Dose-response functions

The second step when determining impacts is the hazard assessment [28]. During the hazard assessment, the impact caused by the exposure to a substance is determined [30]. This is often done using in vitro or in silico testing. The results of the hazard assessment are often presented as dose-response functions. 

Exposure calculation to the emission calculations involving impact of emissions on humans and ecosystem of the emissions means the impact calculation of the dose from the increased concentration. The impact calculation is followed by calculation of impacts (damage in physical units) from this dose, using a dose-response function. The impact of WEEE substances on health and the environment is location specific and is based on conditional, that is to say the way the WEEE is taken care of. Hence, the exposure assessment relates to the population and the ecosystem being exposed to the externalities. 

According to Spadaro and Rabl [41], damage costs of IQ decrement is likely the dominant part of the total damage costs of Pb. The dose-response function has been quite well characterized for Pb, for example by Schwartz [48] in a meta-analysis, who found that the IQ decrement is 0.026 IQ points for a 1 pg/L increase of Pb in blood. Spadaro and Rabl identified two possible ways of linking blood levels of lead to exposure. One of the methods connects incremental exposure of Pb in air to... 

Combining the dose-response function with the exposure/blood level relations, Spadaro and Rabl [41] derived two possible characterization factors of 0.268 and 0.59 IQ points decrement per kg emitted Pb. 

If a nonlinear dose-response function has been determined, it can be used with the expected exposure to estimate a risk. If an RfD or RfC is calculated, the hazard can be expressed as a Hazard Quotient (HQ), defined as the ratio of an exposure estimate over the RfD or RfC, i.e., HQ = Exposure/(RfD or RfC). 

Using ISOCORRAG, MICAT and Russian data, Tidblad et al [19] showed that the inclusion of temperature among the environmental parameters improves considerably the usefulness of the dose-response functions and should be adapted in the revision of ISO 9223 standard. It is reported an increase in corrosion rate with average air temperature in the range of -15 to 30°C. 

Figure 2.3. Dose-response graph for drinking wine. Dose-response function for difficulty in walking and number of glasses of wine consumed. This is an idealized curve, but it illustrates the principle that at low doses (i.e. few glasses) there is little response, then an increasing response to a maximum response. Note that this figure does not take into consideration body weight or any other variables such as gender or frequency of exposure (i.e. time between drinks).

Another approach is to develop a global model that contains plausible models as special cases, defined by alternative values of particular parameters. This converts model uncertainty into uncertainty about the model parameters. Again this can be done using either Bayesian or non-Bayesian approaches. This approach is favored by Morgan and Henrion (1990), who describe how it can be applied to uncertainty about dose-response functions (threshold versus nonthreshold, linear versus exponential). 

Formally, suppose we have a random variable, jc, which has measurements over the range a to b. Also, assume that the probability density function of x can be written as p(x). In addition, assume a second function g, such that g(x ) p(x) =J x). For example, gix) could represent a dose-response function on concentration and p(x) is the probability density function of concentration. The expected value (which is the most likely value or the mean value) of g(J ) isp... 

Development of Dose-Response Functions for Individual Species... 

Calibration curves were fitted, and EC50 values were derived using the nonlinear regression package pro Fit 5.5 (QuantumSoft, Zurich, Switzerland). The results of the calibration curve measurements were fitted to a sigmoidal dose-response function of the following form with a slope faetor of 1 ... 

The BEIR III risk estimates formulated under several dose-response models demonstrate that the choice of the model can affect the estimated excess more than can the choice of the data to which the model is applied. BEIR III estimates of lifetime excess cancer deaths among a million males exposed to 0.1 Gy (10 rad) of low-LET radiation, derived with the three dose-response functions employed in that report, vary by a factor of 15, as shown in Ikble 6.1 (NAS/NRC, 1980). In animal experiments with high-LET radiation, the most appropriate dose-response function for carcinogenesis is often found to be linear at least in the low to intermediate dose range (e.g., Ullrich and Storer, 1978), but the data on bone sarcomas among radium dial workers are not well fitted by either a linear or a quadratic form. A good fit for these data is obtained only with a quadratic to which a negative exponential term has been added (Rowland et al., 1978). 

LET. Although there is general agreement that high-LET radiation is more carcinogenic, than low-LET radiation, the relation between them has not been satisfactorily quantified and may also vary by tumor site. This relationship, of course, dqiends partly on the respective dose-response functions appropriate for high- and low-LET radiation. 

Dose-response model. There is incomplete agreement on the most suitable form of dose-response function for low-LET radiation, and there is no present expectation that human observations will prove decisive. Rather, it appears that appropriate models will require a more adequate understanding of radiation carcinogenesis itself. 

Figure 24.2 Dose-response curve, with emphasis on the shape of the dose-response function below the experimentally observable range and therefore the range of inference where people are realistically exposed.

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