Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies.

Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in meta-analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype-disease log odds ratio by the difference in mean exposure between genotypes. This 'Wald-type' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large-sample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple data-generating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual-level data they require are available. The Wald-type estimator may retain a role as an approximate method for meta-analysis based on summary data.

Is MRI better than CT for detecting a vascular component to dementia? A systematic review and meta-analysis.

BACKGROUND: Identification of causes of dementia soon after symptom onset is important, because appropriate treatment of some causes of dementia can slow or halt its progression or enable symptomatic treatment where appropriate. The accuracy of MRI and CT, and whether MRI is superior to CT, in detecting a vascular component to dementia in autopsy confirmed and clinical cohorts of patients with VaD, combined AD and VaD ("mixed dementia"), and AD remain unclear. We conducted a systematic review and meta-analysis to investigate this question. METHODS: We searched eight databases and screened reference lists to identify studies addressing the review question. We assessed study quality using QUADAS. We estimated summary diagnostic accuracy according to imaging finding, and ratios of diagnostic odds ratios (RDORs) for MRI versus CT and high versus low risk of bias. RESULTS: We included 7 autopsy and 31 non-autopsy studies. There was little evidence that selective patient enrolment and risk of incorporation bias impacted on diagnostic accuracy (p = 0.12 to 0.95). The most widely reported imaging finding was white matter hyperintensities. For CT (11 studies) summary sensitivity and specificity were 71% (95% CI 53%-85%) and 55% (44%-66%). Corresponding figures for MRI (6 studies) were 95% (87%-98%) and 26% (12%-50%). General infarcts was the most specific imaging finding on MRI (96%; 95% CI 94%-97%) and CT (96%; 93%-98%). However, sensitivity was low for both MRI (53%; 36%-70%) and CT (52%; 22% to 80%). No imaging finding had consistently high sensitivity. Based on non-autopsy studies, MRI was more accurate than CT for six of seven imaging findings, but confidence intervals were wide. CONCLUSION: There is insufficient evidence to suggest that MRI is superior to CT with respect to identifying cerebrovascular changes in autopsy-confirmed and clinical cohorts of VaD, AD, and 'mixed dementia'.

Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses.

In this paper, the authors describe different instrumental variable (IV) estimators of causal risk ratios and odds ratios with particular attention to methods that can handle continuously measured exposures. The authors present this discussion in the context of a Mendelian randomization analysis of the effect of body mass index (BMI; weight (kg)/height (m)(2)) on the risk of asthma at age 7 years (Avon Longitudinal Study of Parents and Children, 1991-1992). The authors show that the multiplicative structural mean model (MSMM) and the multiplicative generalized method of moments (MGMM) estimator produce identical estimates of the causal risk ratio. In the example, MSMM and MGMM estimates suggested an inverse relation between BMI and asthma but other IV estimates suggested a positive relation, although all estimates had wide confidence intervals. An interaction between the associations of BMI and fat mass and obesity-associated (FTO) genotype with asthma explained the different directions of the different estimates, and a simulation study supported the observation that MSMM/MGMM estimators are negatively correlated with the other estimators when such an interaction is present. The authors conclude that point estimates from various IV methods can differ in practical applications. Based on the theoretical properties of the estimators, structural mean models make weaker assumptions than other IV estimators and can therefore be expected to be consistent in a wider range of situations.

Using genetic loci to understand the relationship between adiposity and psychological distress: a Mendelian Randomization study in the Copenhagen General Population Study of 53,221 adults.

