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'.

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.

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.

Mendelian randomization studies do not support a role for raised circulating triglyceride levels influencing type 2 diabetes, glucose levels, or insulin resistance.

OBJECTIVE: The causal nature of associations between circulating triglycerides, insulin resistance, and type 2 diabetes is unclear. We aimed to use Mendelian randomization to test the hypothesis that raised circulating triglyceride levels causally influence the risk of type 2 diabetes and raise normal fasting glucose levels and hepatic insulin resistance. RESEARCH DESIGN AND METHODS: We tested 10 common genetic variants robustly associated with circulating triglyceride levels against the type 2 diabetes status in 5,637 case and 6,860 control subjects and four continuous outcomes (reflecting glycemia and hepatic insulin resistance) in 8,271 nondiabetic individuals from four studies. RESULTS: Individuals carrying greater numbers of triglyceride-raising alleles had increased circulating triglyceride levels (SD 0.59 [95% CI 0.52-0.65] difference between the 20% of individuals with the most alleles and the 20% with the fewest alleles). There was no evidence that the carriers of greater numbers of triglyceride-raising alleles were at increased risk of type 2 diabetes (per weighted allele odds ratio [OR] 0.99 [95% CI 0.97-1.01]; P = 0.26). In nondiabetic individuals, there was no evidence that carriers of greater numbers of triglyceride-raising alleles had increased fasting insulin levels (SD 0.00 per weighted allele [95% CI -0.01 to 0.02]; P = 0.72) or increased fasting glucose levels (0.00 [-0.01 to 0.01]; P = 0.88). Instrumental variable analyses confirmed that genetically raised circulating triglyceride levels were not associated with increased diabetes risk, fasting glucose, or fasting insulin and, for diabetes, showed a trend toward a protective association (OR per 1-SD increase in log(10) triglycerides: 0.61 [95% CI 0.45-0.83]; P = 0.002). CONCLUSIONS: Genetically raised circulating triglyceride levels do not increase the risk of type 2 diabetes or raise fasting glucose or fasting insulin levels in nondiabetic individuals. One explanation for our results is that raised circulating triglycerides are predominantly secondary to the diabetes disease process rather than causal.

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.

Genetic variation at the SLC23A1 locus is associated with circulating concentrations of L-ascorbic acid (vitamin C): evidence from 5 independent studies with >15,000 participants.

BACKGROUND: L-ascorbic acid is an essential part of the human diet and has been associated with a wide range of chronic complex diseases, including cardiovascular outcomes. To date, there are no confirmed genetic correlates of circulating concentrations of L-ascorbic acid. OBJECTIVE: We aimed to confirm the existence of an association between common variation at the SLC23A1 gene locus and circulating concentrations of L-ascorbic acid. DESIGN: We used a 2-stage design, which included a discovery cohort (the British Women's Heart and Health Study), a series of follow-up cohorts, and meta-analysis (totaling 15,087 participants) to assess the relation between variation at SLC23A1 and circulating concentrations of L-ascorbic acid. RESULTS: In the discovery cohort, variation at rs33972313 was associated with a reduction in circulating concentrations of L-ascorbic acid (-4.15 micromol/L; 95% CI: -0.49, -7.81 micromol/L; P = 0.03 reduction per minor allele). Pooled analysis of the relation between rs33972313 and circulating L-ascorbic acid across all studies confirmed this and showed that each additional rare allele was associated with a reduction in circulating concentrations of L-ascorbic acid of -5.98 micromol/L (95% CI: -8.23, -3.73 micromol/L; P = 2.0 x 10(-7) per minor allele). CONCLUSIONS: A genetic variant (rs33972313) in the SLC23A1 vitamin C active transporter locus was identified that is reliably associated with circulating concentrations of L-ascorbic acid in the general population. This finding has implications more generally for the epidemiologic investigation of relations between circulating L-ascorbic acid and health outcomes.

Can lactase persistence genotype be used to reassess the relationship between renal cell carcinoma and milk drinking? Potentials and problems in the application of Mendelian randomization.

