|
Items in cart [0] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 187
Issues in Risk Assessment
The Two-Stage Model of Carcinogenesis
INTRODUCTION
In recent years, it has become clear that carcinogenesis is a multistep process that requires deregulation of cellular growth. Cell growth and differentiation are normally under genetic regulation, so it may be assumed that the critical events in carcinogenesis involve genetic damage and inappropriate genetic expression (Weinberg, 1988; 1989). Mathematical models based on those biologic considerations can be simple or complex depending on assumptions about the number and nature of the events required to transform normal cells into cancer cells and about the sequence of events.
The simplest model judged to be consistent with the data available—a model that assumes two critical stages—was selected for evaluation by the Committee on Risk Assessment Methodology (CRAM). The two-stage model has been proposed as an improvement over currently used models for estimating carcinogenic risks to health, because it incorporates biologic considerations, notably cell population kinetics. The principal purposes of this CRAM study were to assess the scientific basis of the two-stage model of carcinogenesis and to evaluate the possible applications of the two-stage model to health risk assessment.
As part of the information-gathering process, the committee held a workshop on November 8, 1990, with presentations by the originators and proponents of the two-stage model and by invited discussants. A
OCR for page 188
Issues in Risk Assessment
workshop summary appears in Appendix A. Postworkshop discussions were also held with the workshop speakers and with representatives of the federal liaison group to clarify the issues. However, this report and its recommendations were prepared solely by the committee.
BIOLOGIC CONSIDERATIONS
Clinicians and pathologists have long recognized that cancer formation in humans is often preceded by a series of preneoplastic changes. Confirmation of the multistage nature of certain human cancers has been obtained by studies of the role of changes in oncogenes and suppressor genes in human colon cancer (Hollstein et al., 1991). Similar observations have been made on laboratory animals that were exposed to carcinogens experimentally (Barbacid, 1987; Balmain and Brown, 1988). Morphologic or histopathologic studies do not always lend themselves well, however, to conclusions as to the biologic potential or ultimate fate of individual precancerous lesions. Some uncertainty exists about the identification of particular lesions as part of a neoplastic process, their place in the pathologic sequence, the inevitability of their progression to the next stage, and the rate of transition when they progress. For risk assessment, it is important to be able to distinguish lesions that are reversible from lesions that will irreversibly lead to neoplastic disease. The frequency with which most preneoplastic lesions pass from stage to stage appears to be low. In such model systems as the production of hepatic tumors in rats that are given known hepatic carcinogens, one can typically produce around thousands of biochemically altered cell foci per liver, which will be followed by the appearance of several adenomas and then by one or two hepatocarcinomas (Moolgavkar et al., 1990a; Cohen and Ellwein, 1991; Luebeck et al., 1991). In examples of that sort, almost all the early lesions do not progress to cancer, but remain the same or regress; thus cancer is a rare biologic outcome. Nevertheless, the consistent association of altered cell foci with later cancer formation has prognostic value and may help in developing preventive measures.
Underlying the structural stages are molecular events, or steps, that define the beginning and end of each stage. As noted before, cancer involves a disturbance of cell growth and cell growth is under genetic regulation, so genetic damage is likely to be important in carcinogenesis.
OCR for page 189
Issues in Risk Assessment
Target genes include those related to cell division and proliferation (pro-to-oncogenes) or those which cause cells to stop dividing (anti-oncogenes or tumor-suppressor genes). The available evidence strongly supports the general concept that the cells of some cancers in humans and laboratory animals contain activated or mutated oncogenes and, in some cancer cells, tumor-suppressor genes are inactive or missing (Weinberg, 1988; 1989). Under active investigation are the extent to which those genetic events are necessary and sufficient to result in cancer and whether the sequence of genetic events is important if more than one genetic event is necessary. Other possible target genes, such as the genes that contribute to cell division cycles or the genes that affect the microenvironment in which developing cancer cell clones might be inhibited or selectively enhanced, have received less attention. It is generally assumed, too, that cell proliferation in general increases the probability of inheritance of random mutations by somatic cells, thus contributing indirectly to the carcinogenic process (Cohen et al., 1991).
