Comparison of logistic-regression based methods for simple mediation analysis with a dichotomous outcome variable

Logistic regression is often used for mediation analysis with a dichotomous outcome. However, previous studies showed that the indirect effect and proportion mediated are often affected by a change of scales in logistic regression models. To circumvent this, standardization has been proposed. The aim of this study was to show the relative performance of the unstandardized and standardized estimates of the indirect effect and proportion mediated based on multiple regression, structural equation modeling, and the potential outcomes framework for mediation models with a dichotomous outcome. We compared the performance of the effect estimates yielded by the three methods using a simulation study and two real-life data examples from an observational cohort study (n = 360). Lowest bias and highest efficiency were observed for the estimates from the potential outcomes framework and for the crude indirect effect ab and the proportion mediated ab/(ab + c') based on multiple regression and SEM. We advise the use of either the potential outcomes framework estimates or the ab estimate of the indirect effect and the ab/(ab + c') estimate of the proportion mediated based on multiple regression and SEM when mediation analysis is based on logistic regression. Standardization of the coefficients prior to estimating the indirect effect and the proportion mediated may not increase the performance of these estimates.