title: Marginalized zero-inflated negative binomial regression with application to dental caries.
abstract: The zero-inflated negative binomial regression model (ZINB) is often employed in diverse fields such as dentistry, health care utilization, highway safety, and medicine to examine relationships between exposures of interest and overdispersed count outcomes exhibiting many zeros. The regression coefficients of ZINB have latent class interpretations for a susceptible subpopulation at risk for the disease/condition under study with counts generated from a negative binomial distribution and for a non-susceptible subpopulation that provides only zero counts. The ZINB parameters, however, are not well-suited for estimating overall exposure effects, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. In this paper, a marginalized zero-inflated negative binomial regression (MZINB) model for independent responses is proposed to model the population marginal mean count directly, providing straightforward inference for overall exposure effects based on maximum likelihood estimation. Through simulation studies, the finite sample performance of MZINB is compared with marginalized zero-inflated Poisson, Poisson, and negative binomial regression. The MZINB model is applied in the evaluation of a school-based fluoride mouthrinse program on dental caries in 677 children.
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27516, U.S.A.
authors.forename: John S
authors.initials: JS
authors.lastname: Preisser
authors.affiliation: Department of Statistics, University of Calcutta, Kolkata, West Bengal 700098, India.
authors.forename: Kalyan
authors.initials: K
authors.lastname: Das
authors.affiliation: Department of Biostatistics, West Virginia University, Morgantown, WV 26506, U.S.A.
authors.forename: D Leann
authors.identifier: http://orcid.org/0000-0001-8614-7190
authors.initials: DL
authors.lastname: Long
authors.affiliation: Departments of Epidemiology and Pediatric Dentistry, University of North Carolina, Chapel Hill, NC 27516, U.S.A.
authors.forename: Kimon
authors.identifier: http://orcid.org/0000-0003-1290-7251
authors.initials: K
authors.lastname: Divaris
mesh_terms: D016010:Binomial Distribution; D002648:Child; D003198:Computer Simulation; D003731:Dental Caries / Q000517:prevention & control; D005260:Female; D005460:Fluorides, Topical / Q000627:therapeutic use; D006801:Humans; D008297:Male; D009067:Mouthwashes; D016012:Poisson Distribution
chemical_list: D005460:Fluorides, Topical; D009067:Mouthwashes
keywords: caries prevention; count data; excess zeros; marginal models; overdispersion