Mathematical Modeling and the Benchmark Dose Method

The rationale supporting use of EDi0 as the benchmark dose is that a 10 percent response is at or just below the limit of sensitivity in most animal studies. Use of the lower confidence limit of the benchmark dose, rather than the best (maximum likelihood) estimate (EDio), as the point of departure accounts for experimental uncertainty the difference between the lower confidence limit and the best estimate does not provide information on the variability of responses in humans. In risk assessments for substances that induce deterministic effects, a dose at which significant effects are not observed is not necessarily a dose that results in no effects in any animals, due to the limited sample size. NOAEL obtained using most study protocols is about the same as an LED10. 

The benchmark dose method was developed to overcome difficulties with determining NOAEL based on dose-response data. The potential advantages of the method include the following (Crump, 1984 1995)  

3 Dose-Response Assessment for Chemicals That Cause Stochastic Effects. For hazardous chemicals that do not have a threshold in the dose-response relationship, which is currently believed to 

Although dose-response assessments for deterministic and stochastic effects are discussed separately in this Report, it should be appreciated that many of the concepts discussed in Section 3.2.1.2 for substances that cause deterministic effects apply to substances that cause stochastic effects as well. The processes of hazard identification, including identification of the critical response, and development of data on dose-response based on studies in humans or animals are common to both types of substances. Based on the dose-response data, a NOAEL or a LOAEL can be established based on the limited ability of any study to detect statistically significant increases in responses in exposed populations compared with controls, even though the dose-response relationship is assumed not to have a threshold. Because of the assumed form of the dose-response relationship, however, NOAEL or LOAEL is not normally used as a point of departure to establish safe levels of exposure to substances causing stochastic effects. This is in contrast to the common practice for substances causing deterministic effects of establishing safe levels of exposure, such as RfDs, based on NOAEL or LOAEL (or the benchmark dose) and the use of safety and uncertainty factors. 

Because of the statistical and biological problems inherent in the identification of a true no-effect level in any study of dose-response, most mathematical models for chemicals that cause stochastic effects have eliminated the concept of a threshold dose below which no 

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