Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Public Health


Epidemiology and Biostatistics

First Advisor

Dr. Philip M. Westgate


Opioid misuse is a nationwide epidemic, with Kentucky having one of the highest opioid overdose-related fatality rates across all US states. These rates have increased significantly over the past decade, with particularly large increases during the COVID-19 pandemic. This dissertation aims to study the behavior of these increases and the methods for the marginal modeling of count outcomes related to opioid overdose.

Opioid overdose-related fatality rates in Kentucky increased significantly during the COVID-19 pandemic. In this chapter, we characterize the changes in opioid overdose fatality rates in Kentucky and identify associations between potential factors and fatality rates. County-level opioid overdose fatality data were used to fit a marginal negative binomial model to determine which factors were associated with opioid overdose fatality rates in 2019 (before the COVID-19 pandemic) and 2021 (2nd COVID-19 pandemic). Results show that adjacent-to-metropolitan county status was associated with opioid overdose fatalities in 2021, indicating a differential effect of COVID-19 on suburban communities.

Rare cluster-level count outcomes are often found in epidemiological settings, such as cluster-randomized trials (CRTs) and observational studies. The goal of this chapter is to compare marginal modeling methods for rare events, with a particular focus on opioid overdose fatalities. For both CRT and observational study settings, simulation studies were conducted to compare the validity of inference and power of the three regression methods. Conditional on a valid standard error estimator, power was similar between the regression methods when the event of interest was very rare, but differed between the methods as the marginal probability of the event increased. Careful consideration is required when choosing a regression method for modeling rare cluster-level count outcomes in the settings studied in this chapter.

Events that can occur more than once are often of interest in epidemiology research. One such event is opioid-related poisonings, which is the focus of the third chapter. Using opioid poisoning data from Kentucky Emergency Medical Services (EMS) records, simulated data sets were used to compare the validity of inference and power of the three marginal modeling methods used in the previous chapter for modeling rare events that can occur more than once per person. Based on the results from the simulation studies, all three regression methods produced test sizes that were close to nominal, although slightly inflated. In terms of power, modified negative binomial and modified overdispersed binomial regression performed similarly, and were more powerful than modified Poisson regression.

Digital Object Identifier (DOI)

Funding Information

This project was supported by:
Data-Driven Responses to Prescription Drug Misuse in Kentucky (grant no. 2017-PM-BX-K026) awarded by the
Bureau of Justice Assistance (BJA) to the Kentucky Injury Prevention and Research Center as bona fide agent for the Kentucky Department for PublicHealth. The BJA is a component of the Department of Justice’s Office of Justice
Program, which includes the Bureau of Justice Statistics, the National Institute of Justice, the Office of Juvenile Justice and Delinquency Prevention, the Office of Victims Crime, and the SMART Office. Viewpoints or opinions in this document are those of the authors and do not necessarily represent the official position or policies of the U.S. Department of Justice.