A Bayesian approach to Mendelian randomization with multiple pleiotropic variants

We propose a Bayesian approach to Mendelian randomization (MR), where instruments are allowed to exert pleiotropic (i.e. not mediated by the exposure) effects on the outcome. By having these effects represented in the model by unknown parameters, and by imposing a shrinkage prior distribution that assumes an unspecified subset of the effects to be zero, we obtain a proper posterior distribution for the causal effect of interest. This posterior can be sampled via Markov chain Monte Carlo methods of inference to obtain point and interval estimates. The model priors require a minimal input from the user. We explore the performance of our method by means of a simulation experiment. Our results show that the method is reasonably robust to the presence of directional pleiotropy and moderate correlation between the instruments. One section of the article elaborates the model to deal with two exposures, and illustrates the possibility of using MR to estimate direct and indirect effects in this situation. A main objective of the article is to create a basis for developments in MR that exploit the potential offered by a Bayesian approach to the problem, in relation with the possibility of incorporating external information in the prior, handling multiple sources of uncertainty, and flexibly elaborating the basic model.

Mendelian randomisation analysis of clustered causal effects of body mass on cardiometabolic biomarkers

Background

Recent advances in data analysis methods based on principles of Mendelian Randomisation, such as Egger regression and the weighted median estimator, add to the researcher’s ability to infer cause-effect links from observational data. Now is the time to gauge the potential of these methods within specific areas of biomedical research. In this paper, we choose a study in metabolomics as an illustrative testbed. We apply Mendelian Randomisation methods in the analysis of data from the DILGOM (Dietary, Lifestyle and Genetic determinants of Obesity and Metabolic syndrome) study, in the context of an effort to identify molecular pathways of cardiovascular disease. In particular, our illustrative analysis addresses the question whether body mass, as measured by body mass index (BMI), exerts a causal effect on the concentrations of a collection of 137 cardiometabolic markers with different degrees of atherogenic power, such as the (highly atherogenic) lipoprotein metabolites with very low density (VLDLs) and the (protective) high density lipoprotein metabolites.

Results

We found strongest evidence of a positive BMI effect (that is, evidence that an increase in BMI causes an increase in the metabolite concentration) on those metabolites known to represent strong risk factors for coronary artery disease, such as the VLDLs, and evidence of a negative effect on protective biomarkers.

Conclusions

The methods discussed represent a useful scientific tool, although they assume the validity of conditions that are (at best) only partially verifiable. This paper provides a rigorous account of such conditions. The results of our analysis provide a proof-of-concept illustration of the potential usefulness of Mendelian Randomisation in genomic biobank studies aiming to dissect the molecular causes of disease, and to identify candidate pharmacological targets.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2178-2) contains supplementary material, which is available to authorized users.

Weighing Evidence "Steampunk" Style via the Meta-Analyser

The funnel plot is a graphical visualization of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modeling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the center of mass of a physical system. We used this analogy to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulas and with a little help from Sherlock Holmes! Following on from the science fair, we have developed an interactive web-application (named the Meta-Analyser) to bring these ideas to a wider audience. We envisage that our application will be a useful tool for researchers when interpreting their data. First, to facilitate a simple understanding of fixed and random effects modeling approaches; second, to assess the importance of outliers; and third, to show the impact of adjusting for small study bias. This final aim is realized by introducing a novel graphical interpretation of the well-known method of Egger regression.

Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse-variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite-sample Type 1 error rates than the inverse-variance weighted method, and is complementary to the recently proposed MR-Egger (Mendelian randomization-Egger) regression method. In analyses of the causal effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol on coronary artery disease risk, the inverse-variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR-Egger regression methods suggest a null effect of high-density lipoprotein cholesterol that corresponds with the experimental evidence. Both median-based and MR-Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants.