arXiv subjects

Stephen Burgess

Publications and source records attributed to Stephen Burgess.

24 records · Page 2Linked to original sources

arXiv2018

Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates

Mendelian randomization uses genetic variants to make causal inferences about a modifiable exposure. Subject to a genetic variant satisfying the instrumental variable assumptions, an association between the variant and outcome implies a causal effect of the exposure on the outcome. Complications arise with a binary exposure that is a dichotomization of a continuous risk factor (for example, hypertension is a dichotomization of blood pressure). This can lead to violation of the exclusion restriction assumption: the genetic variant can influence the outcome via the continuous risk factor even if the binary exposure does not change. Provided the instrumental variable assumptions are satisfied for the underlying continuous risk factor, causal inferences for the binary exposure are valid for the continuous risk factor. Causal estimates for the binary exposure assume the causal effect is a stepwise function at the point of dichotomization. Even then, estimation requires further parametric assumptions. Under monotonicity, the causal estimate represents the average causal effect in `compliers', individuals for whom the binary exposure would be present if they have the genetic variant and absent otherwise. Unlike in randomized trials, genetic compliers are unlikely to be a large or representative subgroup of the population. Under homogeneity, the causal effect of the exposure on the outcome is assumed constant in all individuals; often an unrealistic assumption. We here provide methods for causal estimation with a binary exposure (although subject to all the above caveats). Mendelian randomization investigations with a dichotomized binary exposure should be conceptualized in terms of an underlying continuous variable.

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arXiv2018

Contextualizing selection bias in Mendelian randomization: how bad is it likely to be?

Selection bias affects Mendelian randomization investigations when selection into the study sample depends on a collider between the genetic variant and confounders of the risk factor-outcome association. However, the relative importance of selection bias for Mendelian randomization compared to other potential biases is unclear. We performed an extensive simulation study to assess the impact of selection bias on a typical Mendelian randomization investigation. Selection bias had a severe impact on bias and Type 1 error rates in our simulation study, but only when selection effects were large. For moderate effects of the risk factor on selection, bias was generally small and Type 1 error rate inflation was not considerable. The magnitude of bias was also affected by the strength of confounder-risk factor and confounder-outcome associations, the structure of the causal diagram and selection frequency. The use of inverse probability weighting ameliorated bias when the selection model was correctly specified, but increased bias when selection bias was moderate and the model was misspecified. Finally, we investigated whether selection bias may explain a recently reported finding that lipoprotein(a) is not a causal risk factor for cardiovascular mortality in individuals with previous coronary heart disease.

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arXiv2017

Extending the MR-Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy

Methods have been developed for Mendelian randomization that can obtain consistent causal estimates while relaxing the instrumental variable assumptions. These include multivariable Mendelian randomization, in which a genetic variant may be associated with multiple risk factors so long as any association with the outcome is via the measured risk factors (measured pleiotropy), and the MR-Egger (Mendelian randomization-Egger) method, in which a genetic variant may be directly associated with the outcome not via the risk factor of interest, so long as the direct effects of the variants on the outcome are uncorrelated with their associations with the risk factor (unmeasured pleiotropy). In this paper, we extend the MR-Egger method to a multivariable setting to correct for both measured and unmeasured pleiotropy. We show, through theoretical arguments and a simulation study, that the multivariable MR-Egger method has advantages over its univariable counterpart in terms of plausibility of the assumption needed for consistent causal estimation, and power to detect a causal effect when this assumption is satisfied. The methods are compared in an applied analysis to investigate the causal effect of high-density lipoprotein cholesterol on coronary heart disease risk. The multivariable MR-Egger method will be useful to analyse high-dimensional data in situations where the risk factors are highly related and it is difficult to find genetic variants specifically associated with the risk factor of interest (multivariable by design), and as a sensitivity analysis when the genetic variants are known to have pleiotropic effects on measured risk factors.

