could result in IVs being related to (non-exposure) traits. We recommend that MR studies explore possible IV-non-exposure associations across a much wider range of traits than is usually the case. Where associations are found, confounding by population stratification should be assessed through adjusting for relevant population structure variables. To distinguish vertical from horizontal pleiotropy we suggest using bidirectional MR between the exposure and non-exposure traits and MR of the effect of the non-exposure traits on the outcome of interest. If vertical pleiotropy is plausible, standard MR methods should be unbiased. If horizontal pleiotropy is plausible, we recommend using multivariable MR to control for observed pleiotropic traits and conducting sensitivity analyses which do not require prior knowledge of specific invalid IVs or pleiotropic paths.ResultsWe applied our recommendations to an illustrative example of the effect of maternal insomnia on offspring birthweight in the UK Biobank. We found little evidence that unexpected IV-non-exposure associations were driven by population stratification. Three out of six observed non-exposure traits plausibly reflected horizontal pleiotropy. Multivariable MR and sensitivity analyses suggested an inverse association of insomnia with birthweight, but effects were imprecisely estimated in some of these analyses.ConclusionsWe provide guidance for MR studies where genetic IVs associate with non-exposure traits.Key messagesGenetic variants are increasingly found to associate with more than one social, behavioural or biological trait at genome-wide significance, which is a challenge in Mendelian randomization (MR) studies.Four broad scenarios (i.e. population stratification, vertical pleiotropy, horizontal pleiotropy and reverse causality) could result in an IV-non-exposure trait association.Population stratification can be assessed through adjusting for population structure with individual data, while two-sample MR studies should check whether the original genome-wide association studies have used robust methods to properly account for it.We apply currently available MR methods for discriminating between vertical and horizontal pleiotropy and mitigating against horizontal pleiotropy to an example exploring the effect of maternal insomnia on offspring birthweight.Our study highlights the pros and cons of relying more on sensitivity analyses without considering particular pleiotropic paths versus systematically exploring and controlling for potential pleiotropic paths via known characteristics.

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Evaluating causal associations between previously reported risk factors and epithelial ovarian cancer: a Mendelian randomization analysis

10.1101/472696 ◽

2018 ◽

Cited By ~ 1

Author(s):

James Yarmolinsky ◽

Caroline L Relton ◽

Artitaya Lophatananon ◽

Kenneth Muir ◽

Usha Menon ◽

...

Keyword(s):

