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Mediation analysis seeks to understand the mechanism by which a treatmentaffects an outcome. Count or zero-inflated count outcome are common in manystudies in which mediation analysis is of interest. For example, in dentalstudies, outcomes such as decayed, missing and filled teeth are typically zeroinflated. Existing mediation analysis approaches for count data assumesequential ignorability of the mediator. This is often not plausible becausethe mediator is not randomized so that there are unmeasured confoundersassociated with the mediator and the outcome. In this paper, we develop causalmethods based on instrumental variable (IV) approaches for mediation analysisfor count data possibly with a lot of zeros that do not require the assumptionof sequential ignorability. We first define the direct and indirect effectratios for those data, and then propose estimating equations and use empiricallikelihood to estimate the direct and indirect effects consistently. Asensitivity analysis is proposed for violations of the IV exclusion restrictionassumption. Simulation studies demonstrate that our method works well fordifferent types of outcomes under different settings. Our method is applied toa randomized dental caries prevention trial and a study of the effect of amassive flood in Bangladesh on children's diarrhea.

Mediation Analysis for Count and Zero-Inflated Count Data without Sequential Ignorability and Its Application in Dental Studies