Mediators are intermediate variables in the causal pathway between an exposure and an outcome. Mediation analysis investigates the extent to which exposure effects occur through these variables, thus revealing causal mechanisms. One interesting question in causal inference area is mediation analysis for non-linear models.
In the first part of this dissertation, we consider the estimation of mediation effects in zero-inflated (ZI) models intended to accommodate ‘extra’ zeros in count data. Focusing on the ZI negative binomial (ZINB) models, we provide a mediation formula approach to estimate the (overall) mediation effect in the standard two-stage mediation framework under the key sequential ignorability assumption. We also consider a novel decomposition of the overall mediation effect for the ZI context using a three-stage mediation model. Simulation study results demonstrate low bias of mediation effect estimators and close-to-nominal coverage probability (CP) of confidence intervals. The method is applied to a retrospective cohort study of dental caries in very low birth weight adolescents. For overall mediation effect estimation, sensitivity analysis was conducted to quantify the degree to which key assumption must be violated to reverse the original conclusion.
The second question we focus on is the mediation analysis for a dichotomous outcome in multiple-mediator models. We formulate a joint model (probit-normal) using continuous latent variables for any binary mediators to account for correlations among multiple mediators. A mediation formula approach is proposed to estimate the total mediation effect and decomposed mediation effects based on this parametric model. We conduct a simulation study that demonstrates low bias of mediation effect estimators for two-mediator models with various combinations of mediator types. The results also show that the power to detect a non-zero total mediation effect increases as the correlation coefficient between two mediators increases, while power for individual mediation effects reaches a maximum when the mediators are uncorrelated. We illustrate our approach by applying it to a retrospective cohort study of dental caries in adolescents with low and high socioeconomic status. Sensitivity analysis is performed to assess the robustness of conclusions regarding mediation effects when the assumption of no unmeasured mediator-outcome confounders is violated