Causal mediation analysis in the presence of a common confounder measured with error

Causal mediation analysis (CMA) is commonly used to investigate the extent to which an intermediary variable mediates the effect of the exposure on the outcome. The naive estimators related to CMA can be severely biased when a measurement error is in the common confounder for the exposure‐outcome, exposure‐mediator, and mediator‐outcome relationship. This paper quantifies classical, non‐differential measurement error bias on a common confounder in estimating natural effects. It also proposes three methods based on the method of moments (MoM), regression calibration, and SIMEX for estimating effects associated with CMA in the presence of measurement error in a common confounder. Additionally, the article derives using observed data to estimate the ranges of the extent of measurement error, enabling one to implement sensitivity analyses and assess the robustness of effect estimates even without prior information on the measurement error. The performance of the proposed corrected methods of estimating natural effects is compared using a simulation study. The proposed MoM method performs better in the context of bias and standard error than the other methods considered in such situations.