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 > or = 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.
Gennings
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Department of Biostatistics, Medical College of Virginia/Virginia Commonwealth University, Richmond 23298-0032, USA.
D000236:Adenoma / Q000139:chemically induced; D000818:Animals; D015197:Carcinogenicity Tests; D002273:Carcinogens / Q000633:toxicity*; D004305:Dose-Response Relationship, Drug; D004347:Drug Interactions; D015386:Hazardous Substances / Q000633:toxicity*; D008175:Lung Neoplasms / Q000139:chemically induced; D051379:Mice; D008805:Mice, Inbred A; D011084:Polycyclic Aromatic Hydrocarbons / Q000633:toxicity*; D012107:Research Design; D018570:Risk Assessment; D015262:Xenobiotics / Q000633:toxicity*
D002273:Carcinogens; D015386:Hazardous Substances; D011084:Polycyclic Aromatic Hydrocarbons; D015262:Xenobiotics