Causal Mediation Analysis With a Binary Outcome and Multiple Continuous or Ordinal Mediators: Simulations and Application to an Alcohol Intervention

We investigate a method to estimate the combined effect of multiple continuous/ordinal mediators on a binary outcome: 1) fit a structural equation model with probit link for the outcome and identity/probit link for continuous/ordinal mediators, 2) predict potential outcome probabilities, and 3) compute natural direct and indirect effects. Step 2 involves rescaling the latent continuous variable underlying the outcome to address residual mediator variance/covariance. We evaluate the estimation of risk-difference- and risk-ratio-based effects (RDs, RRs) using the ML, WLSMV and Bayes estimators in Mplus. Across most variations in path-coefficient and mediator-residual-correlation signs and strengths, and confounding situations investigated, the method performs well with all estimators, but favors ML/WLSMV for RDs with continuous mediators, and Bayes for RRs with ordinal mediators. Bayes outperforms WLSMV/ML regardless of mediator type when estimating RRs with small potential outcome probabilities and in two other special cases. An adolescent alcohol prevention study is used for illustration.