Risk Factors ◽

Ovarian Cancer ◽

Cancer Risk ◽

Epithelial Ovarian Cancer ◽

Genetic Variants ◽

Mendelian Randomization ◽

Modifiable Risk Factors ◽

Ovarian Cancer Risk ◽

Genetic Liability ◽

Suggestive Evidence

AbstractBackgroundVarious modifiable risk factors have been associated with epithelial ovarian cancer risk in observational epidemiological studies. However, the causal nature of the risk factors reported, and thus their suitability as effective intervention targets, is unclear given the susceptibility of conventional observational designs to residual confounding and reverse causation. Mendelian randomization uses genetic variants as proxies for modifiable risk factors to strengthen causal inference in observational studies. We used Mendelian randomization to evaluate the causal role of 13 previously reported risk factors (reproductive, anthropometric, clinical, lifestyle, and molecular factors) in overall and histotype-specific epithelial ovarian cancer in up to 25,509 case subjects and 40,941 controls in the Ovarian Cancer Association Consortium.Methods and FindingsGenetic instruments to proxy 13 risk factors were constructed by identifying single nucleotide polymorphisms (SNPs) robustly (P<5×10−8) and independently associated with each respective risk factor in previously reported genome-wide association studies. SNPs were combined into multi-allelic inverse-variance weighted fixed or random-effects models to generate causal estimates. Three complementary sensitivity analyses were performed to examine violations of Mendelian randomization assumptions: MR-Egger regression and weighted median and mode estimators. A Bonferroni-corrected P-value threshold was used to establish “strong evidence” (P<0.0038) and “suggestive evidence” (0.0038<P<0.05) for associations.In Mendelian randomization analyses, there was strong or suggestive evidence that 9 of 13 risk factors had a causal effect on overall or histotype-specific epithelial ovarian cancer. There was strong evidence that genetic liability to endometriosis increased risk of epithelial ovarian cancer (OR per log odds higher liability:1.27, 95% CI: 1.16-1.40; P=6.94×10−7) and suggestive evidence that lifetime smoking exposure increased risk of epithelial ovarian cancer (OR per unit increase in smoking score:1.36, 95% CI: 1.04-1.78; P=0.02). In histotype-stratified analyses, the strongest associations found were between: height and clear cell carcinoma (OR per SD increase:1.36, 95% CI: 1.15-1.61; P=0.0003); age at natural menopause and endometrioid carcinoma (OR per year later onset:1.09, 95% CI: 1.02-1.16; P=0.007); and genetic liability to polycystic ovary syndrome and endometrioid carcinoma (OR per log odds higher liability:0.74, 95% CI:0.62-0.90; P=0.002). There was little evidence for an effect of genetic liability to type 2 diabetes, parity, or circulating levels of 25-hydroxyvitamin D and sex hormone-binding globulin on ovarian cancer or its subtypes. The primary limitations of this analysis include: modest statistical power for analyses of risk factors in relation to some less common ovarian cancer histotypes (low grade serous, mucinous, and clear cell carcinomas), the inability to directly examine the causal effects of some ovarian cancer risk factors that did not have robust genetic variants available to serve as proxies (e.g., oral contraceptives, hormone replacement therapy), and the assumption of linear relationships between risk factors and ovarian cancer risk.ConclusionsOur comprehensive examination of possible etiological drivers of ovarian carcinogenesis using germline genetic variants to proxy risk factors supports a causal role for few of these factors in epithelial ovarian cancer and suggests distinct etiologies across histotypes. The identification of novel modifiable risk factors remains an important priority for the control of epithelial ovarian cancer.

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Model Checking via Testing for Direct Effects in Mendelian Randomization and Transcriptome-wide Association Studies

10.1101/2021.07.09.451811 ◽

2021 ◽

Author(s):

Yangqing Deng ◽

Wei Pan

Keyword(s):

Model Checking ◽

Genetic Variants ◽

Statistical Power ◽

Mendelian Randomization ◽

Association Studies ◽

Real Data ◽

Direct Effects ◽

Statistical Efficiency ◽

Challenging Situation ◽

High Statistical Power

It is of great interest and potential to discover causal relationships between pairs of exposures and outcomes using genetic variants as instrumental variables (IVs) to deal with hidden confounding in observational studies. Two most popular approaches are Mendelian randomization (MR), which usually use independent genetic variants/SNPs across the genome, and transcriptome-wide association studies (TWAS) using cis-SNPs local to a gene, as IVs. In spite of their many promising applications, both approaches face a major challenge: the validity of their causal conclusions depends on three critical assumptions on valid IVs, which however may not hold in practice. The most likely as well as challenging situation is due to the wide-spread horizontal pleiotropy, leading to two of three IV assumptions being violated and thus to biased statistical inference. Although some methods have been proposed as being robust to various degrees to the violation of some modeling assumptions, they often give different and even conflicting results due to their own modeling assumptions and possibly lower statistical efficiency, imposing difficulties to the practitioner in choosing and interpreting varying results across different methods. Hence, it would help to directly test whether any assumption is violated or not. In particular, there is a lack of such tests for TWAS. We propose a new and general GOF test, called TEDE (TEsting Direct Effects), applicable to both correlated and independent SNPs/IVs (as commonly used in TWAS and MR respectively). Through simulation studies and real data examples, we demonstrate high statistical power and advantages of our new method, while confirming the frequent violation of modeling (including IV) assumptions in practice and thus the importance of model checking by applying such a test in MR/TWAS analysis.

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Using multiple genetic variants as instrumental variables for modifiable risk factors

Statistical Methods in Medical Research ◽

10.1177/0962280210394459 ◽

2011 ◽

Vol 21 (3) ◽

pp. 223-242 ◽

Cited By ~ 212

Author(s):

Tom M Palmer ◽

Debbie A Lawlor ◽

Roger M Harbord ◽

Nuala A Sheehan ◽

Jon H Tobias ◽

...

Keyword(s):

Risk Factors ◽

Risk Factor ◽

Missing Data ◽

Instrumental Variables ◽

Genetic Variants ◽

Association Studies ◽

Mendelian Randomisation ◽

Modifiable Risk Factors ◽

Genome Wide Association Studies ◽

Finite Sample

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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