Mendelian randomization using semiparametric linear transformation models

Mendelian randomization (MR) uses genetic information as an instrumental variable (IV) to estimate the causal effect of an exposure of interest on an outcome in the presence of unknown confounding. We are interested in the causal effect of cigarette smoking on lung cancer survival, which is subject to confounding by underlying pulmonary functions. Despite the well-developed IV analyses for the continuous and binary outcomes, the scarcity of methodology for the survival outcome limits its utility for the time-to-event data collected in many observational studies. We propose an IV analysis method in the survival context, estimating causal effects on a transformed survival time and survival probabilities using semiparametric linear transformation models. We study the conditions under which hazard ratio and the effect on survival probability can be approximated. For statistical inference, we construct estimating equations to circumvent the difficulty in deriving joint likelihood of the exposure and the outcome, due to the unknown confounding. Asymptotic properties of the proposed estimators are established without parametric assumptions about confounders. We study the finite sample performance in extensive simulation studies. The MR analysis of a lung cancer study suggests a harmful prognostic effect of smoking pack-years that would have been missed by the crude association.     

Mendelian randomization in nutritional epidemiology

Nutritional epidemiology aims to identify dietary and lifestyle causes for human diseases. Causality inference in nutritional epidemiology is largely based on evidence from studies of observational design, and may be distorted by unmeasured or residual confounding and reverse causation. Mendelian randomization is a recently developed methodology that combines genetic and classical epidemiological analysis to infer causality for environmental exposures, based on the principle of Mendel's law of independent assortment. Mendelian randomization uses genetic variants as proxies for environmental exposures of interest. Associations derived from Mendelian randomization analysis are less likely to be affected by confounding and reverse causation. During the past 5 years, a body of studies examined the causal effects of diet/lifestyle factors and biomarkers on a variety of diseases. The Mendelian randomization approach also holds considerable promise in the study of intrauterine influences on offspring health outcomes. However, the application of Mendelian randomization in nutritional epidemiology has some limitations.     

基于两样本孟德尔随机化方法分析血液代谢物与慢性肾病的因果关系

目的 利用孟德尔随机化方法,探究486种血液代谢物与慢性肾病的因果关系.方法 血液代谢物和慢性肾病全基因组关联分析汇总数据均来自于网络公开数据库,主要采用逆方差加权分析法(inverse-variance weighting,IVW),探究每种血液代谢物与慢性肾病之间的因果关系,并以MR-Egger回归、加权中位数法、...     

Insight into the nature of the CRP-coronary event association using Mendelian randomization

BACKGROUND: It is unclear wheather the association between C-reactive protein (CRP) and incident coronary events is free from bias and confounding. Individuals homozygous for a +1444C>T polymorphism in the CRP gene have higher circulating concentrations of CRP. Since the distribution of this polymorphism occurs at random during gamete formation, its association with coronary events should not be biased or confounded. METHODS: We calculated the weighted mean difference in CRP between individuals with variants of the +1444C>T polymorphism in the CRP gene among 4,659 European men from six studies (genotype-intermediate phenotype studies). We used this difference together with data from previous observational studies to compute an expected odds ratio (OR) for non-fatal myocardial infarction (MI) among individuals homozygous for the T allele. We then performed four new genetic association studies (6,201 European men) to obtain a summary OR for the association between the +1444C>T polymorphism and non-fatal MI (genotype-disease studies). RESULTS: CRP was 0.68 mg/l [95% confidence interval (95% CI) 0.31-1.10; P = 0.0001] higher among subjects homozygous for the +1444-T allele, with no confounding by a range of covariates. The expected ORs among TT subjects for non-fatal MI corresponding to this difference in CRP was 1.20 (95% CI 1.07-1.38) using the Reykjavik Heart study data and 1.25 (1.09-1.43) for all observational studies to 2004. The estimate for the observed adjusted-OR for non-fatal MI among TT subjects was 1.01 (95% CI 0.74-1.38), lower than both expected ORs. CONCLUSIONS: A common CRP gene polymorphism is associated with important differences in CRP concentrations, free from confounding. The null association of this variant with coronary events suggests possible residual confounding (or reverse causation) in the CRP-coronary event association in observational studies, though the confidence limits are still compatible with a modest causal effect. Additional studies of genotype (or haplotype) and coronary events would help clarify whether or not the link between CRP and coronary events in observational studies is causal.     

A comparison of robust Mendelian randomization methods using summary data

The number of Mendelian randomization (MR) analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. Since it is unlikely that all genetic variants will be valid instrumental variables, several robust methods have been proposed. We compare nine robust methods for MR based on summary data that can be implemented using standard statistical software. Methods were compared in three ways: by reviewing their theoretical properties, in an extensive simulation study, and in an empirical example. In the simulation study, the best method, judged by mean squared error was the contamination mixture method. This method had well-controlled Type 1 error rates with up to 50% invalid instruments across a range of scenarios. Other methods performed well according to different metrics. Outlier-robust methods had the narrowest confidence intervals in the empirical example. With isolated exceptions, all methods performed badly when over 50% of the variants were invalid instruments. Our recommendation for investigators is to perform a variety of robust methods that operate in different ways and rely on different assumptions for valid inferences to assess the reliability of MR analyses.     