The concept of two-stage models emerged from Knudson's studies of heritable childhood cancers (Moolgavkar and Knudson, 1981), and was an extension of the work of Armitage and Doll (1957). For retinoblastoma in particular, the relation of tumor incidence to age suggested that one event is necessary in the somatic cells of hereditary carriers and two events are necessary in nonhereditary carriers. Molecular genetic analyses of cells from affected children have revealed that the critical event can be the loss or inactivation of both alleles of the retinoblastoma tumor-suppressor gene (RB1) (Gaillie et al., 1990). The developing retina might contain three types of cells: normal retinoblasts with two normal RB1 alleles, intermediate retinoblasts with one altered or lost RB1 gene, and retinoblasts with both RB1 genes altered. In the herediary form in which one parentally acquired allele is altered, the probability of retinoblastoma is increased, because all the developing retinoblasts have an abnormal RB1 gene and are at risk of a second event. That three or four tumors develop in the typical gene carrier suggests that the second event is not very common. The process is limited, as a child ages, by differentiation of the entire embryonal retinoblast pool into adult nondividing retinal cells.
Other cancers appear more complicated. For example, mutations in both RB1 and p53 suppressor genes are thought to be involved, with a third presumed suppressor gene, in small-cell lung tumors (Takahashi et
OCR for page 190
Issues in Risk Assessment
al., 1989). Data on colon cancer suggest five or six critical events (Vogelstein et al., 1988; Goyette et al., 1992). These examples suggest that more complex models might be required. Conceptually, the two-stage model could be extended to any number of stages.
The biologic basis of carcinogenesis is still incompletely understood. In spite of recent rapid advances at the molecular level, many of the events described cannot yet be demonstrated to be essential for the pathogenesis of cancer. Some might be incidental phenomena with no causal relationship to the carcinogenic process. Research utilizing dose-response modeling can provide insights into which events are necessary and sufficient to produce cancer by demonstrating which mechanistic assumptions are consistent with the dose-response data.
THE TWO-STAGE MODEL
The two-stage model developed by Moolgavkar, Venzon, and Knudson (Moolgavkar and Venzon, 1979; Moolgavkar and Knudson, 1981) postulates two critical events in carcinogenesis that are specific, irreversible, and hereditary (at the cell level). The model supposes three cell compartments: normal stem cells, intermediate cells that have been altered by one genetic event, and malignant cells that have been altered by two genetic events. The size of each compartment is affected by cell birth, death, and differentiation processes and by the rates of transition between cell compartments.
The model is consistent with current concepts regarding the roles of inactivated tumor-suppressor genes and activated oncogenes in carcinogenesis. It explicitly accounts for many processes considered important in carcinogenesis, including cell division, mutation, differentiation, and death and the clonal expansion of populations of cells. Although the various carcinogenic processes might have more than two steps, a major assumption is that each of them can be described as consisting of two critical, genomic events: the first is assumed to give a small growth advantage through partial abrogation of growth control, and the second is assumed to lead to total abrogation of growth control. Among the other assumptions are that a cancer arises from a single cell, that transformations of stem cells are independent events, that each transformed cell will become a tumor, and that the time required to develop from a single transformed cell into a tumor is constant.
OCR for page 191
Issues in Risk Assessment
The mathematical aspects of two-stage model development and application have been described by Moolgavkar, Cohen, and Portier and their associates (Greenfield et al., 1984; Portier, 1987; Ellwein and Cohen, 1988; Moolgavkar, 1988; Moolgavkar and Luebeck, 1990; Portier and Edler, 1990; Tan, 1991). The model permits computation of both the rate at which tumors form (incidence function) and the probability of tumor formation with respect to time. Both stochastic and deterministic forms of the model have been described.
In the schematic representation of the model (Figure 1) as described by Moolgavkar and Knudson (1981), C0, C1, C2, and D represent stem cells, intermediate cells, malignant cells, and differentiated or dead cells. A normal stem cell can divide into two stem cells, die, or be transformed by mutation into an altered intermediate cell. An intermediate cell similarly divides into two intermediate cells, dies, or becomes transformed into a fully malignant cell. a1 is the rate at which cells divide (normal cells at a1, and intermediate cells cells at a2), ß1 the rate at which they die, and µ1 the rate at which they are transformed.
That formulation assumes that normal cells behave independently, which implies that they either die out (generally early in life, which would result in death of the subject) or grow exponentially throughout life. Neither alternative is realistic, so the normal stem cell population
FIGURE 1 Two-stage model paradigm. Source: Moolgavkar and Knudson, 1981.
