Fig 1.
Illustration of data generating model.
A directed acyclic graph showing the relationship between a genetic instrument G, an interaction covariate Zk, exposure X, outcome Y, and one or more confounders U. GZk denotes the interaction G × Zk, and G, Zk, and U are assumed independent.
Fig 2.
An example of GxE2 through confounding.
A path diagram illustrating a case in which the instrument Gi is a determinant of the interaction covariate Zi through a confounder Ui. The bidirectional dashed arrow from Zk to Y represents an association induced due to confounding as a result of not adjusting for U in the second stage MR-GxE model.
Fig 3.
Illustration of general GxE2 violation.
A directed acyclic graph showing the relationship between a genetic instrument G, interaction covariate Zk, exposure X, outcome Y, and one or more confounders U. In this case, the presence of an association between a gene-by-covariate GZk and U violates assumption GxE2.
Fig 4.
Illustration of collider bias when estimating .
A diagram showing a situation in which conditioning on Zk when G and U are simultaneously upstream associated with Zk would induce collider bias, as shown by the dashed bidirectional arrow.
Fig 5.
Plots corresponding to simulations 1–2, identifying interactions and visualising the impact of weak instrument bias for MR-GxE.
Panel A shows a scatter plot of −log10(p − value) for the mean first-stage F-statistic across the set of 100 potential interaction covariates in simulation 1. A solid horizontal line is included representing the Bonferroni correction threshold for statistical significance in panel A. Panel B shows a forest plot of mean causal effect estimates and confidence intervals under varying mean interaction strengths in simulation 2. The dotted vertical line in panel B represents the true causal effect β1 = 1, and arrows are used to indicate confidence intervals exceeding the limits of the forest plot.
Table 1.
Simulated results using differing proportions of non-zero interaction covariates (simulation 3).
Table 2.
Simulated results using differing proportions of non-zero gene-by-covariate interaction with respect to confounders (simulation 4).
Table 3.
Simulated results using differing proportions of non-zero gene-by-covariate interaction with respect to the outcome (simulation 5).
Table 4.
Simulated results illustrating use of Sargan test to identify GxE3 violation (simulation 6).
Fig 6.
Identified gene-by-covariate interactions with respect to genetically predicted body mass index.
A scatter plot showing the first-stage F-statistics for instrument-by-covariate interactions using data from UK Biobank. A horizontal line is included representing the Bonferroni correction for statistical significance. For clarity, blue points represent interactions identified after multiple testing. The 20 strongest interactions have been annotated using their UK Biobank field identification number.
Table 5.
MR-GxE estimates and sensitivity analyses using each candidate interaction covariate and MR-GENIUS.
Fig 7.
A forest plot showing MR-GxE causal effect estimates using the interaction covariates presented in Table 5.
Observation f.4253.0.5 has been omitted for clarity. Red points indicate analyses for which assumptions may likely be violated, while blue points show potentially valid interaction covariates using accompanying sensitivity analyses. Observational, two-stage least squares (TSLS), and MR-GENIUS estimates are also shown as black points.
Table 6.
A summary of the MR-GxE assumptions and proposed sensitivity analyses.