Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Chris Gennings


Individuals are exposed to chemical mixtures while carrying out everyday tasks, with unknown risk associated with exposure. Given the number of resulting mixtures it is not economically feasible to identify or characterize all possible mixtures. When complete dose-response data are not available on a (candidate) mixture of concern, EPA guidelines define a similar mixture based on chemical composition, component proportions and expert biological judgment (EPA, 1986, 2000). Current work in this literature is by Feder et al. (2009), evaluating sufficient similarity in exposure to disinfection by-products of water purification using multivariate statistical techniques and traditional hypothesis testing. The work of Stork et al. (2008) introduced the idea of sufficient similarity in dose-response (making a connection between exposure and effect). They developed methods to evaluate sufficient similarity of a fully characterized reference mixture, with dose-response data available, and a candidate mixture with only mixing proportions available. A limitation of the approach is that the two mixtures must contain the same components. It is of interest to determine whether a fully characterized reference mixture (representative of the random process) is sufficiently similar in dose-response to a candidate mixture resulting from a random process. Four similarity measures based on Euclidean distance are developed to aid in the evaluation of sufficient similarity in dose-response, allowing for mixtures to be subsets of each other. If a reference and candidate mixture are concluded to be sufficiently similar in dose-response, inference about the candidate mixture can be based on the reference mixture. An example is presented demonstrating that the benchmark dose (BMD) of the reference mixture can be used as a surrogate measure of BMD for the candidate mixture when the two mixtures are determined to be sufficiently similar in dose-response. Guidelines are developed that enable the researcher to evaluate the performance of the proposed similarity measures.


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VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

May 2010

Included in

Biostatistics Commons