## Advisory Committee Chair

Lioyd J Edwards

## Advisory Committee Members

Dorothy L Long

Jaeger C Byron

Nengjen Yi

Roy C Martin

## Document Type

Dissertation

## Date of Award

2020

## Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

## Abstract

Longitudinal count data sometimes called panel data come up most often in publichealth and biomedical research, where investigators are interested in assessing the association between an identified exposure and the correlated count outcomes. It is worth mentioning most of these correlated count data exhibit over-dispersion, excess zeros and heterogeneous properties which when ignored during analysis can lead to biased estimates of covariate effects. The traditional zero-inflated count models with random effects have been developed to analyze such correlated count data, however the two sets of regression coefficients from this model, directly allow subgroup interpretations with the first set of coefficients providing inferences on the at-risk class mean (non-excess zero group) and the second set providing inferences on the likelihood of being an excess zero class membership. Most investigators are interested in exposure effects that relate the overall mixture population mean and not subgroup effects that these traditional zero-inflated count models represent. The marginalized zero-inflated Poisson model with random effects have been developed to allow direct inferences that relates the overall population mean while excess zeros are adjusted for, however it may fail to account for over-dispersion and other heterogeneous properties that may exist in data. The outline of this dissertation is as follow: after review of literature the first paperextends the marginalized zero-inflated Poisson regression model with random effects to propose the marginalized zero-inflated negative binomial model with random effects that allow modeling of correlated and over-dispersed count outcomes populated with many zeros. Simulations were performed to assess finite sample characteristics of the model after which it was applied to lesion counts data from the CombiRx study on multiple sclerosis patients. The two marginalized zero-inflated models mentioned above assume the randomeffects included in the models have a multivariate normal distribution with mean zero and constant (homogeneous) variance covariance matrix. Papers 2 and 3 relaxed this assumption to allow parameters in the variance covariance matrix to vary relative to a measured covariate, while overall covariate effects on mean count outcomes are assessed. We demonstrate the practical utility of the models in papers 2 and 3 by applying both to count data from the COMBINE study on alcohol dependence.

## Recommended Citation

Ampah, Steve Boateng, "Marginalized Models With Heterogeneous Random Effects For Zero-Inflated Longitudinal Count Data" (2020). *All ETDs from UAB*. 685.

https://digitalcommons.library.uab.edu/etd-collection/685