An efficient experimental design for detecting departure from additivity in mixtures of many chemicals

Berenbaum (J. Theor. Biol. 114 (1985) 413-431) described a procedure for detecting and characterizing departure from additivity in a combination of c (c greater than or equal to 2) chemicals. The attraction of this approach is that it is based on the concentration-response relationship of each of the individual components and, under the assumption of additivity, it is straight forward to predict the response of a given combination. Deviations between the observed and predicted responses for the combination are associated with departures from additivity. Berenbaum based his conclusions regarding synergism/antagonism on numerical differences which do not take into account inherent biological variability. We have developed a procedure which incorporates experimental variation is based on each individual component's concentration-response relationship, and leads to a conclusion regarding the statistical significance of any departure from additivity. The procedure is illustrated with an example.