BACKGROUND: Increased risk of renal cell carcinoma (RCC) with milk consumption has been reported from observational studies. Whether this represents a causal association or is a result of confounding or bias is unclear. We assessed the potential for using genetic variation in lactase persistence as a tool for the study of this relationship. METHODS: Using a large, hospital-based case-control study, we used observational, phenotypic, and genetic data to determine whether the MCM6 -13910 C/T(rs4988235) variant may be used as a nonconfounded and unbiased marker for milk consumption. RESULTS: Consumption of milk during adulthood was associated with increased risk of RCC [odds ratio (OR), 1.35; 95% confidence interval (95% CI), 1.03-1.76; P=0.03]. Among controls, consumption of milk was associated with the lactase persistence genotype at rs4988235 (OR, 2.39; 95% CI, 1.81-3.15; P=6.9x10(-10)); however, the same genotype was not associated with RCC (OR, 1.01; 95% CI, 0.83-1.22; P=0.9). In controls, milk consumption was associated with confounding factors, including smoking and educational attainment, whereas genotypes at rs4988235 showed negligible association with confounding factors. CONCLUSION: The absence of an association between the MCM6 genotype and RCC suggests that observational associations between milk consumption and RCC may be due to confounding or bias. IMPACT: Although these data suggest that associations between milk consumption and RCC may be spurious, if the association between genotype and behavioral exposure is weak, then the power of this test may be low. The nature of intermediate risk factor instrumentation is an important consideration in the undertaking and interpretation of this type of causal analysis experiment.

The association of C-reactive protein and CRP genotype with coronary heart disease: findings from five studies with 4,610 cases amongst 18,637 participants.

BACKGROUND: It is unclear whether C-reactive protein (CRP) is causally related to coronary heart disease (CHD). Genetic variants that are known to be associated with CRP levels can be used to provide causal inference of the effect of CRP on CHD. Our objective was to examine the association between CRP genetic variant +1444C>T (rs1130864) and CHD risk in the largest study to date of this association. METHODS AND RESULTS: We estimated the association of CRP genetic variant +1444C>T (rs1130864) with CRP levels and with CHD in five studies and then pooled these analyses (N = 18,637 participants amongst whom there were 4,610 cases). CRP was associated with potential confounding factors (socioeconomic position, physical activity, smoking and body mass) whereas genotype (rs1130864) was not associated with these confounders. The pooled odds ratio of CHD per doubling of circulating CRP level after adjustment for age and sex was 1.13 (95%CI: 1.06, 1.21), and after further adjustment for confounding factors it was 1.07 (95%CI: 1.02, 1.13). Genotype (rs1130864) was associated with circulating CRP; the pooled ratio of geometric means of CRP level among individuals with the TT genotype compared to those with the CT/CC genotype was 1.21 (95%CI: 1.15, 1.28) and the pooled ratio of geometric means of CRP level per additional T allele was 1.14 (95%CI: 1.11, 1.18), with no strong evidence in either analyses of between study heterogeneity (I(2) = 0%, p>0.9 for both analyses). There was no association of genotype (rs1130864) with CHD: pooled odds ratio 1.01 (95%CI: 0.88, 1.16) comparing individuals with TT genotype to those with CT/CC genotype and 0.96 (95%CI: 0.90, 1.03) per additional T allele (I(2)<7.5%, p>0.6 for both meta-analyses). An instrumental variables analysis (in which the proportion of CRP levels explained by rs1130864 was related to CHD) suggested that circulating CRP was not associated with CHD: the odds ratio for a doubling of CRP level was 1.04 (95%CI: 0.61, 1.80). CONCLUSIONS: We found no association of a genetic variant, which is known to be related to CRP levels, (rs1130864) and having CHD. These findings do not support a causal association between circulating CRP and CHD risk, but very large, extended, genetic association studies would be required to rule this out.

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.

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.

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.

An empirical comparison of methods for meta-analysis of diagnostic accuracy showed hierarchical models are necessary.

