Complex Mixtures Methods for In Vivo Toxicity Testing (1988) / Chapter Skim
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Appendix E: Cancer Models
Appendix E: Cancer Models
Pages 185-201
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From page 185... ...
When mixture components are tested for carcinogenicity in a laboratory bioassay, inclusion of high-dose multiple-exposure groups might yield little useful information, if human environmental exposure to the mixture occurs only at low doses. In such a case, the results of this appendix suggest that cancer predicted from bioassays of the individual mixture components can yield a good estimate of the cancer risk associated with human exposure to the mixture.
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From page 186... ...
On the basis of this examination, general principles concerning the most efficient approaches for estimating the joint effects of multiple agents at environmental doses are discussed. DERIVATION OF THE MULTISTAGE MODEL THAT ACCOUNTS FOR EXPOSURE TO MULTIPLE CARCINOGENIC AGENTS The multistage model assumes that a cell becomes a cancer cell by progressing through an ordered sequence of stages.
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From page 187... ...
· Each of the cells acts independently with regard to becoming transformed and ultimately leading to a tumor. Then the age-specific death rate due to a specified tumor type in a particular organ can be expressed, to a close approximation, as hate = N dot—W)
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From page 188... ...
A hypothetical biologic example is then described in which the parameters of the model are given a specific numerical form, so that we can investigate the effect of the synergism observed in a carcinogenesis bioassay on environmental-exposure cancer-risk estimates. ILLUSTRATIVE MULTISTAGE MODEL THAT RESULTS IN SYNERGISTIC EFFECT A simple multistage model that results in an effect greater than additive arises from the assumption that each of two carcinogenic agents affects the transition rates of different single stages in the multistage process.
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From page 189... ...
Using this model, the next section describes the dose dependence of the synergistic effect. ESTIMATION OF LARGEST SYNERGISTIC EFFECT DETECTABLE IN 2 x 2 BALANCED-DESIGN EXPERIMENT The experimental design most often used for estimating the joint effects of multiple agents is the balanced 2 x 2 form consisting of four experimental groups: control, a single exposure group for each of two agents, and a joint exposure group at the same doses of the single agents.
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From page 190... ...
That is done so that a response can be measured for each agent, but the greatest possible leeway is left for measuring the joint effect of two agents. Assuming zero tumors in the control group, because the background rate is low, five or more tumors are needed in a test group for the response to be considered statistically significant at the 0.05 level, according to a Fisher exact 2 x 2 test.
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From page 191... ...
They represent a scaling factor to redefine the equation for specific exposure potencies. To obtain a specific equation, we arbitrarily assume that the low-dose response to each of the single agents resulted from exposures at x1 = 0.1 and x2 = 0.2; agent 1 is twice as potent as agent 2.
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From page 192... ...
That model has a large interaction-synergistic effect built into it; it is about the largest that could be measured with a classic 2 x 2 balanced design with 50 animals per exposure group and that would allow the statistical estimation of the multistage model. In many situations, the results of multiple-agent exposure experiments are not available, so estimates of cancer risk associated with environmental exposures must be based on the results of single-agent expenments.
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From page 193... ...
PRACTICAL IMPLICATIONS DISCERNIBLE FROM NUMERICAL INVESTIGATION OF GENERALIZED MULTISTAGE MODEL If the previous examples were representative of the types of dose-response relationships encountered in practice, the following conclusions can be drawn: · Agents with high environmental exposure such as background radiation, cigarette smoke, and some workplace exposures must be investigated very carefully, because, if they act on the same cell type in the same organ, the potential for a strong synergistic effect is great. · The excess cancer risk at low doses from an agent that acts on the same cell type in the same organ as another agentts)
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From page 194... ...
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From page 195... ...
the accuracy is very good for the full span of background rates. ~ ~ , ~ ~ ~ ADDITIVITY OF EXCESS RISKS AT LOW DOSES Interactive effects at moderate to high doses have been demonstrated in toxicologic experiments and observed in epidemiologic studies, but existence of
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From page 196... ...
, k—14. At any fixed time t, it follows from Equation E-23 that the excess risk at low doses may be written as H(xl,x2)
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From page 197... ...
The same argument may be invoked in the case of joint exposure to two substances C, and C2, to demonstrate low-dose linearity and hence additivity of the excess risks associated with C, and C2 separately. Specifically, suppose that the joint response rate can be expressed as P(x,, x2)
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From page 198... ...
(E-30) = (1 MULTIPLICATIVE-RISK MODELS In some cases, the interaction between two substances might be well described by a multiplicative model in which the relative risk associated with the mixture is the product of the relative risks associated with the components.
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From page 199... ...
The response surface described by the fitted model may then be used to extrapolate to lower doses. The preceding section identified models under which the excess risks associated with simultaneous exposures to C ~ and C2 would be additive at sufficiently low doses.
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From page 200... ...
Additivity at low doses was also demonstrated under a general class of additive background models and under the multiplicative risk model when the relative risk for each component in the mixture is small. In addition, it can be shown for a broad range of mathematical dose-response models that the joint risk associated with a complex mixture can be determined on the basis of the background risk and the risks associated with the individual components.
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From page 201... ...
Prediction of low-dose risks generally requires the extrapolation of results obtained at higher doses that induce measurable tumor-response rates. When the excess risks associated with exposures to mixture components can be reasonably considered to be additive, that can be done by downward extrapolation of the dose-response curves for the individual components.
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