Causal Mediation Analysis: Decomposing Effects and Assessing Robustness to Unmeasured Confounding in Observational Research (Motivated by "Sensitivity Analysis in Observational Research: Introducing the E-value" by VanderWeele and Ding)

Causal mediation analysis helps observational researchers move beyond estimating whether an exposure is associated with an outcome to evaluating how that association may operate through intermediate pathways. However, mediated and pathway-specific effects rely on multiple linked relationships—exposure–outcome, exposure–mediator, and mediator–outcome—and are therefore especially vulnerable to uncontrolled confounding and model dependence. Motivated by VanderWeele and Ding’s introduction of the E-value, this report presents causal mediation as a structured framework for effect decomposition while emphasizing sensitivity analysis as a necessary companion for responsible mechanistic interpretation. The report explains the logic of the E-value as an interpretable robustness benchmark: the minimum strength of association an unmeasured confounder would need with both the exposure and the outcome (conditional on measured covariates) to fully explain away an observed association, and it highlights the importance of reporting E-values for both point estimates and confidence limits closest to the null. Using a worked synthetic example, the report demonstrates a practical reporting set—baseline characteristics, estimand definitions, model specifications, mediation effect decomposition, overlap and balance diagnostics, subgroup summaries, and E-value sensitivity results—along with guidance on common threats such as post-exposure adjustment, mediator measurement error, and positivity violations. Together, these elements support transparent, reproducible pathway-oriented inference in real-world observational research.