Sensitivity analysis for causal mediation analysis with Mendelian randomization

Mendelian randomization (MR) is widely used in causal mediation analysis to control unmeasured confounding effects, which is valid under some strong assumptions. It is thus of great interest to assess the impact of violations of these MR assumptions through sensitivity analysis. Sensitivity analyses have been conducted for simple MR-based causal average effect analyses, but they are not available for MR-based mediation analysis studies, and we aim to fill this gap in this paper. We propose to use two sensitivity parameters to quantify the effect due to the deviation of the IV assumptions. With these two sensitivity parameters, we derive consistent indirect causal effect estimators and establish their asymptotic propersties. Our theoretical results can be used in MR-based mediation analysis to study the impact of violations of MR assumptions. The finite sample performance of the proposed method is illustrated through simulation studies, sensitivity analysis, and application to a real genome-wide association study.