Detecting and correcting for bias in Mendelian randomization analyses using gene-by-environment interactions

Background: Mendelian randomization 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 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 Mendelian randomization analyses. Methods: We introduce MR using Gene-by-Environment interactions (MRGxE) as a framework capable of identifying and correcting for pleiotropic bias, drawing upon developments in econometrics and epidemiology. 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 Mendelian randomization approaches, with a particular advantage of MRGxE being the ability to assess the validity of an individual instrument. Results: We investigate the effect of BMI upon systolic blood pressure (SBP) using data from the UK Biobank and the GIANT consortium using a single instrument (a weighted allelic score). We find MRGxE produces findings in agreement with MR Egger regression in a two-sample summary MR setting, however, association estimates obtained across all methods differ considerably when excluding related participants or individuals of non-European ancestry. This could be a consequence of selection bias, though there is also potential for introducing bias by using a mixed ancestry population. Further, we assess the performance of MRGxE with respect to identifying and correcting for horizontal pleiotropy in a simulation setting, highlighting the utility of the approach even when the MRGxE assumptions are violated. Conclusions: By utilising instrument-covariate interactions within a linear regression framework, it is possible to identify and correct for pleiotropic bias, provided the average magnitude of pleiotropy is constant across interaction covariate subgroups.