Abstract: Titration of a combination of drugs or treatment modalities within individual subjects is carried out using an evolutionary operation (EVOP) direct-search procedure such as the Nelder-Mead simplex. 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 also incorporated. Inferences can be made about the efficacy of the combination or about the individual drugs or treatment modalities 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.

Abstract: Methods are provided for the statistical analysis of interactions among agents in a combination of agents (i.e. departures from additivity), with respect to a quantifiable result of exposure to the combination of agents. Examples include the interactions among chemicals in a mixture of chemicals with respect to health disorders caused by exposure to the mixture of chemicals. The invention provides methods for determining how many of the agents in the mixture interact, whether the interaction is synergistic or antagonistic, and the interaction threshold concentration of agents at which interactions are observed. Further, the methods are especially useful for analyzing combinations of three or more agents for which classical methods of analysis would require a prohibitively large number of data points. Software programs for implementing the invention are also provided.

Abstract: Titration of a combination of drugs or treatment modalities within individual subjects is carried out using an evolutionary operation (EVOP) direct-search procedure such as the Nelder-Mead simplex. 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 also incorporated. Inferences can be made about the efficacy of the combination or about the individual drugs or treatment modalities 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.