OBJECTIVE: We used genetic variants that are robustly associated with adiposity to examine the causal association of adiposity with psychological distress. METHODS: We examined the association of adiposity with psychological distress in a large (N = 53,221) general population cohort of 20- to 99-year-old adults from Copenhagen, Denmark. Psychological distress was assessed using four questions that asked about: feeling stressed; not accomplishing very much; wanting to give up; and regular use of antidepressants/sedatives. We used the genetic loci FTO rs9939609 and MC4R rs17782313 as instrumental variables for adiposity quantified by body mass index (BMI) and waist to hip ratio (WHR). RESULTS: In conventional multivariable analyses, BMI and WHR were positively associated with distress. For example, the odds ratio of reporting not accomplishing for each additional standard deviation increase for BMI was 1.11 (95% CI: 1.09, 1.13) and for WHR was 1.10 (95% CI: 1.08, 1.13) in the fully adjusted analyses. In contrast, instrumental variable analyses showed an inverse association of adiposity on distress; corresponding odds ratio in instrumental variable analyses was 0.64 (95% CI: 0.46, 0.89) for BMI and 0.49 (95% CI: 0.25, 0.94) for WHR (P-values for difference between the two approaches both = 0.001). CONCLUSION: The inverse associations of adiposity and psychological distress when genetic variants are used as instrumental variables could be explained by biological pathways linking adiposity and distress. The positive associations of adiposity with distress in multivariable analyses might be explained by residual confounding or reverse causality.

Systematic review: accuracy of anti-citrullinated Peptide antibodies for diagnosing rheumatoid arthritis.

BACKGROUND: Early recognition and treatment of rheumatoid arthritis is important to prevent irreversible joint damage. Anti-citrullinated peptide antibodies (ACPA) have been suggested for early diagnosis. PURPOSE: To compare the accuracy of ACPA and rheumatoid factor in diagnosing rheumatoid arthritis in patients with early symptoms of the disease. DATA SOURCES: 10 medical databases from inception to September 2009, with no language or publication restrictions, and references of included studies. STUDY SELECTION: Two independent reviewers screened searches. Full articles were assessed by one reviewer and checked by a second reviewer to identify studies that reported 2 x 2 data on ACPA for the diagnosis of rheumatoid arthritis (by 1987 American College of Rheumatology criteria). DATA EXTRACTION: One reviewer abstracted data on patient characteristics, ACPA details, and 2 x 2 data and assessed study quality by using the QUADAS tool. A second reviewer checked extractions. DATA SYNTHESIS: 151 studies were included, with considerable heterogeneity in sensitivity (range, 12% to 93%) and specificity (range, 63% to 100%). In cohort studies that investigated second-generation anti-cyclic citrullinated peptide antibodies (anti-CCP2) in patients with early rheumatoid arthritis (<2 years), summary sensitivity and specificity were 57% (95% CI, 51% to 63%) and 96% (CI, 93% to 97%), respectively. Case-control and cross-sectional studies and studies of patients with established rheumatoid arthritis all overestimated sensitivity. Anti-CCP2 had greater specificity than rheumatoid factor (96% vs. 86%), with similar sensitivity. Evidence was insufficient to ascertain whether the combination of anti-CCP2 and rheumatoid factor provides additional benefit over anti-CCP2 alone. LIMITATIONS: Most studies used a diagnostic case-control design, which overestimated sensitivity. Items relating to study quality were rarely reported. Publication bias could not be assessed. CONCLUSION: Anti-CCP2 should be included in the work-up of patients with early symptoms of rheumatoid arthritis.

Alcohol intake and blood pressure: a systematic review implementing a Mendelian randomization approach.