Mendelian randomization analysis of case-control data using structural mean models

'Instrumental Variable' (IV) methods provide a basis for estimating an exposure's causal effect on the risk of disease. In Mendelian randomization studies, where genetic information plays the role of the IV, IV analyses are routinely performed on case-control data, rather than prospectively collected observational data. Although it is a well-appreciated fact that ascertainment bias may invalidate such analyses, ad hoc assumptions and approximations are made to justify their use. In this paper we attempt to explain and clarify why they may fail and show how they can be adjusted for improved performance. In particular, we propose consistent estimators of the causal relative risk and odds ratio if a priori knowledge is available regarding either the population disease prevalence or the population distribution of the IV (e.g. population allele frequencies). We further show that if no such information is available, approximate estimators can be obtained under a rare disease assumption. We illustrate this with matched case-control data from the recently completed EPIC study, from which we attempt to assess the evidence for a causal relationship between C-reactive protein levels and the risk of Coronary Artery Disease.     

Mendelian randomization incorporating uncertainty about pleiotropy

Mendelian randomization (MR) requires strong assumptions about the genetic instruments, of which the most difficult to justify relate to pleiotropy. In a two‐sample MR, different methods of analysis are available if we are able to assume, M₁: no pleiotropy (fixed effects meta‐analysis), M₂: that there may be pleiotropy but that the average pleiotropic effect is zero (random effects meta‐analysis), and M₃: that the average pleiotropic effect is nonzero (MR‐Egger). In the latter 2 cases, we also require that the size of the pleiotropy is independent of the size of the effect on the exposure. Selecting one of these models without good reason would run the risk of misrepresenting the evidence for causality. The most conservative strategy would be to use M₃ in all analyses as this makes the weakest assumptions, but such an analysis gives much less precise estimates and so should be avoided whenever stronger assumptions are credible. We consider the situation of a two‐sample design when we are unsure which of these 3 pleiotropy models is appropriate. The analysis is placed within a Bayesian framework and Bayesian model averaging is used. We demonstrate that even large samples of the scale used in genome‐wide meta‐analysis may be insufficient to distinguish the pleiotropy models based on the data alone. Our simulations show that Bayesian model averaging provides a reasonable trade‐off between bias and precision. Bayesian model averaging is recommended whenever there is uncertainty about the nature of the pleiotropy.     

Mendelian randomization analysis with survival outcomes

Mendelian randomization (MR) is an established approach for assessing the causal effects of heritable exposures on outcomes. Outcomes of interest often include binary clinical endpoints, but may also include censored survival times. We explore the implications of both the Cox proportional hazard model and the additive hazard model in the context of MR, with a specific emphasis on two‐stage methods. We show that naive application of standard MR approaches to censored survival times may induce significant bias. Through simulations and analysis of data from the Women's Health Initiative, we provide practical advice on modeling survival outcomes in MRs.     

孟德尔随机化方法在流行病学病因推断中的应用

目的阐述在观察性流行病学研究中如何运用孟德尔随机化方法进行科学合理的病因推断,以控制混杂因素和反向因果关联对结果的影响.方法以孟德尔独立分配定律为基础,已知不同基因型导致不同的中间表型（即待研究的暴露因素）,用基因-疾病的因果链模拟暴露因素对疾病的作用,推导出暴露对疾病的真实效应值.结果基因-疾病的效应估计值能够反映暴露因素和疾病间的真实联系.由于配子形成时等位基因的随机分配,该效应估计值不会受到传统流行病学研究中的混杂因素的影响.结论孟德尔随机化的应用能够增强观察性流行病学中的病因推断,增进对潜在危险因素的认识,同时可能为研究设计和资料分析提供新思路,具有较大的应用前景.     

An integrated approach to the meta-analysis of genetic association studies using Mendelian randomization

A natural randomization process, sometimes called Mendelian randomization, occurs at conception to determine a person's genotype. By combining information from genotype-disease and genotype-phenotype studies, it is possible to use this Mendelian randomization to derive an estimate of the association between phenotype (risk factor) and disease that is free of the confounding and reverse causation typical of classical epidemiology. When one is synthesizing evidence, studies evaluating genotype-phenotype associations, studies evaluating genotype-disease associations, and studies evaluating both are encountered, and methods should be used that allow for this structure. Plotting the log odds ratio of genotype-disease against the mean genotype-phenotype difference may help investigators detect departures from the assumptions underlying Mendelian randomization. Testing for differences between studies reporting on only the genotype-phenotype or genotype-disease association and those reporting on both associations may help in detecting reporting bias. This integrated approach to the meta-analysis of genotype-phenotype and genotype-disease studies is illustrated here using the example of the methylenetetrahydrofolate reductase (MTHFR) gene, homocysteine level, and coronary heart disease. An integrated meta-analytical approach may increase the precision of this estimate and provide information on the assumptions underlying Mendelian randomization. Serious biases may arise if the assumptions behind the analysis based on Mendelian randomization are not met.     

