Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Dr. Walter Hans Carter Jr.

Second Advisor

Dr. Chris Jennings


The dosing of combination therapies is commonly undertaken empirically by practicing physicians, and there is a lack of a coherent algorithm to approach the problem of combination dosing. Current methods of evaluating multiple drug combinations in clinical trials generally do not provide information regarding the location of more effective dosages when the combination is not found to differ from the standard, even though the absence of a difference does not necessarily mean the new combination is ineffective. Additionally, if a new combination is found to be more effective, often a large proportion of the subjects has not benefited from the trial. This may lead to problems with patient enrollment and adherence to the study protocol, and even with early stopping rules, the time patients spend on inferior treatments may have lasting detrimental effects. This paper describes an evolutionary operation (EVOP) direct-search procedure to titrate combination doses within individual patients. The Nelder-Mead simplex direct-search method is used to titrate a combination of drugs within individual subjects. Desirability functions are incorporated to define the main response of interest and additional responses or constraints. Statistical methodology for determining whether the titrated treatment combination has resulted in an improvement in patient response and for evaluating whether a therapeutic synergism exists is developed. Inferences can be made about the efficacy of the combination or about the individual drugs that comprise the combination. This approach allows every patient the potential to benefit from the combination under study and permits the consideration of multiple endpoints simultaneously.


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Date of Submission