OBJECTIVE: Meta-analysis of studies of the accuracy of diagnostic tests currently uses a variety of methods. Statistically rigorous hierarchical models require expertise and sophisticated software. We assessed whether any of the simpler methods can in practice give adequately accurate and reliable results. STUDY DESIGN AND SETTING: We reviewed six methods for meta-analysis of diagnostic accuracy: four simple commonly used methods (simple pooling, separate random-effects meta-analyses of sensitivity and specificity, separate meta-analyses of positive and negative likelihood ratios, and the Littenberg-Moses summary receiver operating characteristic [ROC] curve) and two more statistically rigorous approaches using hierarchical models (bivariate random-effects meta-analysis and hierarchical summary ROC curve analysis). We applied the methods to data from a sample of eight systematic reviews chosen to illustrate a variety of patterns of results. RESULTS: In each meta-analysis, there was substantial heterogeneity between the results of different studies. Simple pooling of results gave misleading summary estimates of sensitivity and specificity in some meta-analyses, and the Littenberg-Moses method produced summary ROC curves that diverged from those produced by more rigorous methods in some situations. CONCLUSION: The closely related hierarchical summary ROC curve or bivariate models should be used as the standard method for meta-analysis of diagnostic accuracy.

Mendelian randomization: using genes as instruments for making causal inferences in epidemiology.

Observational epidemiological studies suffer from many potential biases, from confounding and from reverse causation, and this limits their ability to robustly identify causal associations. Several high-profile situations exist in which randomized controlled trials of precisely the same intervention that has been examined in observational studies have produced markedly different findings. In other observational sciences, the use of instrumental variable (IV) approaches has been one approach to strengthening causal inferences in non-experimental situations. The use of germline genetic variants that proxy for environmentally modifiable exposures as instruments for these exposures is one form of IV analysis that can be implemented within observational epidemiological studies. The method has been referred to as 'Mendelian randomization', and can be considered as analogous to randomized controlled trials. This paper outlines Mendelian randomization, draws parallels with IV methods, provides examples of implementation of the approach and discusses limitations of the approach and some methods for dealing with these.

A unification of models for meta-analysis of diagnostic accuracy studies.

Studies of diagnostic accuracy require more sophisticated methods for their meta-analysis than studies of therapeutic interventions. A number of different, and apparently divergent, methods for meta-analysis of diagnostic studies have been proposed, including two alternative approaches that are statistically rigorous and allow for between-study variability: the hierarchical summary receiver operating characteristic (ROC) model (Rutter and Gatsonis, 2001) and bivariate random-effects meta-analysis (van Houwelingen and others, 1993), (van Houwelingen and others, 2002), (Reitsma and others, 2005). We show that these two models are very closely related, and define the circumstances in which they are identical. We discuss the different forms of summary model output suggested by the two approaches, including summary ROC curves, summary points, confidence regions, and prediction regions.

Meta-analyses of observational and genetic association studies of folate intakes or levels and breast cancer risk.

BACKGROUND: Evidence from case-control studies suggests that increasing dietary folate intake is associated with a reduced risk of breast cancer. However, large cohort studies have found no such association, and animal studies suggest that folate supplementation may promote tumorigenesis. We conducted a meta-analysis to summarize the available evidence from observational studies on this issue and a meta-analysis of the association between a common polymorphism in the 5,10-methylenetetrahydrofolate reductase (MTHFR) gene, a key enzyme in folate metabolism, and breast cancer risk. METHODS: We searched Medline and ISI Web of Knowledge databases for relevant studies that were published through May 31, 2006. We used random-effects analysis to calculate odds ratios (ORs) for case-control studies or relative risks (RRs) for cohort studies for a 100-microg/d increase in folate intake. Unadjusted odds ratios were calculated for the studies of MTHFR genotype based on published genotype frequencies. RESULTS: A total of 13 case-control studies and nine cohort studies were included in the meta-analysis of folate intake and breast cancer risk. We found a summary OR of 0.91 (95% confidence interval [CI] = 0.87 to 0.96) from the case-control studies and a summary RR of 0.99 (95% CI = 0.98 to 1.01) from the cohort studies for a 100-microg/d increase in folate intake. We found evidence that the case-control studies may have suffered from substantial publication bias. The case-control and cohort studies may have been subject to measurement error, confounding, and possibly spurious associations arising from subgroup analyses; in addition, the case-control studies were potentially subject to recall bias and publication bias. Seventeen studies were included in the meta-analysis of MTHFR C677T genotype and breast cancer risk. We found no difference in breast cancer risk between MTHFR 677 TT homozygotes and CC homozygotes (OR = 1.05, 95% CI = 0.88 to 1.25), and there was no evidence of an interaction between folate intake and MTHFR genotype on breast cancer risk. CONCLUSION: A lack of dietary folate intake is not associated with the risk of breast cancer.