OCR for page 192
Issues in Risk Assessment
is generally modeled as growing deterministically, with intermediate cells arising from normal cells in a nonhomogeneous Poisson process with intensity function X(s)v(s), where X(s) is the (deterministic) size of the normal stem cell population at age s and v(s) is the rate at which stem cells are converted into intermediate cells. With that form of the model, closed-form mathematical expressions can be obtained for the probability of forming a malignant cell by time t, P(t), and the associated instantaneous-hazard function h(t), as long as the parameters are time-independent. By integrating Expression 24 of Moolgavkar et al. (1988), one obtains
and
where
and
OCR for page 193
Issues in Risk Assessment
X(s) and (s) are not separately identifiable, and only their product can be estimated. Intermediate cells behave independently and with exponentially distributed lifespans. Consequently, clones of intermediate cells either die out or increase exponentially in size; there is no provision for growth regulation. Those assumptions are unrealistic, and alternatives have been proposed (Moolgavkar and Luebeck, 1990); however, implementation of more realistic alternatives greatly complicates the mathematical analysis and may not be necessary in providing good estimates of h(t).
The time between the occurrence of the first malignant cell and a clinically detectable cancer or death is generally modeled as a constant (Moolgavkar and Luebeck, 1990). A different assumption could easily be made, but doing so is likely to make the resulting mathematics intractable.
Before the model can be used in risk assessment, the effect of does must be incorporated. That is generally accomplished by treating model parameters as functions of instantaneous dose (Thorslund et al., 1987; Moolgavkar and Luebeck, 1990). Dose can be incorporated into the model by introducing a dose-effect relationship into the transition rate from normal cells to intermediate cells (µ1), into the transition rate from intermediate cells to malignant cells (µ2 ), or into the growth rate of clones of intermediate cells (a2 -ß2). If the dose rate changes over time, then the corresponding parameter that dose affects is time-dependent and the solutions presented earlier do not apply. Explicit formulas for obtaining solutions when the parameters are piece-wise constant are also found in Moolgavkar and Luebeck (1990). Quinn (1989) and Moolgavkar and Luebeck (1990) showed how to obtain numerical solutions with
OCR for page 194
Issues in Risk Assessment
the method of characteristics when the parameters are generally time-dependent.
One of the most important applications of dose-response models in risk assessment is to predict increased risk from exposure to low doses of a chemical. Typically, increased cancer risks on the order of 1/100 cannot be accurately measured in either a standard animal bioassay or an epidemiologic study due to limitations of sample size, yet increased risks in human populations of this magnitude, and even smaller, are of concern.
Small increased risks from low exposures are often estimated by fitting a dose-response model to data collected at higher exposures. The form assumed for the dose-response model is of critical importance to the resulting risk estimate (NRC, 1983). Regulatory agencies have frequently applied models that assume the increased risk is linearly related to exposure (i.e., the increased risk is proportional to the amount of exposure), at least at low exposures. However, it is frequently the case that nonlinear models will fit the data equally well and predict much lower risks at low exposures. The most extreme case of a nonlinear model is a threshold model, which assumes that there is a critical exposure (i.e., a threshold) below which the risk is not increased.
As is the case with simpler descriptive models, the manner in which the effect of dose is modeled will be the determining factor in the predictions of the two-stage model at low doses. If at least one of the transition rates is assumed to vary linearly with dose at low doses and the background incidence of cancer is not zero, then the probability of cancer will vary linearly with dose at low doses, although the low dose linear slope could differ appreciably from that predicted from high dose data. However, if all the dose-related rates are assumed to vary nonlinearly with dose at low doses or to exhibit a threshold dose below which the rate is not affected by dose, then the probability of cancer will likewise vary nonlinearly with dose at low doses or exhibit a threshold below which dose cannot cause cancer, respectively. Consequently, the manner in which dose is introduced into the two-stage model is a critical assumption for risk assessment.
Depending on how the model parameters are selected, there might be a number of parameters to estimate. For example, in their application of the two-stage model to data on 1,797 rats exposed to radon, Moolgavkar and Luebeck (1990) assumed that the number of normal cells was a constant and a clone of malignant cells of any size could be identified as
OCR for page 195
Issues in Risk Assessment
a tumor at necropsy. They also assumed that the rate at which intermediate cells divided (2) was 10 times per week—the measured cell division rate for adenomas in rat lungs. Despite those simplifying assumptions, six parameters still had to be estimated by fitting the model to the cancer bioassay data. Although those data constituted an extraordinarily large data set, the precision with which some of the parameters could be estimated from the tumor data was low.
