Multi-hit models

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. 

Multi-hit model is a non-conservative model, as it assumes that several interactions are needed before a cell can be transformed. 

A Multi-hit Model of Cancer Induction Is Supported by Several Lines of Evidence... 

A EXPERIMENTAL FIGURE 23-5 The incidence of human cancers increases as a function of age. The marked increase in the incidence with age is consistent with the multi-hit model of cancer induction. Note that the logarithm of annual incidence is plotted versus the logarithm of age. [From B. Vogelstein and... 

The multi-hit model, which proposes that multiple mutations are needed to cause cancer, is consistent with the genetic homogeneity of cells from a given tumor, the observed Increase in the incidence of human cancers with advancing age, and the cooperative effect of oncogenic transgenes on tumor formation in mice. 

Figure 14. Comparative dose-response extrapolations for a carcinogen M, multistage model W, Weilbull model L, logit model G, gamma multi-hit model P, probit model. Note how models that fit this data equally well at high doses can produce very different results when extrapolated to low doses (ADB, 1992).

All the models are based upon standard statistical distributions. The Multi-Hit model is based upon a Poisson distribution. The Probit model is based upon a normal distribution, and the One Hit, Multistage and Weibull models rely upon linear probabilities. Such distributions have proven applicability in dealing with substantial percentages of the population (up to 1 in 20). However, the models lose precision when they are pushed to extremes such as 1 in 10, such as encountered in risk assessment. Furthermore, homeostatic mechanisms such as DMA repair and immunological survellance may be poorly evaluated in risk assessment. Such high doses are administered to achieve the siaximum tolerated dose, that these mechanisms are surely overwhelmed in the animal studies. Additionally it should be noted that a risk of one in a million does not mean one tumor in the lifetime of a million people, it means that each individual has one chance in a million of developing a tumor in a lifetime. 

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... 

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 one-hit and linearized multi-stage models usually will predict the highest response rates and the probit model the lowest (Paustenbach, 1989a 1989b). 

Rai K. and Van Ryzin J. (1979) Risk assessment of toxic environmental substances using a generalized multi-hit dose response model. In Energy and Health (eds. N. E. Breslow and A. S. Whittemore). Society for Industrial and Applied Mathematics, Philadelphia, PA. 

The multi-hit hypothesis has also been used to explain the immunological potentiation of some idiosyncratic DILI. In this scenario, a preexisting inflammation in the host serves as "first hit." The drug treatment serves as "second hit." A good animal model for this scenario is rodents pretreated with bacterial membrane preparations such as lipopolysaccharide (LPS), followed by drug treatment. This model has been applied to explain idiosyncratic DILI caused by antibiotics, where the intended patients typically experience preexisting inflammation caused by bacterial infection.68-71... 

In a similar logic, the multi-hit hypothesis can be applied to rodent or other animal models with precompromised host liver functions, either by genetic knockout, knock-in, RNAi knockdown, high-fat diet, alcohol pretreatment, or... 

One of several kinds of mathematical relationships can be used to relate dose and effect in order to translate these data to risk estimates at low doses, e.g., linear, quadratic, logit, Weibull, one-hit, multi-hit. Each model is based on certain biochemical and physiological assumptions and has advantages and disadvantages. No one method has been shown to be better than the others. Often they all show a good fit to the experimental data available for different chemicals at higher doses. 

Dr. Bernard Hanes, our Consulting Biostatistician, assisted us in carrying out a series of risk estimates based on this ntouse bioassay data, using three recognized mathematical models (multi-hit, multi-stage, and one-hit). Table II provides a print-out of "point-estimate" doses at given response values (risk). 

Table III shows cancer risk assesssients for chlordimeform exposure based on urinary excretion of chlordimeform in man and malignant tumor incidence from the mouse bioassay study (male and female mice data combined). Three commonly used mathematical models (multi-hit, multi-stage, and one-hit) are used in the risk estimations.

Various mathematical models have evolved that attempt to incorporate some of the biological concepts and hypotheses. Some of the most commonly used models are the Probit, the Multi-Hit, the One-Hit, the Multi-Stage, and the Weibull. All of these models have the defined property that for zero dose, the risk is zero. However, since the spontaneous background incidence is not zero for most tumors, the models incorporate background, utilizing the concept of independence as ascribed by the correction of Abbott (14) i.e.,... 

An additional limitation of the Multi-Stage model, in fact of all the models discussed, is that generally the maximal incidence is assumed to be 100%. This, in practice, may not be possible since increasing administration may result in death rather than tumor formation. When the Multi-Stage model is used to evaluate the dose response for dimethylnitrosarnine, hepatocar-cinogenicity in the rat (16), it shows a better fit than the One-Hit, but the data does not fit the curve particularly well (Figure 3). The less than perfect fit is possibly because the model forces the maximum incidence to be 100% -- a condition not apparent in the data. 

The model of multi-stage human colorectal carcinogenesis, based on accumulating genetic and epigenetic hits , leading to sequential loss of... 

Statistical models. A number of statistical dose-response extrapolation models have been discussed in the literature (Krewski et al., 1989 Moolgavkar et al., 1999). Most of these models are based on the notion that each individual has his or her own tolerance (absorbed dose that produces no response in an individual), while any dose that exceeds the tolerance will result in a positive response. These tolerances are presumed to vary among individuals in the population, and the assumed absence of a threshold in the dose-response relationship is represented by allowing the minimum tolerance to be zero. Specification of a functional form of the distribution of tolerances in a population determines the shape of the dose-response relationship and, thus, defines a particular statistical model. Several mathematical models have been developed to estimate low-dose responses from data observed at high doses (e.g., Weibull, multi-stage, one-hit). The accuracy of the response estimated by extrapolation at the dose of interest is a function of how accurately the mathematical model describes the true, but unmeasurable, relationship between dose and response at low doses. 

For the most frequently used low-dose models, the multi-stage and one-hit, there is an inherent mathematical uncertainty in the extrapolation from high to low doses that arises from the limited number of data points and the limited number of animals tested at each dose (Crump et al., 1976). The statistical term confidence limits is used to describe the degree of confidence that the estimated response from a particular dose is not likely to differ by more than a specified amount from the response that would be predicted by the model if much more data were available. EPA and other agencies generally use the 95 percent upper confidence limit (UCL) of the dose-response data to estimate stochastic responses at low doses. 

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