On the use of kernel machines for Mendelian randomization

Background: Properly adjusting for unmeasured confounders is critical for health studies in order to achieve valid testing and estimation of the exposure's causal effect on outcomes. The instrumental variable (IV) method has long been used in econometrics to estimate causal effects while accommodating the effect of unmeasured confounders. Mendelian randomization (MR), which uses genetic variants as the instrumental variables, is an application of the instrumental variable method to biomedical research fields, and has become popular in recent years. One often-used estimator of causal effects for instrumental variables and Mendelian randomization is the two-stage least square estimator (TSLS). The validity of TSLS relies on the accurate prediction of exposure based on IVs in its first stage.

Results: In this note, we propose to model the link between exposure and genetic IVs using the least-squares kernel machine (LSKM). Some simulation studies are used to evaluate the feasibility of LSKM in TSLS setting.

Conclusions: Our results show that LSKM based on genotype score or genotype can be used effectively in TSLS. It may provide higher power when the association between exposure and genetic IVs is nonlinear.