Analysis of functional effects of a mixture of five pesticides using a ray design.

The protection of human health from the adverse effects of cumulative environmental exposure to chemical mixtures is an important issue. Of particular interest is the detection and characterization of interaction among chemicals in complex mixtures. Response surface methodology, often supported by factorial designs, is the classical statistical experimental approach. Fixed-ratio ray designs, which may include the use of single chemical data in addition to data along mixture ray(s), have been proposed as an alternative approach. Such designs permit a reduction in the amount of experimental effort when the region of interest can be restricted to exposure-relevant mixing ratios. A ‘single chemicals required’ (SCR) approach and a ‘single chemicals not required’ (SCNR) approach are both described. The methods are illustrated with a five-chemical mixture of organophosphorus pesticides—acephate (ACE), diazinon (DIA), chlorpyrifos (CPF), malathion (MAL) and dimethoate (DIM). Their relative proportions in the mixture were based on the relative dietary human exposure estimates of each chemical as projected by the U.S. EPA Dietary Exposure Evaluation Model (DEEM).