Mediation Analysis Using Marinalized Zero-Inflated Poisson Model

Abstract

Mediation analysis has become exponentially more popular over the last decade as researchers are interested in establishing mechanistic pathways for intervention. Standard statistical methods emphasize quantifying and testing whether a specific exposure impacts a particular health outcome. Mediation analysis addresses the question ‘How is the exposure causing the outcome?’ by examining the extent to which an intermediate variable, called a mediator, influences the relationship between an exposure and an outcome. While multiple mediation strategies exist, the counterfactual approach to mediation allows for mediation effects to be estimated directly with nonlinearities and interactions. The counterfactual approach allows for the effect of the exposure on the outcome to be decomposed to find what portion of the effect is acting through the mediator and external to the mediator.

Although mediation methods have increased drastically, there are still limited options for mediation analysis with zero-inflated count variables. Current use of zero-inflated count variables in mediation analysis are computationally intensive, difficult to derive, or use zero-inflated models that do not directly derive overall population mean estimates leaving research vulnerable to misinterpretation. The marginalized zero-inflated Poisson (MZIP) model allows for direct estimation of the overall population mean while the counterfactual approach to mediation is easy to derive and computationally simple. Thus, we propose merging these two frameworks to estimate mediation effects with zero-inflated count variables.

The purpose of this proposal is to extend mediation methodology using the counterfactual approach to mediation to scenarios where either the mediator or outcome is a zero-inflated count variable. This methodology will allow for rapid derivation of mediation effects, exposure-mediator interactions with effect decomposition, and tools for implementing this novel method in statistical software. The first paper in this dissertation expands mediation methodology to estimate mediation effects with a zero-inflated mediator using MZIP. The second paper develops an approach to mediation with zero-inflated count outcomes using MZIP that provides population-average mediation effects. The final paper introduces R software package implementation of the methods proposed in this dissertation. This package is titled mzipmed and is located on the Comprehensive R Archive Network.