Date of Award:

5-2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

John R. Stevens

Committee

John R. Stevens

Committee

Daniel C. Coster

Committee

Adele Cutler

Committee

Edward W. Evans

Committee

Guifang Fu

Abstract

Dose-response experiments are those that involve giving subjects different amounts of a treatment and observing the outcome. For example, plants may be given fertilizer and their growth could be measured or cancer patients could be given different doses of chemotherapy and their response could be monitored. These experiments are used to understand the relationship between the amount of, and response to, the treatment. Logistic regression models are often used to summarize data from these types of experiments. The dose-response experiment that motivated this dissertation involved treating a grain-pest with a pesticide. Some of the beetles had genes that made them more sensitive to the pesticide. However, the genes were only looked for in the beetles that survived the treatment. Additionally, traditional statistical models yielded unreliable results when they were applied to this data. Both specific summary values (parameter estimates) and likely ranges of values (confidence intervals) were not reasonable. This dissertation developed new statistical methods to improve the statistical modeling of dose-response experiments like this one. Two methods that are used in simpler situations, were applied to this dataset to overcome these problems: a Firth penalty and profile likelihood-based confidence intervals. The Firth penalty improved the parameter estimates and the profile likelihood-based confidence intervals were an improvement over the traditional confidence intervals. Simulations were used to show that proposed methods worked well in a variety of situations. The statistical methods developed here are applicable to other situations not limited to dose-response experiments.

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