One-hit model

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.). 

This model also reduces a one-hit model in the case n=l. However, when quadratic or higher-order polynomials are used, the shape of the curve changes considerably. Even so, at very low doses, provided that a 0, the linear component dominates. The resulting slope is usually much shallower than in the one-hit case, and thus yields a lower risk estimate. 

The most widely-accepted dose response model at the present time is the multi-stage model, which has great flexibility in curve-fitting, and also has a strong physiological justification. Although it is difficult to implement, there are already computer codes in existence that estimate the model parameters (13). The two most widely-used models, until recently, were the one-hit model and the log-probit model. They are both easy to implement, and represent opposite extremes in terms of shape - the former represents the linear non-threshold assumption, whereas the latter has a steep threshold-like curvature. In numerous applications with different substances it has been found that these three... 

The multi-hit models are most suitable for extrapolating the effect of genotoxic substances. It is implicit in these models that aU hits occur in one specific cell that only begins to divide and develop into a tumor when it has received the necessary number of hits. However, this is in poor agreement with experimental data, which show that prohferation of the cells that have had their first hit (the initiated cells) into pre-neoplastic lesions considerably increases the risk of a second hit in an initiated cell. While the one-hit model often oversimplifies the process, the multi-hit models impose an unreasonable tight restriction of the possibdity of more than one critical hit affecting the same cell. 

Fig. 8.6 Estimated risk of liver cancer, P(d), in relation to dose of aflatoxin, d, as determined with different dose-incidence models. The models for the different curves. are as follows OH. one-hit model MS, multi-stage model W, Weibull model MH, multihit model MB, Mantel-Bryan (log-probit model) (from Krewski and Van Ryzin, 1981).

The cancer risk values, which these models generate, are of course very different. For example, for the chemical chlordane, the lifetime risk for one cancer death in one million people ranges from exposures of0.03 pg/L of drinking water for the one-hit model, 0.07 pg/L from the linearized multistage model to 50 pg/L for the probit model. 

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. 

ADI-type calculations were performed for noncarcinogens. For potential carcinogenic risk calculations, a linearized multistage model or a one-hit model was employed and water concentrations equivalent to calculated risks of 10"5, 10 6, and 10r were reported. No selection was made as the specific criterion however, 10-5 was suggested as a reasonable value. 

Concentration values in micrograms per liter are provided in the box on page 728 for 40 substances at the calculated 10-5 risk level at the upper bound. Both a linearized multistage model and the one-hit model (in parentheses) were used (45). Many of these values are now being updated. 

One-hit model, which is a very conservative model. It assumes that there is a single stage for cancer and that one molecular event induces a cell transformation. 

The LNT-based dose-response model for cancer, being a cumulative distribution function, begins at zero and is proportional to doses (i.e., is linear at low doses, resulting in the LNT hypothesis). The early form of the LNT model is the one-hit model ... 

If a single change to the DNA of a cell can transform it, and a transformed cell can be irreversibly propagated leading to cancer, then Ulctc can be no threshold, although the risk may be low. This is often referred to as the one-hit model. 

I also (Crouch 1996) evaluated the data of Gold et al. (see above) while illustrating the use of uncertainty distributions for interspecies extrapolations, but used the multistage model (rather than the one-hit model used to derive TDsqs) and a different adjustment to a standard lifetime. I demonstrated the lognormality of rat-to-mouse, mouse-to-hamster, and hamster-to-rat interspecies ratios of a carcinogenic potency parameter, and I also demonstrated that the available information was inconsistent with allometric scaling between these rodents with any power law. 

Fig. 2 Cumulative risk of CRC among gene carriers in HNPCC. The gene carriers cumulative risk of CRC increases as an almost perfectly linear function of time above the third decade of life, with a CRC risk of 1.6% per year. This linear relationship does not fit the classical multistep model of carcinogenesis, but is compatible with a one-hit model of carcinogenesis. (Redrawn with the data of Voskuil et al., 1997.)...

Observed cancer deaths One-hit Models fitted Proportional hazards to qavaqe data Multistage with Multistage with time-to-tumor variable dosing Model fitted to Inhalation data One-hit terminal sacrifice tumors ... 

Both the calculated (i.e., simulated) response and the predicted (i.e., estimated) response are based on the one-hit model as described in the text. 

Figure 4. A portion of the dose-response curve generated from the pharmacokinetic model of Figure 2 in which the parent chemical (Pss) is the carcinogenic entity and the response is calculated with the one-hit model ( see Equation 4)...

The use of linear correction factors is compatible with the basic assumptions of the One Hit model and depending upon the biological steps involved the Ikiltistage and Wiebull models as well. By analogy the risk is dependent upon a total cumulative lifetime dose and this accusiulation constitutes an "averaging" of exposure. A recent publication by Crump (22) addresses this issue in a more mathematically eloquent fashion. 

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