Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Dr. Chris Gennings


An alternative to the full factorial design, the ray design is appropriate for investigating a mixture of c chemicals, which are present according to a fixed mixing ratio, called the mixture ray. Using single chemical and mixture ray data, we can investigate interaction among the chemicals in a particular mixture. Statistical models have been used to describe the dose-response relationship of the single agents and the mixture; additivity is tested through the significance of model parameters associated with the coincidence of the additivity and mixture models.It is often assumed that a chemical or mixture must be administered above an unknown dose threshold in order to produce an effect different from background. Risk assessors often assume that interactions are a high-dose phenomenon, indicating that doses below the unknown interaction threshold are associated with additivity. We developed methodology that allows the user to simultaneously estimate the dose threshold and the interaction threshold. This methodology allows us to test for interaction and, secondarily, to test for a region of additivity. The methodology and optimal design characteristics were illustrated using a mixture of nine haloacetic acids.The application of statistical optimality criteria to the development of experimental designs is vital to the successful study of complex mixtures. Since the optimal design depends on the model of interest and the planned method of analysis, developments in statistical methodology should necessarily correspond to consideration of the experimental design characteristics necessary to implement them. The Flexible Single Chemical Required methodology is based on an implicit statement of additivity. We developed a method for constructing the parameter covariance matrix, which forms the basis of many alphabetic optimality criteria, for the implicit FSCR models. The method was demonstrated for a fixed-ratio mixture of 18 chemicals; the original mixture experiment comprises the first stage data, and the optimal second stage design was presented. Waldtype procedures for hypothesis testing in nonlinear models are based on a linear approximation. As a result, likelihood ratio-based procedures may be preferred over Waldtype procedures. We developed a procedure for using the likelihood ratio-based lower confidence bound as an optimality criterion, which can be used to find the optimal second stage design for improving the inference on a particular model parameter. The method was demonstrated for a single agent, as a means of improving the inference on the dose threshold.


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Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

June 2008

Included in

Biostatistics Commons