Models for analyzing zero-inflated and overdispersed count data: an application to cigarette and marijuana use

Area of Science:

• Biostatistics
• Tobacco Control Research
• Epidemiology

Background:

• Count outcomes are common in tobacco research but often exhibit excess zeros and overdispersion, violating assumptions of standard regression models.
• Traditional methods assuming normal distributions are inappropriate for such data, potentially leading to erroneous conclusions.
• This study addresses the need for appropriate statistical methods to analyze complex count data in tobacco use research.

Purpose of the Study:

• To compare and contrast various regression models for analyzing count data with excess zeros and overdispersion.
• To illustrate the application of these models using smoking data from youth e-cigarette users.
• To provide recommendations for selecting appropriate models based on data characteristics and research questions.

Main Methods:

• Evaluation of Poisson, zero-inflated Poisson (ZIP), hurdle Poisson (HUP), negative binomial (NB), zero-inflated negative binomial (ZINB), and hurdle negative binomial (HUNB) regression models.
• Assessment of models based on their ability to handle zero-inflation and overdispersion.
• Application of models to analyze cigarette and marijuana smoking reports from a youth e-cigarette user study, with predictors including gender, age, and e-cigarette use.

Main Results:

• Analysis of 69 subjects revealed significant zero-inflation (36% no cigarettes, 64% no marijuana) and overdispersion in smoking counts.
• The zero-inflated negative binomial (ZINB) and hurdle negative binomial (HUNB) models demonstrated the best fit for cigarette counts.
• For marijuana counts, NB, HUNB, and ZINB models showed good fit, with ZINB offering superior interpretability.

Conclusions:

• The negative binomial (NB) model is suitable for overdispersed smoking data without zero-inflation.
• In the presence of zero-inflation, ZINB or HUNB models are recommended to capture additional heterogeneity.
• Model selection should consider zero-inflation assumptions, study design, and research objectives, alongside model fit and interpretability.