On testing for drug/chemical interactions: definitions and inference.

The notion of zero interaction in the statistical literature is not always equivalent to what is found in the toxicology literature. A discussion about when they are the same is provided here. Design issues are of paramount importance in the analysis of drug combinations (mixtures of chemicals) when the number of constituents in the combination is larger than, say, three as the usual factorial designs are not feasible. An economical design necessary and sufficient to support the estimation of an additivity model is single drug (chemical) dose-response data. Once estimated, the additivity surface can be used to make comparisons to the observed data at combination points of interest. Examples are provided to demonstrate the methods.