Detecting and correcting for bias in Mendelian randomization analyses using Gene-by-Environment interactions

Abstract

Background: Mendelian randomization (MR) has developed into an established method for strengthening causal inference and estimating causal effects, largely due to the proliferation of genome-wide association studies. However, genetic instruments remain controversial, as horizontal pleiotropic effects can introduce bias into causal estimates. Recent work has highlighted the potential of gene-environment interactions in detecting and correcting for pleiotropic bias in MR analyses.

Methods: We introduce MR using Gene-by-Environment interactions (MRGxE) as a framework capable of identifying and correcting for pleiotropic bias. If an instrument-covariate interaction induces variation in the association between a genetic instrument and exposure, it is possible to identify and correct for pleiotropic effects. The interpretation of MRGxE is similar to conventional summary MR approaches, with a particular advantage of MRGxE being the ability to assess the validity of an individual instrument.

Results: We investigate the effect of adiposity, measured using body mass index (BMI), upon systolic blood pressure (SBP) using data from the UK Biobank and a single weighted allelic score informed by data from the GIANT consortium. We find MRGxE produces findings in agreement with two-sample summary MR approaches. Further, we perform simulations highlighting the utility of the approach even when the MRGxE assumptions are violated.

Conclusions: By utilizing instrument-covariate interactions in MR analyses implemented within a linear-regression framework, it is possible to identify and correct for horizontal pleiotropic bias, provided the average magnitude of pleiotropy is constant across interaction-covariate subgroups.

Keywords: MRGxE; Mendelian randomization; gene–environment interaction; invalid instruments; pleiotropy.

Figure 1.

A directed acyclic graph (DAG) showing the assumed relationship between each variable in MRGxE.

Figure 2.

A set of DAGs illustrating interaction-covariate confounding structures indicated by dashed lines. Scenarios (a), (b) and (d) induce bias in MRGxE estimates. However, this is not the case for Scenario (c) or when the confounder is associated with either $G$ or $Z$ individually.

Figure 3.

A scatterplot showing the MRGxE estimate indicated as a dashed line. Each point represents ascending quintiles of the Townsend Deprivation Index, in this case showing the strength of the instrument–exposure association to increase with increasing socio-economic deprivation.