BACKGROUND: Alcohol has been reported to be a common and modifiable risk factor for hypertension. However, observational studies are subject to confounding by other behavioural and sociodemographic factors, while clinical trials are difficult to implement and have limited follow-up time. Mendelian randomization can provide robust evidence on the nature of this association by use of a common polymorphism in aldehyde dehydrogenase 2 (ALDH2) as a surrogate for measuring alcohol consumption. ALDH2 encodes a major enzyme involved in alcohol metabolism. Individuals homozygous for the null variant (*2*2) experience adverse symptoms when drinking alcohol and consequently drink considerably less alcohol than wild-type homozygotes (*1*1) or heterozygotes. We hypothesise that this polymorphism may influence the risk of hypertension by affecting alcohol drinking behaviour. METHODS AND FINDINGS: We carried out fixed effect meta-analyses of the ALDH2 genotype with blood pressure (five studies, n = 7,658) and hypertension (three studies, n = 4,219) using studies identified via systematic review. In males, we obtained an overall odds ratio of 2.42 (95% confidence interval [CI] 1.66-3.55, p = 4.8 x 10(-6)) for hypertension comparing *1*1 with *2*2 homozygotes and an odds ratio of 1.72 (95% CI 1.17-2.52, p = 0.006) comparing heterozygotes (surrogate for moderate drinkers) with *2*2 homozygotes. Systolic blood pressure was 7.44 mmHg (95% CI 5.39-9.49, p = 1.1 x 10(-12)) greater among *1*1 than among *2*2 homozygotes, and 4.24 mmHg (95% CI 2.18-6.31, p = 0.00005) greater among heterozygotes than among *2*2 homozygotes. CONCLUSIONS: These findings support the hypothesis that alcohol intake has a marked effect on blood pressure and the risk of hypertension.

Exploring the developmental overnutrition hypothesis using parental-offspring associations and FTO as an instrumental variable.

BACKGROUND: The developmental overnutrition hypothesis suggests that greater maternal obesity during pregnancy results in increased offspring adiposity in later life. If true, this would result in the obesity epidemic progressing across generations irrespective of environmental or genetic changes. It is therefore important to robustly test this hypothesis. METHODS AND FINDINGS: We explored this hypothesis by comparing the associations of maternal and paternal pre-pregnancy body mass index (BMI) with offspring dual energy X-ray absorptiometry (DXA)-determined fat mass measured at 9 to 11 y (4,091 parent-offspring trios) and by using maternal FTO genotype, controlling for offspring FTO genotype, as an instrument for maternal adiposity. Both maternal and paternal BMI were positively associated with offspring fat mass, but the maternal association effect size was larger than that in the paternal association in all models: mean difference in offspring sex- and age-standardised fat mass z-score per 1 standard deviation BMI 0.24 (95% confidence interval [CI]: 0.22 to 0.26) for maternal BMI versus 0.13 (95% CI: 0.11, 0.15) for paternal BMI; p-value for difference in effect < 0.001. The stronger maternal association was robust to sensitivity analyses assuming levels of non-paternity up to 20%. When maternal FTO, controlling for offspring FTO, was used as an instrument for the effect of maternal adiposity, the mean difference in offspring fat mass z-score per 1 standard deviation maternal BMI was -0.08 (95% CI: -0.56 to 0.41), with no strong statistical evidence that this differed from the observational ordinary least squares analyses (p = 0.17). CONCLUSIONS: Neither our parental comparisons nor the use of FTO genotype as an instrumental variable, suggest that greater maternal BMI during offspring development has a marked effect on offspring fat mass at age 9-11 y. Developmental overnutrition related to greater maternal BMI is unlikely to have driven the recent obesity epidemic.

How much of the data published in observational studies of the association between diet and prostate or bladder cancer is usable for meta-analysis?

Epidemiologic investigations often report dose-response associations, which may be combined in meta-analyses. The authors examined how often the log odds, risk, or hazard ratio per unit increase in exposure, and its standard error, can be estimated from results reported from observational studies of diet and prostate or bladder cancer so that results are usable in meta-analyses estimating dose-response associations. Eight electronic databases were searched for studies reporting on the association of diet, nutrition, or physical activity with these cancers. A total of 767 papers reported 3,284 results; 1,999 (61%) results, reported in 545 (71%) papers, were usable in dose-response meta-analyses. The most important reason that results were not usable was the absence of sufficient information on exposure levels in the different groups. The proportion of results usable in "high-low" meta-analyses (comparisons of extreme categories) was similar (62%). Results that showed evidence of an association were more likely to be usable than results that found no such evidence. Insufficient detail in reporting of results of observational studies can lead to exclusion of these results from meta-analyses and is an important threat to the validity of systematic reviews of such research. Results providing evidence of associations may be overrepresented in meta-analyses of observational studies.

