When two drugs with overtly similar therapeutic effects are administered together the constituent drugs may produce an effect that is greater than expected from the individual potencies. Such superadditive (synergistic) combinations have obvious clinical importance, especially in possible new treatments of drug abuse. Therapeutically a synergistic pair for treatment allows reduced doses and consequent reduction in the frequency and severity of adverse reactions. From a toxicological perspective synergism between a new medication for drug abuse and the abused drug (or others being taken) jeopardizes the safety of the potential medication. Besides these therapeutic considerations the detection of synergism provides quantitative information that may aid in uncovering mechanism. On the other hand, drug interactions can be subadditive(antagonistic). Methodology for determining whether a drug combination is superadditive or subadditive requires quantitative information and a statistical demonstration that the combination attains a prescribed level of effect with a combination dose that is significantly different than that calculated from simple additivity. Moreover, synergism or antagonism may occur with one dose combination and not occur with another set of doses of the same drug pair. Statistical analysis is essential. Statistical methodology, derived years ago, and widely applied since then, has been limited to quantal assays in which the drugs yield parallel linear regressions of percent effect on log(dose). Non-parallel dose-effect data and all experiments with graded effects, could not, until recently, be analyzed with these methods and much combination data, especially data from drug discrimination and reinforcement studies, cannot be readily analyzed for synergism. The kind of laboratory based experiments conducted to assess behavioral effects related to an abused drug may require new metrics for use in the dose-response analysis that is the basis of the statistical analysis. The work proposed here is aimed at deriving the needed metrics, statistical formulas, associated experimental design techniques and computer programs that are applicable to drug combinations especially as these pertain to medications development for treating drug abuse. Experimental laboratory methods used in assessing behaviors and effects associated with addiction and drugs of abuse, and which are practical and cost effective in combination studies, provide the basis of these derivations. Accordingly, at least four standard but different experimental designs will be studied and, for each, statistical methodology developed, as well as a newer response-surface methodology. A comparison of the methods, based on the precision of the estimated parameters, the number of subjects needed, and the number of individual and combination doses, will be made and applied to published combination drug data.
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