Dose-response models, various

Table 6.1 —Lifetime excess cancer mortality from a single exposure to 10 rad oflow-LET radiation per miOion males, as estimated with the absolute risk projection model and various dose-response models ...

Basic elements in an analysis of pollution control options are indicated schematically in Fig. 2. We will not discuss costs here, but concentrate on the left-hand-side of the figure. The 2 upper levels may be referred to as the objective part of the analysis. The aim is to determine the measurable consequence of the various control options under consideration. Normally this will involve dispersion — and exposure models. These are in principle not too difficult to handle, though in practical cases the uncertainties may be large due to insufficient data for example. The dose-response model is, however, a real challenge in most cases (see Section 4). 

Another method of detecting a dose-response relationship is to fit the data to various models for dose-response curves. This method statistically determines whether or not a dose-response model (such as a Logistic function) fits the data points more accurately than simply the mean of the values this method is described fully in Chapter 12. The most simple model would be to assume no dose-response relationship and calculate the mean of the ordinate data as the response for each concentration of ligand (horizontal straight line parallel to the abscissal axis). A more complex model would be to fit the data to a sigmoidal dose-response function (Equation 11.2). A sum of squares can be calculated for the simple model (response — mean of all response) and then for a fit of the data set refit to the four parameter Logistic shown... 

Risk Characterization. Using both (a) the results of the qualitative hazard identification to express the WOE that an agent poses a cancer risk and (b) the quantitative information obtained from the dose-response modeling together with the results of the exposure assessment, the risk characterization step fundamentally describes the risk associated with exposure to an agent at various levels of exposure for the circumstances of concern. 

The critical studies of MeHg examined a range of neurodevelopmental outcomes. Selection of the most appropriate BMD requires consideration of the biological significance of the effects, including the sensitivity and severity of the outcomes, consideration of the abiUty to detect both exposure and effects, and selection of an appropriate dose-response model. To examine and compare the results of the critical studies, BMD calculations were conducted and compared for various end points. These results are presented and discussed in detail in Chapter 7. 

Table IV and Figure 4 give an example of this behavior for these models applied to the incidence of liver hepatomas in slice exposed to various levels of DDT (41). This example in Table IV shows that each of the six dose-response models fit the observed data nearly equally well (the nultistage siodel fits the data as well as the others). Therefore, the data in the observable...

FIGURE 3.6 Classical model of agonism. Ordinates response as a fraction of the system maximal response. Abscissae logarithms of molar concentrations of agonist, (a) Effect of changing efficacy as defined by Stephenson [24], Stimulus-response coupling defined by hyperbolic function Response = stimulus/(stimulus-F 0.1). (b) Dose-response curves for agonist of e = 1 and various values for Ka. 

So far, we have reviewed the various ways in which complex dose-response curves in intact-tissue bioassays can be the result, the pharmacological resultant, of two or more interacting activities. Now, if all that these bioassays achieved was to blur and obscure the underlying activities, they would have to give way to the newer, analytically simpler assays based on chemistry and biochemistry. However, the beauty of intact-tissue bioassays is that they are analytically tractable by using families of dose-response curves and appropriate mathematical models, the complexity of intact hormone-receptor systems can, indeed, be interpreted. Bioassay allows them to be studied as systems in ways denied to simple biochemical assays. 

For non-threshold mechanisms of genotoxic carcinogenicity, the dose-response relationship is considered to be linear. The observed dose-response curve in some cases represents a single ratedetermining step however, in many cases it may be more complex and represent a superposition of a number of dose-response curves for the various steps involved in the tumor formation (EC 2003). Because of the small number of doses tested experimentally, i.e., usually only two or three, almost all data sets fit equally well various mathematical functions, and it is generally not possible to determine valid dose-response curves on the basis of mathematical modeling. This issue is addressed in further detail in Chapter 6. 

---