Titrating and evaluating multi-drug regimens within subjects.

The dosing of combination therapies is commonly undertaken empirically by practising physicians, and a coherent algorithm to approach the problem of combination dosing is currently lacking. Current methods of evaluating multiple drug combinations in clinical trials fail to provide information regarding the location of more effective doses 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. Moreover, in studies where the new combination is found more effective, often a large proportion of the study participants obtain no benefit from the trial. Even with early stopping rules, the time these subjects spend on inferior treatments can have lasting detrimental effects, leading to problems with patient enrolment and adherence to study protocol. This paper describes an evolutionary operation (EVOP) direct-search procedure to titrate combination doses within individual patients. The Nelder-Mead simplex direct-search algorithm is used to titrate combinations of drugs within individual subjects. Desirability functions are utilized 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 subject response and for evaluating for therapeutic synergism is developed. Inferences can then be made about the efficacy of the combination or about the individual drugs that comprise the combination. The advantages of this approach include affording every patient the potential to benefit from the combination under study and permitting the consideration of multiple endpoints simultaneously. Copyright 2003 John Wiley & Sons, Ltd.