Dissertation Defense Announcement

The College of Arts and Sciences announces the Final Dissertation Defense of

Peter Ngutu

for the Degree of Doctor of Philosophy

on July 10, 2018 at 10:00 AM in Dunn Hall, Room 109

Advisor: Dale Bowman

Regression Models for Analyzing Clustered Multinomial and Continuous outcomes under the assumption of Exchangeability

ABSTRACT: We derive an expression for the joint distribution of exchangeable multinomial random variables and continous random variables for the purpose of analyzing clustered multinomial and continous data. In the past such clustered discrete and continous data could be analyzed with the use of quasi-likelihood procedures and generalized estimating equations to estimate marginal mean response parameters. Recently, the idea of exchangeability has been introduced to handle such data but research has focused primarily on analysis of clustered binary and continous outcomes. In applications to areas such as developmental toxicity studies, where discrete and contionus measures are recorded on each fetus, the discrete data may not necessarily be binary. For example, we may want to look at fetal death, malformation and normal fetuses as three possible outcomes separately. An impediment to a full likelihood-based analysis of such clustered multinomial data is the lack of a mathematically tractable representation of the joint distribution. The assumption of exchangeability is often reasonable in these fields of study where outcomes are measured within clusters and cluster responses can be assumed to be exchangeable in the sense that their joint distribution is invariant to permutation. We use this assumption to formulate fully parametric regression models for clusters of bivariate data with multinomial and contionus components. Tractable expressions for likelihood equations are derived and iterative schemes are given for computing efficient maximum likelihood estimates of the marginal mean, correlations, variances and higher moments. Regression models are then proposed having marginal interpretations and reproducible model structures. We demonstrate the use of the exchangeable procedure with an application to a developmental toxicity study involving fetal weight, malformation and death outcomes.