Mendelian randomization-Egger (MR-Egger) is an analysis method for Mendelian randomization using summarized genetic data. MR-Egger consists of three parts: (1) a test for directional pleiotropy, (2) ...a test for a causal effect, and (3) an estimate of the causal effect. While conventional analysis methods for Mendelian randomization assume that all genetic variants satisfy the instrumental variable assumptions, the MR-Egger method is able to assess whether genetic variants have pleiotropic effects on the outcome that differ on average from zero (directional pleiotropy), as well as to provide a consistent estimate of the causal effect, under a weaker assumption— the InSIDE (INstrument Strength Independent of Direct Effect) assumption. In this paper, we provide a critical assessment of the MR-Egger method with regard to its implementation and interpretation. While the MR-Egger method is a worthwhile sensitivity analysis for detecting violations of the instrumental variable assumptions, there are several reasons why causal estimates from the MR-Egger method may be biased and have inflated Type 1 error rates in practice, including violations of the InSIDE assumption and the influence of outlying variants. The issues raised in this paper have potentially serious consequences for causal inferences from the MR-Egger approach. We give examples of scenarios in which the estimates from conventional Mendelian randomization methods and MR-Egger differ, and discuss how to interpret findings in such cases.
ABSTRACT
Genome‐wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source ...of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual‐level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse‐variance weighted average of variant‐specific associations and a likelihood‐based approach for summarized data give similar estimates and precision to the two‐stage least squares method for individual‐level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P‐value in a linear regression of the risk factor for each variant is less than 1×10−5, then weak instrument bias will be small. We use these methods to estimate the causal association of low‐density lipoprotein cholesterol (LDL‐C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL‐C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual‐level data, although the necessary assumptions cannot be so fully assessed.
ABSTRACT
Mendelian randomization analyses are often performed using summarized data. The causal estimate from a one‐sample analysis (in which data are taken from a single data source) with weak ...instrumental variables is biased in the direction of the observational association between the risk factor and outcome, whereas the estimate from a two‐sample analysis (in which data on the risk factor and outcome are taken from non‐overlapping datasets) is less biased and any bias is in the direction of the null. When using genetic consortia that have partially overlapping sets of participants, the direction and extent of bias are uncertain. In this paper, we perform simulation studies to investigate the magnitude of bias and Type 1 error rate inflation arising from sample overlap. We consider both a continuous outcome and a case‐control setting with a binary outcome. For a continuous outcome, bias due to sample overlap is a linear function of the proportion of overlap between the samples. So, in the case of a null causal effect, if the relative bias of the one‐sample instrumental variable estimate is 10% (corresponding to an F parameter of 10), then the relative bias with 50% sample overlap is 5%, and with 30% sample overlap is 3%. In a case‐control setting, if risk factor measurements are only included for the control participants, unbiased estimates are obtained even in a one‐sample setting. However, if risk factor data on both control and case participants are used, then bias is similar with a binary outcome as with a continuous outcome. Consortia releasing publicly available data on the associations of genetic variants with continuous risk factors should provide estimates that exclude case participants from case‐control samples.
Background Mendelian randomization is used to test and estimate the magnitude of a causal effect of a phenotype on an outcome by using genetic variants as instrumental variables (IVs). Estimates of ...association from IV analysis are biased in the direction of the confounded, observational association between phenotype and outcome. The magnitude of the bias depends on the F-statistic for the strength of relationship between IVs and phenotype. We seek to develop guidelines for the design and analysis of Mendelian randomization studies to minimize bias.
Methods IV analysis was performed on simulated and real data to investigate the effect on bias of size of study, number and choice of instruments and method of analysis.
