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). Use of the SCR and SCNR methods for binary endpoints are demonstrated using a dichotomized gait score as an indication of toxicity. For both methods, the overall hypothesis of additivity was rejected, indicating significant departure from additivity when the five pesticides were combined at the specified mixing ratio. By comparison of the predicted response under additivity to the modeled response of the experimental mixture data this departure from additivity was characterized as synergy (greater than additive toxicity). To examine the influence of malathion in the mixture, it was removed from the five-pesticide mixture (full ray) and the remaining four chemicals (reduced ray) were combined at the same relative proportions used in the full fixed-ratio ray There was not a significant departure from additivity along the ray with the four remaining pesticides omitting malathion. Thus, although malathion was not dose-responsive alone, it significantly interacted with the other pesticides.