Graphical presentation of diagnostic information.

BACKGROUND: Graphical displays of results allow researchers to summarise and communicate the key findings of their study. Diagnostic information should be presented in an easily interpretable way, which conveys both test characteristics (diagnostic accuracy) and the potential for use in clinical practice (predictive value). METHODS: We discuss the types of graphical display commonly encountered in primary diagnostic accuracy studies and systematic reviews of such studies, and systematically review the use of graphical displays in recent diagnostic primary studies and systematic reviews. RESULTS: We identified 57 primary studies and 49 systematic reviews. Fifty-six percent of primary studies and 53% of systematic reviews used graphical displays to present results. Dot-plot or box-and- whisker plots were the most commonly used graph in primary studies and were included in 22 (39%) studies. ROC plots were the most common type of plot included in systematic reviews and were included in 22 (45%) reviews. One primary study and five systematic reviews included a probability-modifying plot. CONCLUSION: Graphical displays are currently underused in primary diagnostic accuracy studies and systematic reviews of such studies. Diagnostic accuracy studies need to include multiple types of graphic in order to provide both a detailed overview of the results (diagnostic accuracy) and to communicate information that can be used to inform clinical practice (predictive value). Work is required to improve graphical displays, to better communicate the utility of a test in clinical practice and the implications of test results for individual patients.

Evidence-based diagnosis.

Making an accurate diagnosis is essential to ensure that a patient receives appropriate treatment and correct information regarding their prognosis. Characteristics of diagnostic tests are quantified in test accuracy studies, but many such studies have methodological flaws. The HSRC evidence-based diagnosis programme has focused on methods for systematic reviews of test accuracy studies, and the wider context in which tests are ordered and interpreted. We carried out a range of projects relating to literature searching, quality assessment, meta-analysis, presentation of results, and interactions between doctors and patients during the diagnostic process. We have shown that systematic reviews of test accuracy studies should search a range of databases and that current diagnostic filters do not have sufficient accuracy to be used in test accuracy reviews. Summary quality scores should not be used in test accuracy reviews; the Quality Assessment of Studies of Diagnostic Accuracy included in Systematic Reviews (QUADAS) tool for assessing test accuracy studies is acceptable for quality assessment. We have shown that the hierarchical summary receiver operating characteristic (HSROC) and bivariate models for meta-analysis of test accuracy are statistically equivalent in many circumstances, and have developed an add-on module for the statistical software package Stata that enables these statistically rigorous models to be fitted by those without expert statistical knowledge. Three areas that would benefit from further research are literature searching, synthesis of results from individual patient data and presentation of results.

Clustered environments and randomized genes: a fundamental distinction between conventional and genetic epidemiology.

BACKGROUND: In conventional epidemiology confounding of the exposure of interest with lifestyle or socioeconomic factors, and reverse causation whereby disease status influences exposure rather than vice versa, may invalidate causal interpretations of observed associations. Conversely, genetic variants should not be related to the confounding factors that distort associations in conventional observational epidemiological studies. Furthermore, disease onset will not influence genotype. Therefore, it has been suggested that genetic variants that are known to be associated with a modifiable (nongenetic) risk factor can be used to help determine the causal effect of this modifiable risk factor on disease outcomes. This approach, mendelian randomization, is increasingly being applied within epidemiological studies. However, there is debate about the underlying premise that associations between genotypes and disease outcomes are not confounded by other risk factors. We examined the extent to which genetic variants, on the one hand, and nongenetic environmental exposures or phenotypic characteristics on the other, tend to be associated with each other, to assess the degree of confounding that would exist in conventional epidemiological studies compared with mendelian randomization studies. METHODS AND FINDINGS: We estimated pairwise correlations between nongenetic baseline variables and genetic variables in a cross-sectional study comparing the number of correlations that were statistically significant at the 5%, 1%, and 0.01% level (alpha = 0.05, 0.01, and 0.0001, respectively) with the number expected by chance if all variables were in fact uncorrelated, using a two-sided binomial exact test. We demonstrate that behavioural, socioeconomic, and physiological factors are strongly interrelated, with 45% of all possible pairwise associations between 96 nongenetic characteristics (n = 4,560 correlations) being significant at the p < 0.01 level (the ratio of observed to expected significant associations was 45; p-value for difference between observed and expected < 0.000001). Similar findings were observed for other levels of significance. In contrast, genetic variants showed no greater association with each other, or with the 96 behavioural, socioeconomic, and physiological factors, than would be expected by chance. CONCLUSIONS: These data illustrate why observational studies have produced misleading claims regarding potentially causal factors for disease. The findings demonstrate the potential power of a methodology that utilizes genetic variants as indicators of exposure level when studying environmentally modifiable risk factors.

