Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Edward Boone

Second Advisor

David Edwards


The enormous increase of exposure to toxic materials and hazardous chemicals in recent years is a major concern due to the adverse effect resulting from such exposure on human health specifically and all organisms in general. Among the major concerns of toxicologists is to determine an acceptable level(s) of exposure to such hazardous substance(s). Current approaches often evaluate each endpoint and stressor individually. Herein we propose two novel approaches to simultaneously determine the Benchmark Dose Tolerable Region (BMDTR) for multiple endpoints and multiple stressors studies when stressors experience no more than additive effects by adopting a Bayesian approach to compute the non-linear hierarchical model. A main concern while assessing the combined toxicological effect of chemical mixture is the anticipated type of the combined action (i.e. synergistic or antagonistic), thus it was essential to extend the two proposed methods to handle this situation, which imposes more challenges due to the non-linearity of the tolerable region. Furthermore, we proposed a new method to determine the endpoint probabilities for each endpoint, which reflects the importance of each endpoint in determining the boundaries of the Benchmark Dose Tolerable Region (BMDTR). This method was also extended for situations where there is an interaction effect between stressors. The results obtained from this method were consistent with the resulting BMDTR approach in both scenarios (i.e. additive effect and non-additive effect). In addition, we developed new criteria for determining ray designs for follow-up experiments for toxicology studies based on the popular D- A- and E- optimality criteria introduced initially by (Keifer, 1959) for both scenarios (i.e. additive effect and non-additive effect). Moreover, the endpoint probabilities were used to extend these criteria in to weighted versions, where the main motivation behind using these probabilities is to segregate necessary information from un-necessary information through inducing them as weights in to the Fisher Information Matrix. Illustrative examples from simulated data were provided to illustrate all methods and criteria.


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