All ETDs from UAB

Advisory Committee Chair

David Redden

Advisory Committee Members

Kathryn Burgio

Charles Katholi

Leslie McClure

Joshua Richman

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) School of Public Health


Generalized linear mixed models (GLMM) are among the commonly used statistical methods for the analyses of binary data from cluster randomized trials (CRT). GLMMs extend the linear mixed models to accommodate, among others, binary outcomes. The linear predictor of GLMMs contains fixed effects and random effects to model the correlation among responses in a cluster. These random effects are usually assumed to be normally distributed but this assumption may not hold in practice. Also, the cluster sizes may vary within a trial for several reasons including loss to follow-up. This variation in cluster sizes can result in unequal cluster sizes. Another assumption that we often come across during the planning of CRTs is that the treatment arm intraclass correlation coefficients (ICCs), which measure the degree of similarity among the members of a cluster, are equal. In the conduct of CRTs, ICCs are selected during the planning stage of the study and as a result the ICCs in all treatment arms are often assumed to be equal. However, that assumption may not hold in practice or at the end of a trial the ICCs may be found to be different. The fact that the random effects distribution is not guaranteed to be normal in practice and that variation in cluster sizes can occur coupled with fact that ICCs in all treatment arms are not always the same warrants an investigation of the violation of these assumptions. As a result, in this dissertation we will investigate, through a simulation study, the consequences of the violation of the distributional assumptions of the random effects for equal and unequal cluster sizes on GLMM analyses when the total number of clusters is small; Type I error, power and precision of ICC estimation will be examined. Also, an investigation into whether assuming equal ICCs in the treatment arms of a cluster randomized trial has an effect on the test of marginal proportions using generalized linear mixed models and generalized estimating equations(GEE) will be conducted through a simulation study. The study will look into the relationship between the results of a likelihood ratio test of the equality of ICCs of the two treatment arms in a CRT and the statistical properties, Type I error rates and power, of the test of marginal proportions using GLMM and GEE. Results from the two methods will be compared to determine whether either of them is more robust to a violation of the equality of ICCs assumption.

Included in

Public Health Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.