C-reactive protein and its role in metabolic syndrome: mendelian randomisation study.

BACKGROUND: Circulating C-reactive protein (CRP) is associated with the metabolic syndrome and might be causally linked to it. Our aim was to generate estimates of the association between plasma CRP and metabolic syndrome phenotypes that were free from confounding and reverse causation, to assess the causal role of this protein. METHODS: We examined associations between serum CRP concentration and metabolic syndrome phenotypes in the British Women's Heart and Health Study. We then compared these estimates with those derived from a mendelian randomised framework with common CRP gene haplotypes to generate unconfounded and unbiased estimates of any causal associations. FINDINGS: In a sample of British women, body-mass index (BMI), systolic blood pressure, waist-to-hip ratio, serum concentrations of HDL cholesterol and triglycerides, and insulin resistance were all associated with plasma CRP concentration. CRP haplotypes were associated with plasma CRP concentration (p<0.0001). With instrumental variable analyses, there was no association between plasma CRP concentration and any of the metabolic syndrome phenotypes analysed. There was strong evidence that linear regression and mendelian randomisation based estimation gave conflicting results for the CRP-BMI association (p=0.0002), and some evidence of conflicting results for the association of CRP with the score for insulin resistance (p=0.0139), triglycerides (p=0.0313), and HDL cholesterol (p=0.0688). INTERPRETATION: Disparity between estimates of the association between plasma CRP and phenotypes comprising the metabolic syndrome derived from conventional analyses and those from a mendelian randomisation approach suggests that there is no causal association between CRP and the metabolic syndrome phenotypes.

Does elevated plasma fibrinogen increase the risk of coronary heart disease? Evidence from a meta-analysis of genetic association studies.

OBJECTIVE: The purpose of this study was to assess whether a genetic variant associated with higher fibrinogen levels is associated with increased coronary heart disease (CHD) risk, as a test of the causal influence of fibrinogen on CHD. METHODS AND RESULTS: We performed a meta-analysis of case-control and prospective studies of the G-455-->A and C-148-->T beta-fibrinogen promoter region variants, in relation to CHD risk. The 19 studies found included 12,393 cases and 21,649 controls. Fibrinogen levels were robustly related to the genetic variants (mean increase per allele, 0.117 g/L; 95% CI, 0.091-0.142 g/L). However, the genetic variants were unrelated to CHD risk (odds ratio per allele, 0.976; 95% CI, 0.916-1.040). The predicted causal odds ratio for a 1 g/L higher plasma fibrinogen level, given the genetic variant-fibrinogen and genetic variant-CHD associations, was 0.81 (95% CI, 0.46-1.40). CONCLUSIONS: Although imprecise, the predicted causal effect of fibrinogen on CHD is clearly different from the odds ratio of 1.8 (95% CI, 1.6-2.0) for an increase of 1 g/L derived from a meta-analysis of observational studies. This evidence suggests that lowering the fibrinogen level may not, in itself, reduce CHD risk.

