Handling Measurement Error and Omitted Confounders Considering Informativeness of the Confounding Effect under Mediation Modeling

In the article, we focused on the issues of measurement error and omitted confounders while conducting mediation analysis under experimental studies. Depending on informativeness of the confounders between the mediator (M) and outcome (Y), we described two approaches. When researchers are confident that primary confounders are included (e.g., based on theory, literature), mediation effects can be estimated using Bayesian estimation with informative priors for the correlation of residuals between latent M and Y (ρ). Simulation study results showed that mediation analysis without accounting for secondary confounders yielded inaccurate inferences about mediation effects. Without prior knowledge about the primary confounders between M and Y, we suggest using sensitivity analysis to probe robustness of mediation analysis results. ρ was used as the sensitivity parameter and an R shiny app was developed to conduct sensitivity analysis: https://qwang17.shinyapps.io/sensitivity/. Both unidimensional and multidimensional models are allowed under our developed R shiny app to conduct sensitivity analysis. Two real data examples were used for illustrating the procedure of sensitivity analysis. We ended the article by making recommendations and entertaining future directions in mediation analysis.