All ETDs from UAB

Advisory Committee Chair

Kui Zhang

Advisory Committee Members

Inmaculada Aban

Charity Morgan

Hon Yuen

Document Type

Dissertation

Date of Award

2015

Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

Abstract

The goal of this research is to develop new statistical models for the analysis of count data even if data exhibit over dispersion or under dispersion and has multiple inflated counts. Although many statistical models are available for the analysis of count data, there is no available statistical model that can address the presence of more than expected multiple counts together with over/under dispersion. In our first paper, we develop a multiple-inflation negative binomial (MINB) model and use the expectation maximization (EM) algorithm along with a numerical optimization to obtain maximum likelihood estimates. We applied the one step smoothly clipped absolute deviation (SCAD) for the variable selection. In the second paper, we develop a multiple-inflation generalized Poisson (MIGP) model and also use the EM algorithm along with a numerical optimization to obtain maximum likelihood estimates. In the third paper, we apply our novel MINB and MIGP models to data related to oral hygiene among systemic sclerosis (SSc) patients. Based on the results from simulated data sets, we find that the MINB model, when used to analyze count data in the presence of multiple inflations and over dispersion, outperformed other existing models in terms of the average square loss (ASL). In our second paper, we obtain similar results for the MIGP model. We find that the MIGP model had the smallest ASL among the other models which can be used to model over dispersed counts. Furthermore, in the second paper, we applied the MIGP model in real data set of social survey. In the third paper, after applying the MINB and MIGP models for analysis of oral hygiene data for systemic sclerosis (SSc) patients, we find that there is no significant association between the dental caries and SSc subtypes after adjusting for "Age" and "Income". This discovery suggests that modeling the count data without incorporating the multiple inflated counts in the analysis could provide substantially misleading results. Therefore, we strongly recommend considering the multiple inflation models when inflation in multiple counts is present.

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