Is the Product Method More Efficient Than the Difference Method for Assessing Mediation?

Mediation analysis is widely used in biomedical research to quantify the extent to which the effect from an exposure on a health outcome is through a mediator and the extent to which the effect is direct. A traditional approach for quantifying mediation is through the difference method. The other popular approach uses a counterfactual framework from which the product method arises. However, there is little prior work to articulate which method is more efficient for estimating 2 key quantities in mediation analysis, the natural indirect effect and mediation proportion. To fill in this gap, we investigated the asymptotic relative efficiency for mediation measure estimators given by the product method and the difference method. We considered 4 data types characterized by continuous and binary mediators and outcomes. Under certain conditions, we show analytically that the product method is equally efficient to the difference method, or more efficient. However, our numerical studies demonstrate that the difference method is usually at least 90% as efficient as the product method under realistic scenarios in epidemiologic research, especially for estimating the mediation proportion. We demonstrate the efficiency results by analyzing the MaxART study (Eswatini, 2014-2017), which aimed to evaluate the effectiveness of the early access to antiretroviral therapy among human immunodeficiency virus-positive patients.