Dose-response data modeling

Toxicology Animals Maximal dose-response data Realistic models of human disease ... 

There are statistical procedures available to determine whether the data can be fit to a model of dose-response curves that are parallel with respect to slope and all share a common maximal response (see Chapter 11). In general, dose-response data can be fit to a three-parameter logistic equation of the form... 

The following example is based on a risk assessment of di(2-ethylhexyl) phthalate (DEHP) performed by Arthur D. Little. The experimental dose-response data upon which the extrapolation is based are presented in Table II. DEHP was shown to produce a statistically significant increase in hepatocellular carcinoma when added to the diet of laboratory mice (14). Equivalent human doses were calculated using the methods described earlier, and the response was then extrapolated downward using each of the three models selected. The results of this extrapolation are shown in Table III for a range of human exposure levels from ten micrograms to one hundred milligrams per day. The risk is expressed as the number of excess lifetime cancers expected per million exposed population. 

The science policy components of risk assessment have led to what have come to be called default assumptions. A default is a specific, automatically applied choice, from among several that are available (in this case it might be, for example, a model for extrapolating animal dose-response data to humans), when such a choice is needed to complete some undertaking (e.g., a risk assessment). We turn in the next chapter to the conduct of risk assessment and the ways in which default assumptions are used under current regulatory guidelines. We might say we have arrived at the central subject of this book. 

Modeling of gas transport is also useful for correlating dose-response data obtained under different conditions. Brain suggested that the total dose of an inhaled gas is relate to ventilation rate, duration of exposure, and gas concentration before inhalation. Folinsbee et al. exposed human subjects to ozone at 0.37, 0.5, or 0.75 ppm for 2 h while they were at rest or exerdsing intermittently. The primary response of the subjects was an alteration in the exercise ventilatory pattern. They... 

Quantitative Stmcture-Activity Relationships (QSARs) are estimation methods developed and used in order to predict certain effects or properties of chemical substances, which are primarily based on the structure of the substance. They have been developed on the basis of experimental data on model substances. Quantitative predictions are usually in the form of a regression equation and would thus predict dose-response data as part of a QSAR assessment. QSAR models are available in the open literature for a wide range of endpoints, which are required for a hazard assessment, including several toxicological endpoints. 

FIGURE 7.5 Cucumber shoot weight dose-response data and model. 

Fig. 3. Experimental dose-response data on G-beads from previous work (Simons et al, 2003, 2004) fitted to simulations of the ternary complex model including soluble G protein (Fig. 1C). The inclusion of soluble G protein in the model (Fig. 1C) is required due to the presence of extra G protein from the solubilized receptors and without which resulted in simulations that overestimated bead-bound receptors. Note that the same equilibrium dissociation constant values were used for the interactions with G protein on bead as with soluble G protein (Gtotbead and Gtots0l). Although the individual kinetic reaction rate constants for the interactions with soluble G protein might be faster than those for the bead-bound G protein, their ratios (the equilibrium dissociation constants) are expected to remain the same. The calibrated GFP per bead as...

For noncarcinogenic hazardous chemicals, NCRP believes that the threshold for deterministic effects in humans should be estimated using EPA s benchmark dose method, which is increasingly being used to establish allowable doses of noncarcinogens. A benchmark dose is a dose that corresponds to a specified level of effects in a study population (e.g., an increase in the number of effects of 10 percent) it is estimated by statistical fitting of a dose-response model to the dose-response data. A lower confidence limit of the benchmark dose (e.g., the lower 95 percent confidence limit of the dose that corresponds to a 10 percent increase in number of effects) then is used as a point of departure in establishing allowable doses. 

Fig. 3.6. Illustration of use of benchmark dose method to estimate nominal thresholds for deterministic effects in humans. The benchmark dose (EDio) and LEDi0 are central estimate and lower confidence limit of dose corresponding to 10 percent increase in response, respectively, obtained from statistical fit of dose-response model to dose-response data. The nominal threshold in humans could be set at a factor of 10 or 100 below LED10, depending on whether the data are obtained in humans or animals (see text for description of projected linear dose below point of departure).

