title: Marginal regression models for clustered count data based on zero-inflated Conway-Maxwell-Poisson distribution with applications.
abstract: Community water fluoridation is an important public health measure to prevent dental caries, but it continues to be somewhat controversial. The Iowa Fluoride Study (IFS) is a longitudinal study on a cohort of Iowa children that began in 1991. The main purposes of this study (http://www.dentistry.uiowa.edu/preventive-fluoride-study) were to quantify fluoride exposures from both dietary and nondietary sources and to associate longitudinal fluoride exposures with dental fluorosis (spots on teeth) and dental caries (cavities). We analyze a subset of the IFS data by a marginal regression model with a zero-inflated version of the Conway-Maxwell-Poisson distribution for count data exhibiting excessive zeros and a wide range of dispersion patterns. In general, we introduce two estimation methods for fitting a ZICMP marginal regression model. Finite sample behaviors of the estimators and the resulting confidence intervals are studied using extensive simulation studies. We apply our methodologies to the dental caries data. Our novel modeling incorporating zero inflation, clustering, and overdispersion sheds some new light on the effect of community water fluoridation and other factors. We also include a second application of our methodology to a genomic (next-generation sequencing) dataset that exhibits underdispersion.
authors.affiliation: Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, Kentucky 40202, U.S.A.
authors.forename: Hyoyoung
authors.initials: H
authors.lastname: Choo-Wosoba
authors.affiliation: Department of Preventive and Community Dentistry Department of Epidemiology, University of Iowa, Iowa City, Iowa 52242, U.S.A.
authors.forename: Steven M
authors.initials: SM
authors.lastname: Levy
authors.affiliation: Department of Biostatistics, University of Florida, Gainesville, Florida 32610, U.S.A.
authors.forename: Somnath
authors.initials: S
authors.lastname: Datta
mesh_terms: D001699:Biometry / Q000379:methods; D016000:Cluster Analysis; D003198:Computer Simulation; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D060766:Drinking Water; D005457:Fluoridation; D023281:Genomics; D059014:High-Throughput Nucleotide Sequencing; D006801:Humans; D015233:Models, Statistical; D016012:Poisson Distribution; D012044:Regression Analysis
chemical_list: D060766:Drinking Water
keywords: Bootstrap; Caries data; Expectation-solution algorithm; Generalized estimating equation; Generalized linear model; Genomics; Iowa Fluoride Study