When is the difference method conservative for assessing mediation?

Assessment of indirect effects is useful for epidemiologists interested in understanding the mechanisms of exposure-outcome relationships. A traditional way of estimating indirect effects is to use the "difference method," which is based on regression analysis in which one adds a possible mediator to the regression model and examines whether the coefficient for the exposure changes. The difference method has been criticized for lacking a causal interpretation when it is used with logistic regression. In this article, we use the counterfactual framework to define the natural indirect effect (NIE) and assess the relationship between the NIE and the difference method. We show that under appropriate assumptions, the difference method consistently estimates the NIE for continuous outcomes and is always conservative for binary outcomes. Thus, the difference method can be used to provide evidence for the presence of mediation but not for the absence of mediation.