Causal Direct and Indirect Effects: The Link between Traditional Logistic Regression and Potential Outcomes Framework for Binary Outcomes

Introduction: The application of the potential outcomes framework is one of the most important recent developments in mediation analysis. Key to the potential outcomes framework is the decomposition of total treatment effects into causal direct and indirect effects in the presence of exposure-mediator interaction. For models with a continuous mediator and outcome and in the presence of exposure-mediator interaction, the potential outcomes estimators can be linked to simple effect estimates in traditional mediation analysis. The aim of this study was to demonstrate the similarities and differences between the traditional estimators and potential outcomes estimators for mediation analysis with binary outcomes and exposure-mediator interaction, and to describe the implications of these similarities and differences for the application of mediation analysis in practice.

Methods: We performed both analytical comparisons and a simulation study to compare the traditional estimators and potential outcomes estimators of the total effect, the direct effects, and indirect effects. We also used a data example to demonstrate the similarities and differences between the traditional and potential outcomes estimators.

Results: We showed that, for models with a binary outcome and in the presence of exposure-mediator interaction, the controlled direct effect, pure natural indirect effect, and total natural indirect effect from the potential outcomes framework correspond to simple direct and mediated effects in traditional mediation analysis. Additionally, we showed that there are no direct links between the pure natural direct effect, total natural direct effect, and total effect from the potential outcomes framework and the simple direct effects and total effect in traditional mediation analysis.

Conclusion: We recommend the use of the potential outcomes framework for the mediation analysis of models with a binary outcome and exposure-mediator interaction.