Application of a six-parameter model illustrates one of the key advantages of the two-stage model, as well as one of its disadvantages. Unlike the parameters of descriptive models (e.g., statistical models not derived from underlying biologic mechanisms), the parameters of the two-stage model are required to relate to actual biologic phenomena. Thus, Moolgavkar and Luebeck made the assumption that intermediate cells are equivalent to adenoma cells. This assumption implies that adenomas progress to carcinomas and is open to investigation. Generally, the two-stage model is more useful than mainly descriptive models for testing mechanistic hypotheses of this type, because several models can be developed based on alternative biologic hypotheses, which can then be tested on the basis of goodness-of-fit. Descriptive models are developed by fitting them to data, and hypotheses regarding underlying biologic mechanisms generally cannot be tested on the basis of fit.
A disadvantage of the two-stage model illustrated by the analysis of Moolgavkar and Luebeck is the potentially large number of model parameters to be estimated. To estimate as many as six parameters reliably might require large numbers of animals exposed to various dose patterns and with serial sacrifices. Thus, most examples of application of the two-stage model have used large data sets—e.g., the ED01 study of 2-AAF (Cohen and Ellwein, 1990) and the study involving 1,797 animals exposed to radon (Moolgavkar and Luebeck, 1990). Such extensive data sets are available for only a few chemicals.
An alternative to estimating large numbers of parameters from tumor bioassay data is estimating specific parameters with data from other sources. Moolgavkar and Luebeck's estimation of the cell division rate of intermediate cells on the basis of the cell division rate in adenomas illustrates the approach. Although the approach is potentially quite useful, the knowledge needed for its general application is not yet available. In general, it requires an understanding of the steps in carcinogenesis and identification of cell types produced in the progression from normal to
OCR for page 196
Issues in Risk Assessment
malignant cells, measures of the proliferation rates of intermediate cells and the rates of transformation of cells from one-stage to another, and whenever these quantities are dose-related, measures of the response of the parameters to dose. The latter measures are critical in determining the dose-response relationship and consequently assessing risk and estimating potency. Ideally, one would be able to measure the dose-response relationship accurately at doses to which humans are likely to be exposed (which might be much lower than the doses that produced measurable tumor responses in a standard animal bioassay); otherwise, one must assume a functional form for the relationship, which can introduce large uncertainties.
Environmental agents, as well as interindividual genetic differences in their metabolism, can affect tumor incidence through their effects on either mutation rates or the kinetics of cell division and differentiation, or both (Nebert, 1989; 1991a,b; Nebert et al., 1991, 1993 and references reviewed therein). Numerous studies in both mice and humans have demonstrated striking genetic differences in benzo[a]pyrene-induced tumor initiation, in cigarette smoke-induced tumor initiation (and probably tumor promotion), and in dioxin-induced toxicity (and possibly tumor promotion). A mutagenic substance can increase the intermediate-cell population (be an initiator) and can also cause conversion to malignancy (be a complete carcinogen). If only the kinetics of cell division and differentiation are affected by a substance, two general outcomes would be possible: in one, cell division and differentiation would be increased equally, resulting in increased mutation rates related to the increased cell division rate; in the second, the rate of cell division would be increased disproportionately to the rate of differentiation, and the increase would result in greater numbers of cells at risk of mutation.
APPLICATIONS OF THE TWO-STAGE MODEL TO ANIMAL DATA
Applications of the two-stage model have been few, because of limited data availability. Standard two year chronic carcinogenicity bioassays are not designed to provide information on the contribution of cell proliferation to tumor rates, and there are few data on the time-and dose-response effects of agents on cell proliferation. As a result, models that have been developed have generally relied on indirect measures of cell
OCR for page 197
Issues in Risk Assessment
proliferation, such as increases in organ weights, or on measures of cell proliferation performed in independent experiments with protocols that provide less than ideal data for modeling purposes. Generating adequate data for the characterization of dose-response relationships for cell proliferation rates and of their contribution to tumor rates is a critical need.
