Correcting for effect modification in the doubly-ranked non-linear Mendelian randomization method

The doubly-ranked non-linear Mendelian randomization method can yield biased estimates when instrument strength varies across individuals due to gene-environment (GxE) interactions. We propose a simple strategy to mitigate this bias by modelling GxE interactions and removing the fitted GxE component from the exposure before stratification by the doubly-ranked method. In simulations, the proposed GxE correction strategy eliminated GxE-induced bias with null, linear and non-linear exposure-outcome relationships, and it did not introduce bias even when the effect modifier of the IV-exposure association was a confounder or was correlated with a mediator or collider of the exposure-outcome association. In empirical analyses of serum 25(OH)D, BMI, and LDL-C, falsification tests showed bias in the uncorrected doubly-ranked method. Under the selected panel of effect modifiers, the extent of bias attenuation achieved by GxE correction varied by exposures. GxE correction was most effective for LDL-C, with further support from analyses using negative controls (age at recruitment and sex) and coronary artery disease as a positive control. These findings provide proof of principle evidence that our proposed GxE correction strategy can mitigate GxE-induced bias in practice. Where applicable, we recommend implementing this GxE correction strategy as a sensitivity analysis to assess the robustness of findings from the doubly-ranked method.