Despite previous warnings against the use of the difference-in-coefficients method for estimating the indirect effect when the outcome in the mediation model is binary, the difference-in-coefficients method remains readily used in a variety of fields. The continued use of this method is presumably because of the lack of awareness that this method conflates the indirect effect estimate and non-collapsibility. In this paper, we aim to demonstrate the problems associated with the difference-in-coefficients method for estimating indirect effects for mediation models with binary outcomes. We provide a formula that decomposes the difference-in-coefficients estimate into (1) an estimate of non-collapsibility, and (2) an indirect effect estimate. We use a simulation study and an empirical data example to illustrate the impact of non-collapsibility on the difference-in-coefficients estimate of the indirect effect. Further, we demonstrate the application of several alternative methods for estimating the indirect effect, including the product-of-coefficients method and regression-based causal mediation analysis. The results emphasize the importance of choosing a method for estimating the indirect effect that is not affected by non-collapsibility.
Keywords: Binary outcome; indirect effect; logistic regression; mediation analysis; probit regression.