Estimation of mediation effects for zero-inflated regression models.

The goal of mediation analysis is to identify and explicate the mechanism that underlies a relationship between a risk factor and an outcome via an intermediate variable (mediator). In this paper, 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 models, we provide a mediation formula approach to estimate the (overall) mediation effect in the standard two-stage mediation framework under a 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. Estimation of the components of the overall mediation effect requires an assumption involving the joint distribution of two counterfactuals. Simulation study results demonstrate low bias of mediation effect estimators and close-to-nominal coverage probability of confidence intervals. We also modify the mediation formula method by replacing 'exact' integration with a Monte Carlo integration method. The method is applied to a 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.