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arXiv2017

Mendelian randomization with fine-mapped genetic data: choosing from large numbers of correlated instrumental variables

Mendelian randomization uses genetic variants to make causal inferences about the effect of a risk factor on an outcome. With fine-mapped genetic data, there may be hundreds of genetic variants in a single gene region any of which could be used to assess this causal relationship. However, using too many genetic variants in the analysis can lead to spurious estimates and inflated Type 1 error rates. But if only a few genetic variants are used, then the majority of the data is ignored and estimates are highly sensitive to the particular choice of variants. We propose an approach based on summarized data only (genetic association and correlation estimates) that uses principal components analysis to form instruments. This approach has desirable theoretical properties: it takes the totality of data into account and does not suffer from numerical instabilities. It also has good properties in simulation studies: it is not particularly sensitive to varying the genetic variants included in the analysis or the genetic correlation matrix, and it does not have greatly inflated Type 1 error rates. Overall, the method gives estimates that are not so precise as those from variable selection approaches (such as using a conditional analysis or pruning approach to select variants), but are more robust to seemingly arbitrary choices in the variable selection step. Methods are illustrated by an example using genetic associations with testosterone for 320 genetic variants to assess the effect of sex hormone-related pathways on coronary artery disease risk, in which variable selection approaches give inconsistent inferences.

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arXiv2017

Bayesian Mendelian Randomization

Our Bayesian approach to Mendelian Randomisation uses multiple instruments to assess the putative causal effect of an exposure on an outcome. The approach is robust to violations of the (untestable) Exclusion Restriction condition, and hence it does not require instruments to be independent of the outcome conditional on the exposure and on the confounders of the exposure-outcome relationship. The Bayesian approach offers a rigorous handling of the uncertainty (e.g. about the estimated instrument-exposure associations), freedom from asymptotic approximations of the null distribution and the possibility to elaborate the model in any direction of scientific relevance. We illustrate the last feature with the aid of a study of the metabolic mediators of the disease-inducing effects of obesity, where we elaborate the model to investigate whether the causal effect of interest interacts with a covariate. The proposed model contains a vector of unidentifiable parameters, $β$, whose $j$th element represents the pleiotropic (i.e., not mediated by the exposure) component of the association of instrument $j$ with the outcome. We deal with the incomplete identifiability by assuming that the pleiotropic effect of some instruments is null, or nearly so, formally by imposing on $β$ Carvalho's horseshoe shrinkage prior, in such a way that different components of $β$ are subjected to different degrees of shrinking, adaptively and in accord with the compatibility of each individual instrument with the hypothesis of no pleiotropy. This prior requires a minimal input from the user. We present the results of a simulation study into the performance of the proposed method under different types of pleiotropy and sample sizes. Comparisons with the performance of the weighted median estimator are made. Choice of the prior and inference via Markov chain Monte Carlo are discussed.

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arXiv2015

Integrating summarized data from multiple genetic variants in Mendelian randomization: bias and coverage properties of inverse-variance weighted methods

Mendelian randomization is the use of genetic variants as instrumental variables to assess whether a risk factor is a cause of a disease outcome. Increasingly, Mendelian randomization investigations are conducted on the basis of summarized data, rather than individual-level data. These summarized data comprise the coefficients and standard errors from univariate regression models of the risk factor on each genetic variant, and of the outcome on each genetic variant. A causal estimate can be derived from these associations for each individual genetic variant, and a combined estimate can be obtained by inverse-variance weighted meta-analysis of these causal estimates. Various proposals have been made for how to calculate this inverse-variance weighted estimate. In this paper, we show that the inverse-variance weighted method as originally proposed (equivalent to a two-stage least squares or allele score analysis using individual-level data) can lead to over-rejection of the null, particularly when there is heterogeneity between the causal estimates from different genetic variants. Random-effects models should be routinely employed to allow for this possible heterogeneity. Additionally, over-rejection of the null is observed when associations with the risk factor and the outcome are obtained in overlapping participants. The use of weights including second-order terms from the delta method is recommended in this case.

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