Kai Wang

Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Industrial and Managements Systems Engineering

Committee Chair

Feng Yang

Committee Co-Chair

Xi Chen

Committee Member

Majid Jaridi

Committee Member

Xiaopeng Ning

Committee Member

Dale Porter


One of the most fundamental steps in risk assessment is to quantify the exposure-response relationship for the material/chemical of interest. This work develops a new statistical method, referred to as SKQ (stochastic kriging with qualitative factors), to synergistically model exposure-response data, which often arise from multiple sources (e.g., laboratories, animal providers, and shapes of nanomaterials) in toxicology studies. Compared to the existing methods, SKQ has several distinct features. First of all, SKQ integrates data across multiple sources, and allows for the derivation of more accurate information from limited data. Second, SKQ is highly flexible and able to model practically any continuous response surfaces (e.g., dose-time-response surface). Third, SKQ is able to accommodate variance heterogeneity across experimental conditions, and to provide valid statistical inference (i.e., quantify uncertainties of the model estimates). Through empirical studies, we have demonstrated SKQ's ability to efficiently model exposure-response surfaces by pooling information across multiple data sources.;Based on the SKQ modeling and inference, a design of experiments (DOE) procedure is developed to guide biological experiments for the efficient quantification of exposure-response relationships. Built on SKQ, the DOE procedure inherits the advantages of SKQ and is particularly tailored for experimental data arising from multiple sources, with non-normality and variance heterogeneity, and mapping nonlinear exposure-response relationships. The design procedure is built in a sequential two-stage paradigm that allows for a learning process: In the first stage, preliminary experiments are performed to gain information regarding the underlying exposure-response curve and variance structure; in the second stage, the prior information obtained from the previous stage is utilized to guide the second-stage experiments. Matlab's global optimization function MultiStart is employed to search for optimal designs that will lead to exposure-response models of the highest quality.;SKQ and SKQ-based DOE fit into the mosaic of efficient decision-making methods for assessing the risk of a tremendously large variety of nanomaterials, and helps to alleviate the sustainability concerns regarding the enormous new nanomaterials.