response model is used to facilitate a point estimate of a BMD—corresponding to a BMR of 5%—for each chemical alone. A mixture BMD is estimated from the dose-additive model and compared with that estimated from the observed mixture data at the specified mixing ratio. Furthermore, the dose-additive model is used to demonstrate that the mixture BMD is not constant across mixing ratios. That is, the point estimate of the mixture BMD predicted under dose addition is shown to be numerically different if observed and hypothetical mixing ratios of the five chemicals are used. The illustration is concluded with a description of a tiered analytic strategy for mixtures.


Data were kindly provided by Earl Gray, Jr., in the Reproductive Toxicology Division, National Health and Environmental Effects Research Laboratory, Office of Research and Development, Environmental Protection Agency, Research Triangle Park, NC.

Experimental Data. Pregnant Sprague-Dawley rats were dosed by gavage on gestation day (GD) 8-18 with either vehicle control (dose, 0), a dose of one of the chemicals, or a dose of the mixture of five phthalates (BBP, DBP, DEHP, DIBP, and DPP) in a mixing ratio of 3:3:3:3:1. DEP was also evaluated in the single-chemical studies but showed no effect; the DEP data have been retained because they provide additional information on variability. Both single-chemical and mixture studies were conducted in blocks (incomplete block design) with one or two dams per treatment per block with two to four blocks per chemical for a total of 166 litters across chemicals and doses. Testosterone was extracted on GD 18 from the testes of the first three males in each litter and measured with radioimmunoassay. Details are given in Howdeshell et al. (2008). The average of the two measurements (one per testis) for each fetus was used in the analysis herein.

Initial Statistical Analysis. A mixed-effects analysis of variance was used to test for differences in control-group means while adjusting for intralitter correlated data. There was a significant difference in the control-group means of testosterone (in nanograms per milliliter of medium) between studies and a significant block effect, so the data from all studies were adjusted by the average control-group value per block (giving percent of control).

Construction of an Additivity Model. The general strategy for the analysis of the data was to use the single-chemical data to fit a nonlinear logistic model of the mean (μ) testosterone concentration (percent of control) for the five single chemicals and for the fixed-ratio mixture (in terms of total dose), that is,

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