Author ORCID Identifier

Defense Date


Document Type


Degree Name

Doctor of Philosophy


Systems Modeling and Analysis

First Advisor

Edward Boone

Second Advisor

David Edwards


All forms of life are being exposed to different levels of harmful chemicals that can cause various and serious side effects. Toxicological experiments enable researchers to test these chemicals on animal to determine their major effects. Although optimal and acceptable dose levels have been investigated, researchers continue to strive to minimize side effects and the chemical dosages. Dose-response models and other benchmark approaches play a role in determining the acceptable exposure levels of hazardous chemicals. Parametric techniques, used to determine the tolerable dosages, utilizing ANOVA and non-linear regression models are well represented in the literature. We determined the benchmark dose tolerable region for multiple chemicals and multiple endpoints using the Bayesian approach. We then considered improving the tolerable region, which contains the safest dosage, by using a sequential Bayesian design. Sequential Bayesian design uses criteria to determine the optimal follow-up experimental design step by considering the parametric dose-response model. Using our developed criterion, our goal is to define the tolerable region and, hence, the tolerable dosage that results in the fewest adverse side effects.

The biggest drawbacks of parametric approaches is the need to specify the “correct” model, which can be difficult depending on the nature of the data. Recently, there has been an interest in nonparametric approaches for tolerable dosage estimation since it does not depend on parameters information or a predefined distribution. We focused on a monotonically decreasing dose-response model, where the response is a percent to control. This imposes two constraints on the nonparametric approach: the dose-response function must be monotonic and always positive. We propose a Bayesian solution to this problem using a novel class of nonparametric models by considering new basis functions, the Alamri Monotonic spline (AM-spline). Our approach is illustrated using two simulated datasets and two experimental datasets from pesticide related research from the US Environmental Protection Agency.

The toxicology experiment considers the effect of combined multiple chemicals that requires a higher-dimensional dose-response model. Furthermore, multivariate parametric and the multivariate nonparametric models have difficulty fitting rough data, which motivated us to develop the AM-spline to fit that aspect. This new model, the Alamri Monotonic K Dimensional spline (AMKD-spline), is a development of the univariate AM-spline model. Our approach is illustrated using three simulated datasets and one experimental dataset from pesticide-related research from the US Environmental Pro- tection Agency.


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Available for download on Tuesday, July 01, 2025