The benchmark dose method makes use of all the dose-response data by fitting a dose-response model to the data, whereas the determination of a NOAEL generally involves a comparison of responses at discrete and well separated doses with responses in control subjects. 

Statistical models. A number of statistical dose-response extrapolation models have been discussed in the literature (Krewski et al., 1989 Moolgavkar et al., 1999). Most of these models are based on the notion that each individual has his or her own tolerance (absorbed dose that produces no response in an individual), while any dose that exceeds the tolerance will result in a positive response. These tolerances are presumed to vary among individuals in the population, and the assumed absence of a threshold in the dose-response relationship is represented by allowing the minimum tolerance to be zero. Specification of a functional form of the distribution of tolerances in a population determines the shape of the dose-response relationship and, thus, defines a particular statistical model. Several mathematical models have been developed to estimate low-dose responses from data observed at high doses (e.g., Weibull, multi-stage, one-hit). The accuracy of the response estimated by extrapolation at the dose of interest is a function of how accurately the mathematical model describes the true, but unmeasurable, relationship between dose and response at low doses. 

For the most frequently used low-dose models, the multi-stage and one-hit, there is an inherent mathematical uncertainty in the extrapolation from high to low doses that arises from the limited number of data points and the limited number of animals tested at each dose (Crump et al., 1976). The statistical term confidence limits is used to describe the degree of confidence that the estimated response from a particular dose is not likely to differ by more than a specified amount from the response that would be predicted by the model if much more data were available. EPA and other agencies generally use the 95 percent upper confidence limit (UCL) of the dose-response data to estimate stochastic responses at low doses. 

Pharmacokinetic models. An important advance in risk assessment for hazardous chemicals has been the application of pharmacokinetic models to interpret dose-response data in rodents and humans (EPA, 1996a Leung and Paustenbach, 1995 NAS/NRC, 1989 Ramsey and Andersen, 1984). Pharmacokinetic models can be divided into two categories compartmental or physiological. A compartmental model attempts to fit data on the concentration of a parent chemical or its metabolite in blood over time to a nonlinear exponential model that is a function of the administered dose of the parent. The model can be rationalized to correspond to different compartments within the body (Gibaldi and Perrier, 1982). 

Fig. 3.10. Illustration of close correlation between observable dose-response data and results of different statistical models but very different model extrapolations into the unobservable response range (Paustenbach, 1995).

Inspired by this work (24), we used Bayesian methods (24) with molecular function class fingerprints of maximum diameter 6 (53) to identify substructures that were shown to be important in recent TB screening datasets (21-23). Bayesian models were built with the previously described Molecular Libraries Small Molecule Repository (MLSMR) 220,463 library (4,096 active compounds) (15) and dose-response data using 2,273 molecules (475 active compounds). In addition, these models were tested (15) with the National Institute of Allergy and Infectious Diseases (NIAID) data and GVK Biosciences (Hyderabad, India) datasets used by Prathipati et al. (24). We have validated the models with compounds left out of the original models, in some cases showing up to tenfold enrichments in finding active compounds in the top-ranked 600 molecules (22). 

Data are recorded using e.g. TIDA software (HEKA Electronics, Lambrecht, Germany) and the results are typically expressed as fraction of baseline current. Concentration-response data can be fitted to an equation of the following form 1/10 = 1/(1 + flcom-poundl/ICso)) such that the IC50 can be calculated with a sigmoidal dose-response curve model. 

Saccharin is not metabolized and does not react with DNA. Although it was mutagenic in vitro, this was only at high concentrations. It was concluded that saccharin was not a genotoxic carcinogen. Assuming that there was no threshold was, therefore, not appropriate. A threshold model could be applied to the dose-response data from these safety evaluation studies. 

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