Use of factorial designs in combination toxicity studies.

The use of factorial designs, in which n chemicals are studied at xn dose levels (x treatment groups), has been put forward as one of the valuable statistical approaches for hazard assessment of chemical mixtures. Very recently a "2(5) study' was presented to describe interactions between the carcinogenic activity of five polycyclic aromatic hydrocarbons and a "5(3) study' was used to identify the non-additive effects of three compounds on developmental toxicity. Full factorial designs, however, lead to very costly experiments and, even if only two dose levels are used, it is not always possible to perform conventional toxicity tests using 2n test groups to identify possible interactions between all chemicals of interest. One way to deal with this problem is the use of fractionated factorial designs. These fractionated designs still identify most of the interactions between the compounds and determine which compounds are important in causing effects, but have the advantage that the number of test groups is manageable. Fractional factorial designs have been shown to be an efficient (i.e. cost-effective) approach to: (a) identify interactive effects between seven trace elements and cadmium accumulation in the body; and (b) describe cases of non-additivity in a mixture of nine chemicals tested in a 4-wk toxicity study in rats.