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      Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression

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          Abstract

          Background: The number of Mendelian randomization 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. However, some genetic variants may not be valid instrumental variables, in particular due to them having more than one proximal phenotypic correlate (pleiotropy).

          Methods: We view Mendelian randomization with multiple instruments as a meta-analysis, and show that bias caused by pleiotropy can be regarded as analogous to small study bias. Causal estimates using each instrument can be displayed visually by a funnel plot to assess potential asymmetry. Egger regression, a tool to detect small study bias in meta-analysis, can be adapted to test for bias from pleiotropy, and the slope coefficient from Egger regression provides an estimate of the causal effect. Under the assumption that the association of each genetic variant with the exposure is independent of the pleiotropic effect of the variant (not via the exposure), Egger’s test gives a valid test of the null causal hypothesis and a consistent causal effect estimate even when all the genetic variants are invalid instrumental variables.

          Results: We illustrate the use of this approach by re-analysing two published Mendelian randomization studies of the causal effect of height on lung function, and the causal effect of blood pressure on coronary artery disease risk. The conservative nature of this approach is illustrated with these examples.

          Conclusions: An adaption of Egger regression (which we call MR-Egger) can detect some violations of the standard instrumental variable assumptions, and provide an effect estimate which is not subject to these violations. The approach provides a sensitivity analysis for the robustness of the findings from a Mendelian randomization investigation.

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          'Mendelian randomization': can genetic epidemiology contribute to understanding environmental determinants of disease?

          Associations between modifiable exposures and disease seen in observational epidemiology are sometimes confounded and thus misleading, despite our best efforts to improve the design and analysis of studies. Mendelian randomization-the random assortment of genes from parents to offspring that occurs during gamete formation and conception-provides one method for assessing the causal nature of some environmental exposures. The association between a disease and a polymorphism that mimics the biological link between a proposed exposure and disease is not generally susceptible to the reverse causation or confounding that may distort interpretations of conventional observational studies. Several examples where the phenotypic effects of polymorphisms are well documented provide encouraging evidence of the explanatory power of Mendelian randomization and are described. The limitations of the approach include confounding by polymorphisms in linkage disequilibrium with the polymorphism under study, that polymorphisms may have several phenotypic effects associated with disease, the lack of suitable polymorphisms for studying modifiable exposures of interest, and canalization-the buffering of the effects of genetic variation during development. Nevertheless, Mendelian randomization provides new opportunities to test causality and demonstrates how investment in the human genome project may contribute to understanding and preventing the adverse effects on human health of modifiable exposures.
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            Mendelian randomization as an instrumental variable approach to causal inference.

            In epidemiological research, the causal effect of a modifiable phenotype or exposure on a disease is often of public health interest. Randomized controlled trials to investigate this effect are not always possible and inferences based on observational data can be confounded. However, if we know of a gene closely linked to the phenotype without direct effect on the disease, it can often be reasonably assumed that the gene is not itself associated with any confounding factors - a phenomenon called Mendelian randomization. These properties define an instrumental variable and allow estimation of the causal effect, despite the confounding, under certain model restrictions. In this paper, we present a formal framework for causal inference based on Mendelian randomization and suggest using directed acyclic graphs to check model assumptions by visual inspection. This framework allows us to address limitations of the Mendelian randomization technique that have often been overlooked in the medical literature.
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              Explaining heterogeneity in meta-analysis: a comparison of methods.

              Exploring the possible reasons for heterogeneity between studies is an important aspect of conducting a meta-analysis. This paper compares a number of methods which can be used to investigate whether a particular covariate, with a value defined for each study in the meta-analysis, explains any heterogeneity. The main example is from a meta-analysis of randomized trials of serum cholesterol reduction, in which the log-odds ratio for coronary events is related to the average extent of cholesterol reduction achieved in each trial. Different forms of weighted normal errors regression and random effects logistic regression are compared. These analyses quantify the extent to which heterogeneity is explained, as well as the effect of cholesterol reduction on the risk of coronary events. In a second example, the relationship between treatment effect estimates and their precision is examined, in order to assess the evidence for publication bias. We conclude that methods which allow for an additive component of residual heterogeneity should be used. In weighted regression, a restricted maximum likelihood estimator is appropriate, although a number of other estimators are also available. Methods which use the original form of the data explicitly, for example the binomial model for observed proportions rather than assuming normality of the log-odds ratios, are now computationally feasible. Although such methods are preferable in principle, they often give similar results in practice. Copyright 1999 John Wiley & Sons, Ltd.
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                Author and article information

                Journal
                Int J Epidemiol
                Int J Epidemiol
                ije
                intjepid
                International Journal of Epidemiology
                Oxford University Press
                0300-5771
                1464-3685
                April 2015
                06 June 2015
                06 June 2015
                : 44
                : 2
                : 512-525
                Affiliations
                1MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, UK, 2MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK and 3Department of Public Health and Primary Care, University of Cambridge, Cambridge, UK
                Author notes
                *Corresponding author. MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge CB2 0SR. E-mail: jack.bowden@ 123456mrc-bsu.cam.ac.uk
                Article
                dyv080
                10.1093/ije/dyv080
                4469799
                26050253
                e7329be8-8077-472d-9592-cb6e556b3f45
                © The Author 2015; Published by Oxford University Press on behalf of the International Epidemiological Association.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 01 April 2015
                Page count
                Pages: 14
                Categories
                Mendelian Randomization Methodology

                Public health
                mendelian randomization,invalid instruments,meta-analysis,pleiotropy,small study bias,mr-egger test

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