Bias Formulas for Estimating Direct and Indirect Effects When Unmeasured Confounding Is Present

Area of Science:

• Epidemiology
• Biostatistics
• Causal Inference

Background:

• Mediation analysis estimates direct and indirect effects of exposures on outcomes.
• Unmeasured confounding between mediators and outcomes can bias these estimates.
• Accurate mediation analysis is crucial for understanding complex causal pathways.

Purpose of the Study:

• To investigate the impact of unmeasured confounding on direct and indirect effect estimates.
• To develop and evaluate formulas for adjusting mediation analysis in the presence of unmeasured confounding.
• To assess the performance of these formulas across different outcome types (binary, count, continuous).

Main Methods:

• Formulation of confounder effects on mediator and outcome using regression models.
• Derivation of adjustment formulas under normality assumption for confounders.
• Simulation studies to evaluate formula performance with various confounder types and outcome distributions.
• Application of formulas to a real-world case-control study.

Main Results:

• Developed intuitive regression-based formulas for adjusting mediation analysis for unmeasured confounding.
• Simulations showed good performance for linear models and with binary confounders.
• Logistic regression formulas performed well for normally distributed confounders but showed overcorrection with binary confounders for rare binary outcomes.
• Real-world data application demonstrated substantial bias from unmeasured confounding.

Conclusions:

• Unmeasured confounding poses a significant threat to the validity of mediation analysis.
• The proposed formulas offer a method to adjust for unmeasured confounding, enhancing the reliability of direct and indirect effect estimates.
• Careful consideration of confounder distribution is necessary when applying logistic regression adjustment formulas.