The best-known examples of applications of the two-stage model to animal data are those for 2-acetylaminofluorene (2-AAF) in the mouse liver and bladder (Cohen and Ellwein, 1990), for saccharin in the rat bladder (Ellwein and Cohen, 1988), for radon in the rat lung (Moolgavkar et al., 1990b), and for N-nitrosomorpholine (NNM) in the rat liver (Moolgavkar et al., 1990a). In the case of 2-AAF, a genotoxic agent, liver tumor rates are consistent with its effect on the rates of transition between cell stages and have a linear dose-response relationship, as does the rate of DNA adduct formation. In the bladder, a linear rate of DNA adduct formation is observed as well, but the tumor rate is consistent with a nonlinear increase in the rate of cell proliferation at high doses and with an effect of dose on rates of transition between cell stages. Saccharin, a nongenotoxic agent, appears to induce bladder cancer as a result of toxicity-induced regenerative hyperplasia, and its dose-response model is thus based on an effect on the cell growth rate function and not on transition rates. The model that was developed for radon is consistent with a primary effect on the rate of first transition between cell stages, a less-pronounced effect on the rate of second transition, and an increase in the proliferation rate of intermediate cells. Analysis of the data on liver foci development associated with NNM indicates that it is a strong initiator that has a primary effect on the rate of transition to intermediate cells (as detected by foci formation) and that it has a weak promoting effect as well (as determined by its effect on the rate of foci proliferation).
The modeling approaches of Cohen and Ellwein and of Moolgavkar differ. Moolgavkar applies standard statistical methods (e.g., maximum likelihood) that have well-understood statistical properties, to a closed-form solution of the two-stage model. Uncertainty in model parameters and goodness-of-fit of the model to the experimental data can be investigated using standard statistical methods. However, the procedure requires closed-form solutions for the two-stage model, which are only available for a few special cases (although more general cases can be approximated quite closely by the cases for which solutions are available). When a simulation approach is used or a closed-form solution
OCR for page 206
Issues in Risk Assessment
Thorslund and Charnley model with those from the alternative model at both the experimental doses and the lower doses for which additional risk was estimated. The predictions of cell-proliferation rates agree closely both at the experimental doses and at lower doses. Extremely small differences in cell-proliferation rate can result in large differences in additional risk. At doses of 0.1 and 0.01 ppm, the two cell-proliferation rates differ only in the sixth decimal place, whereas the resulting extra risks differ by factors of about 4 and 7 orders of magnitude, respectively. Thus, tiny changes in the cell-proliferation rate can make enormous differences in the resulting risk estimates. Given the variation that is normal in biologic systems, it is highly unlikely that such small differences in cell-proliferation rate could ever be accurately distinguished. An additional source of uncertainty could be introduced by assuming that as a weak mutagen, chlordane could have an effect on the transition rates in addition to the cell growth rates. This assumption could alter the risk estimates even more.
TABLE 6 Low Dose Cancer Risk Estimates for Chlordane Derived from Two-Stage Modelsa
Dose, ppm
Additional Risks
Cell-proliferation Rate, G(x)
Thorslund and Charnley Model
Alternative Model
Thorslund and Charnley Model
Alternative Model
1.0
1.6 × 10-5
3.7 × 10-4
0.063144
0.063286
0.1
1.6 × 10-9
3.9 × 10-5
0.063140
0.063149
0.01
1.6 × 10-13
6.2 × 10-6
0.063140
0.063141
0
--
--
0.063140
0.063140
aBased on data in Table 2 on liver tumors in male mice.
In the committee's discussions of these results, it was suggested that they might be due to the use of the approximation to the two-stage model
OCR for page 207
Issues in Risk Assessment
and that the exact form of the model might not exhibit such instabilities. To explore that issue, the exact form of the two-stage model was fitted to the chlordane data on male rats. As in the application of the approximate model, chlordane was assumed to affect the division and death of intermediate cells. The following specific parameter values were used in the fitting:
As before, x is the dose of chlordane. The two specific forms of G(x) (Expressions 17 and 18) applied to the approximate solution were also applied here in connection with the exact solution. The resulting exact solutions are virtually indistinguishable from the corresponding approximate solutions. Table 7 shows that both exact models fit the data on male mice almost exactly, just as the approximate models do. Table 8
TABLE 7 Chlordane Data: Fit of Alternative Exact Two-Stage Models
Dose, ppm
Number Male Mice with Liver Tumors
Observed
Predicted
Expression 18
Expression 17
0
3/33 (9%)
3.0 (9%)
3.0 (9%)
5
5/55 (9%)
5.5 (10%)
5.7 (10%)
25
41/52 (79%)
41.2 (79%)
41.2 (79%)
50
32/39 (82%)
32.1 (82%)
32.1 (82%)
shows virtually the same risks at low doses for the exact models as shown in Table 6 for the approximate models.
