Linearized multistage model, estimation

This study, like that of Fisher and Allen (1993), incorporated a linear multistage model. However, the mechanism of trichloroethylene carcinogenicity appears to be non-genotoxic, and a non-linear model (as opposed to the linearized multistage model) has been proposed for use along with PBPK modeling for cancer risk assessment. The use of this non-linear model has resulted in a 100-fold increase in the virtually safe lifetime exposure estimates (Clewell et al. 1995). 

The linearized multistage model (used by the EPA). This determines the cancer slope factor, which can be used to predict cancer risk at a specific dose. It assumes a linear extrapolation to a zero-dose threshold (Fig. 2.10). This factor is an estimate (expressed in mg/kg/day) of the probability that an individual will develop cancer if exposed to the chemical for 70 years. 

In 1980, the Ambient Water Quality Criteria USEPA Carcinogen Assessment Group (CAG) by using a further modified linear multistage model as well as a one-hit model, arrived at a value of 0.2 /zg/L/day as the upper 95 confidence estimate of the dose in drinking water contributing an excess lifetime risk of 1 in 1 million. 

The use of MLEs of probability coefficients for radionuclides but UCLs for chemicals that induce stochastic responses is the most important issue that would need to be resolved to achieve a consistent approach to estimating risks for the purpose of waste classification. For some chemicals, the difference between MLE and UCL can be a factor of 100 or more. The difference between using fatalities or incidence as the measure of response is unlikely to be important. Use of the linearized, multistage model to extrapolate the dose-response relationship for chemicals that induce stochastic effects, as recommended by NCRP, should be reasonably consistent with estimates of the dose-response relationship for radionuclides, and this model has been used widely in estimating probability coefficients in chemical risk assessments. The difference in the number of organs or tissues that are taken into account, although it cannot be reconciled at the present time, should be unimportant. 

For the above reasons, the linearized multistage model is used as a default when estimating risks for short-term exposures from lifetime carcinogenesis bioassays. In all of the above referenced publications on the multistage model, the maximum number of stages modeled was six. 

The tumor count data from the animal carcinogenicity experiment is then used to estimate the relationship between the ED and t imor incidence using standard tumor incidence models. The most commonly used model is the linearized multistage model (Anderson, et al., 1983), which is a modified version of the multistage model of Armitage and Doll (1954). There are numerous other models that have been employed, some of which are based upon statistical arguments and some of which attempt to mimic biological theory (see eg Krewski and Brown, 1980). ... 

Because relatively low intakes (compared to those experienced by test animals) are most likely from environmental exposure at Superfund hazardous waste sites, it generally can be assumed that the dose-response relationship will be linear on the low-dose portion of the multistage model dose-response curve. The equation above can apply to these linear low-dose situations. This linear equation is valid only at low risk levels (i.e., below the estimated risk of 0.01). For risk above 0.01 the one-hit equation should be used ... 

In order to avoid the disadvantages, seen or inferred, of the simple addition of q values, various analysts have either calculated or assumed a distribution (for each tumor type) representing the likelihood for the plausible range of estimates of the linear term (q ) of the multistage model (qi), and then they used the Monte Carlo procedure to add the distributions rather than merely adding specific points on the distributions such as the maximum likelihood estimate (MLE) or 95% confidence limit. A combined potency estimate (q for all sites) is then obtained as the 95% confidence limit on the summed distribution. This resembles the approach for multiple carcinogens by Kodell et al. (1995) noted above. 

It should be noted that both the single-hit model and the multistage model (when Aj >0) become approximately linear at low dose levels. This low dose linearity is an important aspect of "conservative" extrapolation models. Many researchers believe that the true dose-response at low exposure levels is convex, i.e. may have some degree of upward curvature. Therefore, linearity, which represents an "upper bound" to the general class of convex functions, provides conservative extrapolated risk estimates at low doses ("conservative" in the sense of producing higher estimated risks than other convex functions). 

These results show that the inclusion of additional low dose data has little effect on the VSD estimates. For bladder neoplasms, which show a highly convex dose-response, the lower confidence limit on the VSD based on the multistage model is increased only 18 (from 3.07 x 10 to 3.63 x 10 ), while that based on the log normal model is hardly changed. For liver neoplasms, which show a nearly linear dose-response, the lower confidence limit on the VSD is increased only 23% for the multistage model and is decreased for the log normal model, the differences in the VSD estimates from these two extrapolation models is little affected by these additional low dose data for bladder neoplasms, the additional data decreases the difference from a log... 

Oncogenic Risk Calculations. On the basis of the expos ire analysis and potential oncogenic risk (oncogenic potency might be more descriptive), a risk analysis will be performed according to statistical methods like linear extrapolation (one-hit model) or multistage estimation (9.). 

X 10 g/kg/day (9). For this same cancer risk, the CDC has estimated a "virtually safe dose" of 28 x 10 g/kg/day (hereafter, CDCl) (5,6). These estimates are based on a linear-derived multistage extrapolation model that is usually used for genotoxic agents such as ionizing radiation. However, the results to date indicate that... 

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