Causal Inference for Mediation Analysis with Binary Variables

Introduction: The potential outcomes framework for mediation is a state-of-the-art method of estimating causal effects of interventions on outcomes. This method is based on counterfactual logic and, when combined with confounding variable assumptions, allows researchers to make causal inferences. Mediation is an integral part of prevention research, providing information about the effective components of interventions. The identification of effective program components is enhanced when the causal relations between variables can be reliably estimated.

When the mediator and outcome are continuous and there is no interaction between the X and M, potential outcome estimates of mediation equal traditional estimates; when there is an interaction, potential outcomes estimates are similar to direct and mediated effects in the treatment and control groups from a traditional analysis. However, these correspondences between methods do not always hold for discrete variables. The present study compares traditional and potential outcomes mediation when X, M, and Y are binary.

Methods: A Monte Carlo simulation study compared potential outcomes and traditional analysis of the single mediator model. Potential outcomes mediation was conducted using counterfactual definitions, while traditional mediation was conducted with logistic regression. The study used sample sizes of 300 and 900 and parameter sizes that correspond to zero, small, medium, and large effects for each of the three paths of the single mediator model. Both methods were also applied to substantive data from a smoking prevention study to illustrate the process for conducting and interpreting potential outcomes mediation and to present the differences between the traditional and potential outcome estimators.

Results: Results show that potential outcomes performed better than logistic regression in terms of Type 1 errors. Both methods had acceptable Type 1 error rates, with potential outcomes having smaller rates across most conditions. However, power was higher for the product of coefficients mediated effect that was estimated with logistic regression, and power was lower for the True Natural Indirect Effect (TNIE) that was estimated using potential outcomes mediation.

Conclusions: The potential outcomes framework is a tool that can improve causal inference in mediation analysis. When X, M, and Y are binary, Type 1 error rates with this method are similar to traditional mediation with logistic regression. However, power to detect the TNIE is lower than the traditional product of coefficients.