Estimating the natural indirect effect and the mediation proportion via the product method

Area of Science:

• Statistical Methods
• Epidemiology
• Biostatistics

Background:

• Mediation analysis is crucial for understanding indirect effects.
• Natural indirect effect (NIE) and mediation proportion (MP) are key measures.
• The product method is a standard approach for estimating NIE and MP.

Purpose of the Study:

• To develop and investigate finite-sample performance of NIE and MP estimators using the product method.
• To propose closed-form interval estimators for NIE and MP.
• To introduce exact expressions for NIE and MP with binary outcomes, bypassing the rare outcome assumption.

Main Methods:

• Utilized the theory of multivariate delta method for continuous/binary outcomes and mediators.
• Proposed closed-form interval estimators and compared them to bootstrap methods.
• Derived exact expressions for NIE and MP in binary outcome scenarios, contrasting with approximate methods relying on the rare outcome assumption.

Main Results:

• Proposed interval estimators showed satisfactory coverage for continuous outcomes (sample size ≥500) and binary outcomes (sample size ≥20,000, cases ≥500).
• Approximate estimators for binary outcomes performed well only when outcome prevalence was <5%, showing bias with common outcomes.
• Exact estimators for binary outcomes demonstrated robust performance across all outcome prevalences.

Conclusions:

• The proposed interval estimator is valid for confidence interval construction in typical epidemiological sample sizes.
• Exact estimators for binary outcomes offer greater robustness and stability for NIE and MP estimation.
• An R package, mediateP, has been developed to implement these point and variance estimation methods.