Hyoyoung Choo-Wosoba, PhD candidate, Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences

"Marginal regression models for clustered count data based on zero-inflated Conway-Maxwell-Poisson distribution with applications"

The main purposes of this research were to quantify fluoride exposures from both dietary and non-dietary sources and to associate longitudinal fluoride exposures with dental caries (cavities).We propose a regression model for clustered count data exhibiting excessive zeros and a wide range of dispersion patterns. A zero-inflated version of the CMP distribution is used to describe the marginal distribution of a cluster member given its covariate vector. Two estimation methods (MPL and MES) are introduced. Finite sample behaviors of the estimators and the resulting confidence intervals are studied using an extensive simulation study. One of our primary results from the simulations is that estimators from the MPL method are largely comparable to the estimators from the MES algorithm with respect to accuracy. We also demonstrated that a cluster bootstrap method is capable of producing reasonable variance estimates for both sets of estimators.

By applying our methodology to the data from the Iowa Fluoride Study, we show that frequent tooth brushing and greater daily fluoride intake are protective of caries development, whereas soda pop intake is a risk factor for the same. In addition, we provide an application of an under-dispersion case with a maze Hybrid experiment data.

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