Bias in causal estimates from Mendelian randomization studies with weak instruments

Mendelian randomization studies using genetic instrumental variables (IVs) are now being commonly used to estimate the causal association of a phenotype on an outcome. Even when the necessary underlying assumptions are valid, estimates from analyses using IVs are biased in finite samples. The source and nature of this bias appear poorly understood in the epidemiological field. We explain why the bias is in the direction of the confounded observational association, with magnitude relating to the statistical strength of association between the instrument and phenotype. We comment on the size of the bias, from simulated data, showing that when multiple instruments are used, although the variance of the IV estimator decreases, the bias increases. We discuss ways to analyse Mendelian randomization studies to alleviate the problem of weak instrument bias.     

Power calculation for the general two-sample Mendelian randomization analysis

Mendelian randomization (MR) study has become a powerful approach to assess the potential causal effect of a risk exposure on an outcome. Most current MR studies are conducted under the two-sample setting by combining summary data from two separate genome-wide association studies (GWAS), with one providing measures on associations between genetic markers and the risk exposure, and the other on associations between genetic markers and the outcome. We develop a power calculation procedure for the general two-sample MR study, allowing for the use of multiple genetic markers, and shared participants between the two GWAS. This procedure requires a few easy-to-interpret parameters and is validated through extensive simulation studies.     

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.     

弓形虫感染与精神分裂症的两样本孟德尔随机化研究

目的 采用两样本孟德尔随机化方法探究弓形虫感染和精神分裂症之间的因果关系.方法 利用汇总的大样本GWAS数据提取与弓形虫血清抗体密切相关的遗传位点作为工具变量,分别运用MR-Egger回归、加权中位数和逆方差加权法进行孟德尔随机化分析,以OR值及95％CI评价弓形虫感染与精神分裂症之间是否存在关联.采用Egger-in...     

孟德尔随机化法在因果推断中的应用

孟德尔随机化（Mendelian Randomization,MR）研究设计,遵循“亲代等位基因随机分配给子代”的孟德尔遗传规律,如果基因型决定表型,基因型通过表型而与疾病发生关联,因此可以使用基因型作为工具变量来推断表型与疾病之间的关联。近年来,MR的研究设计随着统计学方法、大样本GWAS数据、表观遗传学以及各种“组学”技术的不断发展,在探讨复杂暴露因素与疾病结局因果关联中应用日益广泛。本文对近年来出现的MR研究设计策略、可靠性评价及局限性进行介绍。     

A genetic instrument for Mendelian randomization of fibrinogen

Mendelian randomization studies on fibrinogen commonly use a single genetic variant as an instrument, but this may explain only a small proportion of the total phenotypic variance. We examined the contribution of multiple common single nucleotide polymorphisms (SNPs) and haplotypes in the entire fibrinogen gene cluster to plasma fibrinogen levels in two prospective cohorts, for use as instruments in future Mendelian randomization studies. Genotypes for 20 SNPs were determined in 2,778 middle-age (49-64 years) men from the Second-Northwick-Park-Heart Study (NPHS-II). These were replicated in 3,705 men from the Whitehall-II study (WH-II). Plasma fibrinogen levels were determined six times in NPHS-II and three times in WH-II. The minor alleles of four SNPs from the FGB gene, two from the FGA gene, and one from the FGG gene were associated with higher plasma fibrinogen levels. SNP rs1800790 (-455G>A) commonly used in Mendelian randomization studies was associated with R2=1.22% of the covariate adjusted residual variance in fibrinogen level. A variable selection procedure identified one additional SNP: rs2070011 (FGA) altogether explaining R2=1.45% of the residual variance in fibrinogen level. Using these SNPs no evidence for causality between the fibrinogen levels and coronary heart diseases was found in instrumental variables analysis. In the replication cohort, WH-II, the effects of the two SNPs on fibrinogen levels were consistent with the NPHS-II results. There is statistical evidence for several functional sites in the fibrinogen gene cluster that determine an individual's plasma fibrinogen levels. Thus, a combination of several SNPs will provide a stronger instrument for fibrinogen Mendelian randomization studies.     

The many weak instruments problem and Mendelian randomization

Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual variants, two‐stage least squares (2SLS) is biased, whereas the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS, LIML, and CUE instrumental variable estimators using the individual height variants. We further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments. In conclusion, the allele scores and CUE gave consistent estimates of the causal effect. In our empirical example, estimates using the allele score were more efficient. CUE with corrected standard errors, however, provides a useful additional statistical tool in applications with many weak instruments. The CUE may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.