Evaluation of a Proportional Response Addition Approach to Mixture Risk Assessment and Predictive Toxicology Using Data on Four Trihalomethanes from the U.S. EPA's Multiple-Purpose Design Study

Abstract

In this study, proportional response addition (Prop-RA), a model for predicting response from chemical mixture exposure, is demonstrated and evaluated by statistically analyzing data on all possible binary combinations of the four regulated trihalomethanes (THMs). These THMs were the subject of a multipurpose toxicology study specifically designed to evaluate Prop-RA. The experimental design used a set of doses common to all components and mixtures, providing hepatotoxicity data on the four single THMs and the binary combinations. In Prop-RA, the contribution of each component to mixture toxicity is proportional to its fraction in the mixture based on its response at the total mixture dose. The primary analysis consisted of 160 evaluations. Statistically significant departures from the Prop-RA prediction were found for seven evaluations, with three predications that were greater than and four that were less than the predicted response; interaction magnitudes (n-fold difference in response vs. prediction) ranged from 1.3 to 1.4 for the former and 2.6 to 3.8 for the latter. These predictions support the idea that Prop-RA works best with chemicals where the effective dose ranges overlap. Prop-RA does not assume the similarity of toxic action or independence, but it can be applied to a mixture of components that affect the same organ/system, with perhaps unknown toxic modes of action.

Keywords: Scheffé confidence interval; hepatotoxicity; independent action; linear contrasts; mixture risk estimation; predictive computational toxicology; toxicological interaction.

Figure 1

Design for evaluating Prop-RA using binary mixtures. Total dose = dosage of each component alone, or mixture dosage (sum of component dosages). Three total doses of 0.1, 1.0, and 3.0 mmol/kg/day were used with each component and with the 1:1 mixture. Only the higher dosages of 1.0 and 3.0 mmol/kg/day were used with the environmental mixture (2.7:1 for this example of CHCl₃:BDCM). Comparing the height of each two-colored bar with the height of the adjacent bars shows that the mixture dosage is also one of the dosages for each of the component chemicals.

Figure 2

Data on percent relative liver weight (PcLiv) show fairly consistent variance over the components and mixture. (a): CHCl₃, BDCM, and the mixture (1:1 ratio) at dosage = 0.1 mmol/kg/day. (b): CHCl₃, CHBr₃, and the mixture (1:1 ratio) at dosage = 1.0 mmol/kg/day. Note: the vertical dimension of each outlier box shows the interquartile range with the horizontal line in the box denoting the median; the dots are jittered data points.

Figure 3

Data on ALT activity (IU/liter) for exposure to CHCl₃, BDCM, and the mixture (2.7:1 ratio) at dosage = 1.0 mmol/kg/d from CHCl₃:BDCM-rep, showing the stabilizing influence on variance by the log transform (boxes are more uniform in length). (a): Response as ALT. (b): Response as log10(ALT). Note: the vertical dimension of each outlier box shows the interquartile range with the horizontal line in the box denoting the median; the dots are jittered data points.

Figure 4

Consistency of data with the Prop-RA prediction for PcLiv and LogALT. Circles indicate concordance between data and Prop-RA prediction. Filled-in symbols denote statistically significant departure from the Prop-RA prediction for that dose–mixture combination. The red 45-degree line is added to show concordance; it is not a linear regression. (a) PcLiv = relative liver weight (percent). Rhombus: shows a statistically significant departure from Prop-RA for binary combination BDCM:CDBM (dosage = 3.0 mmol/kg/day, mixing ratio = 2.4:1). (b) LogALT = log10(ALT). Rhombus: shows a statistically significant departure from Prop-RA for binary combination CHCl₃:CHBr₃ (dosage = 3.0 mmol/kg/day, mixing ratio = 1:1). Square: shows a statistically significant departure from Prop-RA for binary combination CDBM:CHBr₃ (dosage = 3.0 mmol/kg/day, mixing ratio = 10:1).

Figure 5

Consistency of data with the Prop-RA prediction for LogAST and LogSDH. Circles indicate concordance between data and Prop-RA prediction. Filled-in symbols denote statistically significant departure from the Prop-RA prediction for that dose–mixture combination. The red 45-degree line is added to show concordance; it is not a linear regression. (a) LogAST = log10(AST). Rhombus: shows a statistically significant departure from Prop-RA for binary combination CHCl₃:CDBM (dosage = 0.1 mmol/kg/day, mixing ratio = 1:1). Square: shows statistically significant departure from Prop-RA for binary combination CHCl₃:BDCM (dosage = 1.0 mmol/kg/day, mixing ratio = 2.7:1). Triangle: shows statistically significant departure from Prop-RA for binary combination CDBM:CHBr₃ (dosage = 3.0 mmol/kg/day, mixing ratio = 10:1). (b) LogSDH = log10(SDH). Rhombus: shows a statistically significant departure from Prop-RA for binary combination BDCM:CHBr₃ (dosage = 3.0 mmol/kg/day, mixing ratio = 1:1).

Figure 6

Dose ranges (horizontal line segments, excluding controls) of the hypothetical chemicals A–E for a given response of interest. The vertical line is the lowest maximum component dose level (25 µM), that of chemical A, at which 100% response was experimentally observed. There is no dose range overlap of chemical A with any other component, forcing an estimated response level based on possibly extreme extrapolation.