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In work involving modeling of response surfaces to describe the effects of cancer chemotherapy treatments, it is important to define activity and therapeutic synergism in a statistically defensible manner. This requires the construction of confidence intervals around the estimated optimal treatment which has been achieved by use of an indirect method first proposed by Box and Hunter. Activity for a drug or a combination can be claimed at 100(1 - alpha)% level of confidence when the 100(1 - alpha)% confidence interval about the optimal treatment excludes a zero dose. Results of treatment of B16 melanoma and Lewis lung carcinoma with 3,4-dihydroxybenzohydroxamic acid are used to demonstrate this definition. Extensions of this concept lead to a statistically valid definition of therapeutic synergism. If the confidence region about the optimum combination of k drugs does not contact any of the k - 1 dimensional subspaces, then a k drug therapeutic synergism can be claimed. In the event that a k drug therapeutic synergism cannot be claimed, there may be subsets of the drugs which do combine with therapeutic synergy. These concepts are demonstrated by two- and three-drug combination experiments in L1210-bearing C57BL/6 x DBA/2 F1 (B6D2F1) mice. Razoxane and dacarbazine show therapeutic synergism at a 95% confidence level. A three-drug combination of 5-fluorouracil, Teniposide, and mitomycin C is considered. In this case, although the estimated optimum treatment includes 48.1 mg of 5-fluorouracil per kg, 15.9 mg of Teniposide per kg, and 3.9 mg of mitomycin C per kg, the confidence region generated failed to confirm at an 80% level of confidence that 5-fluorouracil was a necessary component of the best treatment.
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