Mediation with Zero-Inflated Count Outcomes for Substance Use Data: Negative Binomial, Poisson, and Hurdle Models

Introduction: Many studies of substance use are concerned with examining mechanisms for reducing substance use behaviors in addition to ultimate outcomes. Researchers often use mediation analysis to achieve this aim. Additionally, a common issue in substance use research is the presence of many zeroes in a count outcome variable, such as number of drinks per week or number of substances used in the past month. There are developed mediation methods for categorical outcomes, including continuous, count, and binary outcomes. However, less research has examined mediators of zero-inflated (ZI) count outcomes, and those approaches are not easily extended to ZI count models, which model zeroes and counts separately and split the mediated effect into two parts.

Methods: I describe the process of mediation analysis for ZI count outcomes, and call attention to the specific issues that arise when count outcomes are ZI. A method is described to assess mediation for ZI count outcomes that is applicable for a variety of generalized linear models (GzLMs), including ZI Poisson (ZIP), ZI negative binomial (ZINB), and additionally hurdle models.

Results: Once the model is chosen, mediated effects can be calculated and tests of mediation can be conducted, including bootstrapped confidence intervals of the conditional mediated effects. The differences between mediation for ZI and non-ZI models are highlighted using several examples of substance use data.

Conclusions: After illustrating how a recent mediation method for zero-inflated counts can be applied to prevention data, future directions for mediation with zero-inflated count outcomes are discussed, including extensions to longitudinal models.