Association of C-reactive protein with blood pressure and hypertension: life course confounding and mendelian randomization tests of causality.

BACKGROUND: C-reactive protein (CRP) has repeatedly been associated with blood pressure and prevalent and incident hypertension, but whether a causal link exists is uncertain. METHODS AND RESULTS: We assessed the cross-sectional relations of CRP to systolic blood pressure, pulse pressure, and prevalent hypertension in a representative sample of >3500 British women aged 60 to 79 years. For both outcomes, substantial associations were observed. However, these associations were greatly attenuated by adjustment for a wide range of confounding factors acting over the life course. We further investigated causality using a Mendelian randomization approach by examining the association of the 1059G/C polymorphism in the human CRP gene with CRP and with blood pressure, pulse pressure, and hypertension. The polymorphism was associated with a robust difference in CRP, and the expectation would be for higher blood pressure and pulse pressure and greater prevalence of hypertension among those carrying the genetic variant associated with higher CRP levels. This was not observed, and the predicted causal effects of CRP on blood pressure, pulse pressure, and hypertension using instrumental variables methods were close to 0, although with wide CIs. CONCLUSIONS: CRP levels are associated with blood pressure, pulse pressure, and hypertension, but adjustment for life course confounding and a Mendelian randomization approach suggest the elevated CRP levels do not lead to elevated blood pressure.

Likelihood-based estimation of microsatellite mutation rates.

Microsatellites are widely used in genetic analyses, many of which require reliable estimates of microsatellite mutation rates, yet the factors determining mutation rates are uncertain. The most straightforward and conclusive method by which to study mutation is direct observation of allele transmissions in parent-child pairs, and studies of this type suggest a positive, possibly exponential, relationship between mutation rate and allele size, together with a bias toward length increase. Except for microsatellites on the Y chromosome, however, previous analyses have not made full use of available data and may have introduced bias: mutations have been identified only where child genotypes could not be generated by transmission from parents' genotypes, so that the probability that a mutation is detected depends on the distribution of allele lengths and varies with allele length. We introduce a likelihood-based approach that has two key advantages over existing methods. First, we can make formal comparisons between competing models of microsatellite evolution; second, we obtain asymptotically unbiased and efficient parameter estimates. Application to data composed of 118,866 parent-offspring transmissions of AC microsatellites supports the hypothesis that mutation rate increases exponentially with microsatellite length, with a suggestion that contractions become more likely than expansions as length increases. This would lead to a stationary distribution for allele length maintained by mutational balance. There is no evidence that contractions and expansions differ in their step size distributions.

No role for quality scores in systematic reviews of diagnostic accuracy studies.

BACKGROUND: There is a lack of consensus regarding the use of quality scores in diagnostic systematic reviews. The objective of this study was to use different methods of weighting items included in a quality assessment tool for diagnostic accuracy studies (QUADAS) to produce an overall quality score, and to examine the effects of incorporating these into a systematic review. METHODS: We developed five schemes for weighting QUADAS to produce quality scores. We used three methods to investigate the effects of quality scores on test performance. We used a set of 28 studies that assessed the accuracy of ultrasound for the diagnosis of vesico-ureteral reflux in children. RESULTS: The different methods of weighting individual items from the same quality assessment tool produced different quality scores. The different scoring schemes ranked different studies in different orders; this was especially evident for the intermediate quality studies. Comparing the results of studies stratified as "high" and "low" quality based on quality scores resulted in different conclusions regarding the effects of quality on estimates of diagnostic accuracy depending on the method used to produce the quality score. A similar effect was observed when quality scores were included in meta-regression analysis as continuous variables, although the differences were less apparent. CONCLUSION: Quality scores should not be incorporated into diagnostic systematic reviews. Incorporation of the results of the quality assessment into the systematic review should involve investigation of the association of individual quality items with estimates of diagnostic accuracy, rather than using a combined quality score.

Using multiple genetic variants as instrumental variables for modifiable risk factors.

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.