Results Bias is shown to increase as the expected F-statistic decreases, and can be reduced by using parsimonious models of genetic association (i.e. not over-parameterized) and by adjusting for measured covariates. Using data from a single study, the causal estimate of a unit increase in log-transformed C-reactive protein on fibrinogen (μmol l) is shown to increase from −0.005 (P = 0.99) to 0.792 (P = 0.00003) due to injudicious choice of instrument. Moreover, when the observed F-statistic is larger than expected in a particular study, the causal estimate is more biased towards the observational association and its standard error is smaller. This correlation between causal estimate and standard error introduces a second source of bias into meta-analysis of Mendelian randomization studies. Bias can be alleviated in meta-analyses by using individual level data and by pooling genetic effects across studies.
Conclusions Weak instrument bias is of practical importance for the design and analysis of Mendelian randomization studies. Post hoc choice of instruments, genetic models or data based on measured F-statistics can exacerbate bias. In particular, the commonly cited rule of thumb that F > 10 avoids bias in IV analysis is misleading.
Instrumental variable analysis is an approach for obtaining causal inferences on the effect of an exposure (risk factor) on an outcome from observational data. It has gained in popularity over the ...past decade with the use of genetic variants as instrumental variables, known as Mendelian randomization. An instrumental variable is associated with the exposure, but not associated with any confounder of the exposure–outcome association, nor is there any causal pathway from the instrumental variable to the outcome other than via the exposure. Under the assumption that a single instrumental variable or a set of instrumental variables for the exposure is available, the causal effect of the exposure on the outcome can be estimated. There are several methods available for instrumental variable estimation; we consider the ratio method, two-stage methods, likelihood-based methods, and semi-parametric methods. Techniques for obtaining statistical inferences and confidence intervals are presented. The statistical properties of estimates from these methods are compared, and practical advice is given about choosing a suitable analysis method. In particular, bias and coverage properties of estimators are considered, especially with weak instruments. Settings particularly relevant to Mendelian randomization are prioritized in the paper, notably the scenario of a continuous exposure and a continuous or binary outcome.
Abstract
A conventional Mendelian randomization analysis assesses the causal effect of a risk factor on an outcome by using genetic variants that are solely associated with the risk factor of ...interest as instrumental variables. However, in some cases, such as the case of triglyceride level as a risk factor for cardiovascular disease, it may be difficult to find a relevant genetic variant that is not also associated with related risk factors, such as other lipid fractions. Such a variant is known as pleiotropic. In this paper, we propose an extension of Mendelian randomization that uses multiple genetic variants associated with several measured risk factors to simultaneously estimate the causal effect of each of the risk factors on the outcome. This “multivariable Mendelian randomization” approach is similar to the simultaneous assessment of several treatments in a factorial randomized trial. In this paper, methods for estimating the causal effects are presented and compared using real and simulated data, and the assumptions necessary for a valid multivariable Mendelian randomization analysis are discussed. Subject to these assumptions, we demonstrate that triglyceride-related pathways have a causal effect on the risk of coronary heart disease independent of the effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol.
Mendelian randomization investigations are becoming more powerful and simpler to perform, due to the increasing size and coverage of genome-wide association studies and the increasing availability of ...summarized data on genetic associations with risk factors and disease outcomes. However, when using multiple genetic variants from different gene regions in a Mendelian randomization analysis, it is highly implausible that all the genetic variants satisfy the instrumental variable assumptions. This means that a simple instrumental variable analysis alone should not be relied on to give a causal conclusion. In this article, we discuss a range of sensitivity analyses that will either support or question the validity of causal inference from a Mendelian randomization analysis with multiple genetic variants. We focus on sensitivity analyses of greatest practical relevance for ensuring robust causal inferences, and those that can be undertaken using summarized data. Aside from cases in which the justification of the instrumental variable assumptions is supported by strong biological understanding, a Mendelian randomization analysis in which no assessment of the robustness of the findings to violations of the instrumental variable assumptions has been made should be viewed as speculative and incomplete. In particular, Mendelian randomization investigations with large numbers of genetic variants without such sensitivity analyses should be treated with skepticism.
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