Dose-Response Models

Uncertainty on tlie other hand, represents lack of knowledge about factors such as adverse effects or contaminant levels which may be reduced with additional study. Generally, risk assessments carry several categories of uncertainly, and each merits consideration. Measurement micertainty refers to tlie usual eiTor tliat accompanies scientific measurements—standard statistical teclmiques can often be used to express measurement micertainty. A substantial aniomit of uncertainty is often inlierent in enviromiiental sampling, and assessments should address tliese micertainties. There are likewise uncertainties associated with tlie use of scientific models, e.g., dose-response models, and models of environmental fate and transport. Evaluation of model uncertainty would consider tlie scientific basis for the model and available empirical validation. 

Benchmark Dose Model—A statistical dose-response model applied to either experimental toxicological or epidemiological data to calculate a BMD. 

Physiologically Based Pharmacodynamic (PBPD) Model—A type of physiologically-based dose-response model which quantitatively describes the relationship between target tissue dose and toxic end points. These models advance the importance of physiologically based models in that they clearly describe the biological effect (response) produced by the system following exposure to an exogenous substance. 

Model equations can be augmented with expressions accounting for covariates such as subject age, sex, weight, disease state, therapy history, and lifestyle (smoker or nonsmoker, IV drug user or not, therapy compliance, and others). If sufficient data exist, the parameters of these augmented models (or a distribution of the parameters consistent with the data) may be determined. Multiple simulations for prospective experiments or trials, with different parameter values generated from the distributions, can then be used to predict a range of outcomes and the related likelihood of each outcome. Such dose-exposure, exposure-response, or dose-response models can be classified as steady state, stochastic, of low to moderate complexity, predictive, and quantitative. A case study is described in Section 22.6. 

Figure 22.3 The drug dose-response model was augmented by nsing data for the comparator drug. Because the mechanism of the drugs was the same, this comprised additional data for the model. This enhanced the predictive power of the model, in a better estimate for central tendency (solid line compared with dotted line) bnt also in smaller confidence intervals. This is especially prononnced at the higher doses— precisely where data on the drug were sparse. See color plate.

C Low dose effects usually not measurable directly In human or animal observations Need to extrapolate observed high dose effects to low or zero dose range by theoretical dose-response models ... 

Assumptions in Risk Extrapolation. Risk extrapolation cannot be performed as a mechanical exercise, due to the need for judgment in the selection of data and application of dose-response models. In particular, there are a number of implicit assumptions inherent in risk extrapolation. They may be summarized as follows ... 

Dose-Response Extrapolation Models. A dose-response model is simply a hypothetical mathematical relationship between dose-rate and probability of response. For example, the simplest form of such a model asserts that probability of tumor initiation is a linear multiple of dose-rate (provided the dosage is well below the organism s acute effect threshold for the substance in question). In general, we will express dose-response models as follows ... 

The most widely-accepted dose response model at the present time is the multi-stage model, which has great flexibility in curve-fitting, and also has a strong physiological justification. Although it is difficult to implement, there are already computer codes in existence that estimate the model parameters (13). The two most widely-used models, until recently, were the one-hit model and the log-probit model. They are both easy to implement, and represent opposite extremes in terms of shape - the former represents the linear non-threshold assumption, whereas the latter has a steep threshold-like curvature. In numerous applications with different substances it has been found that these three... 

Gilbert ME. 1997. Towards the development of a biologically based dose-response model of lead neurotoxicity. American Zoologist 37(4) 389-398. 

Cothem, C.R., D.J. Crawford-Brown, and M.E. Wrenn. 1990. Application of environmental dose-response models to epidemiology and animal data for the effects of ionizing radiation. Environ. Inter. 16 127-140. 

Winter, C.K. (2003). Exposure and dose-response modeling for food chemical risk assessment, in Schmidt, R.H. and Rodrick, G.E., eds.. Food Safety Handbook, Wiley-Interscience, Hoboken, pp. 73-88. 

For carcinogens a linear, no-threshold dose-response model (Figure 8.1) is assumed to apply at low dose, unless data are available in specific cases to demonstrate that such a model is inappropriate. 

If people receive this dose of methylene chloride each day for a full lifetime, then according to the EPA dose-response model, the upper bound on excess lifetime cancer risk is ... 

The linear, no-threshold, dose-response model is accurate for very low exposures. 

Human beings are more sensitive to the carcinogenic effects of methylene chloride than are the experimental animals used for hazard and dose-response modeling. 

Microbiologists have developed ways to model microbial growth and, using assumptions related to the expected behavior of organisms under different environmental conditions, these models are then coupled with dose-response models with the result that risks (responses) can be estimated, given a certain degree of knowledge about initial microbe counts and the environmental conditions (related... 

The most important research needs are related to the determination of the responses of natural ecosystems and agroecosystems to chronic exposure to oxidant pollutants. In particular, chronic-dose-response models are needed to understand the responses of the dominant primary-producer species constituting forest ecosystems in both the eastern and the western United States. The resulting alteration of interactions with other sub ems-—e.g., consumers and decomposers—must also be investigated. 

Concentration response data are analyzed by a nonlinear regression logistic dose response model. Each of the crude extracts are fractionated into 10-15 subfractions. For each crude extract and the associated subfractions, ICsos and IC90S are determined as outlined above. All crude and subfractions of a particular marine organism are assayed simultaneously (within one assay) and include ribavirin as reference drugs using only A/WY/03/2003 virus. 

Haanstra, L. Doehnan, P. An ecological dose response model approach of short and long-term effects of heavy metals on arylsulphatase activity in soil. Biol. Pert. Soils 1991, 11, 18-23. 

For continuous data, there are still a number of outstanding issues regarding the benchmark including (Crump 2002) (1) definition of an adverse effect (2) whether to calculate the BMD from a continuous health outcome, or first convert the continuous response to a binary (yes/no) response (3) quantitative definition of the BMD, in particular in such a manner that BMD from continuous and binary data are commensurate (4) selection of a mathematical dose-response model for calculating a BMD (5) selection of the level of risk to which the BMD corresponds and (6) selection of a statistical methodology for implementing the calculation. 

Bradford Hill, A. 1965. The environment and diseases Association or causation Proc. R. Soc. Med. 58 295-300. Calabrese, E.J. 2005. Paradigm lost, paradigm found The re-emergence of hormesis as a fundamental dose response model in the toxicological sciences. Environ. Pollut. 138 379 12. 

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