The two exact and two approximate dose-responses are depicted
OCR for page 208
Issues in Risk Assessment
TABLE 8 Low Dose Cancer Risk Estimates for Chlordane Derived from Exact Two-Stage Models
Dose, ppm
Additional Risks
Expression 18 for G(x)
Expression 17 for G(x)
1.0
1.7 × 10-5
6.4 × 10-4
0.1
1.7 × 10-9
4.0 × 10-5
0.01
1.7 × 10-13
3.8 × 10-6
graphically in Figures 2 and 3. Figure 2 shows that the exact expression for the probability of response, P(x), agrees closely with the approximate solution throughout the complete range of exposures when both are based on the same expression for G(x). It also shows that the two expressions for G(x) provide comparable response probabilities at the experimental exposure levels (0 ppm, 5 ppm, 25 ppm, and 50 ppm) and at all exposure levels below 5 ppm. Figure 3, which is the same as Figure 2 except that log scales are used and the vertical axis is the additional probability of response induced by exposure [P(x) - P(0)], shows that the exact solution for additional probability also agrees closely with the corresponding approximate solution over a wide exposure range, including very low exposures. It also shows that the two expressions for G(x) provide similar results for additional risk at high exposures but very different values at low exposures.
Thus, the exact models produce results in this case that are virtually indistinguishable from those produced by the approximate models that use the same cell-proliferation rate function G(x). The two expressions for G(x) provide very similar response probabilities at the experimental exposure levels (and therefore are indistinguishable based on the experimental data) but predict divergent estimates of additional risk at low exposures. Consequently, there is virtually no difference between the exact and approximate two-stage solutions in this case, and the exact model is subject to the same instabilities as the approximate model.
This type of instability is likely to be the rule, rather than the exception. A general model for the probability of cancer arising from a dose x can be written as
OCR for page 209
Issues in Risk Assessment
FIGURE 2 Comparison of exact and approximate two-stage models applied to chlordane data on male mice.
OCR for page 210
Issues in Risk Assessment
FIGURE 3 Comparison of exact and approximate two-stage models at low exposures applied to chlordane data on male mice.
OCR for page 211
Issues in Risk Assessment
where ß1,…,ßk are parameters that are unaffected by dose and G(x) is the parameter that is affected by dose. In the chlordane example, G(x) represented cell-proliferation rate, although for the purposes of the current argument it could be any biologic parameter that is affected by dose. At low doses, the probability is approximately
Thus, the dose-response relationship will behave at low doses like a linear function of G(x). That implies that the dose-response relationship for cancer at low doses will mimic that of the parameter that dose affects. The Red Book (NRC, 1983) showed that different dose-response curves for P(x) could be obtained that fit data in the observable range but yield results for incremental risk (above background) that differ by many orders of magnitude in the low dose range. The same arguments apply to G(x) and therefore, through Equation 20 relating P(x) to G(x), to P(x) again.
Those considerations suggest steps that are critical in using a two-stage model (or any other biologically based model) for low dose extrapolation. Identifying the biologic steps that lead to cancer and determining which ones are affected by the chemical insult are the first steps in the process. Another is the specification of the dose-response relationship for the parameter G(x) (cell-proliferation rate, mutation rate, etc.) or parameters that are affected by the chemical insult. Regardless of how detailed and reliable the model is otherwise, if it does not specify a mathematical form for G(x), the quantitative predictions of the model at low doses are essentially arbitrary. More precisely, given a specific two-stage model that fits a given set of dose-response data adequately, the function G can be adjusted so that the adjusted model describes the data equally well but corresponds to estimates of additional cancer risk over the background risk that differ from estimates based on the original
OCR for page 212
Issues in Risk Assessment
model by arbitrarily large factors at any dose below the lowest experimental dose.
Prescribing with confidence the mathematical form of the dose-response relationship for any particular biologic parameter that depends on dose is likely to be difficult. Kopp and Portier (1989) found that when the approximate form of the model fails to characterize accurately the cumulative distribution function of the time to tumor onset, bias may result in the estimates of the remaining parameters. The critical need in applying biologically based models will be for data on the response of the model parameters that are affected by dose. While the committee encourages the use of formal statistical methods, the application of such methods to estimate model parameters from bioassay data does not resolve uncertainty about the relationship of these parameters to dose at low doses. Bioassay data such as those for benzo[a]pyrene in Table 1 and chlordane in Table 2 do not provide a basis for determining the shape of a dose-response relationship at low doses. These data sets would be consistent with a model that predicted zero incremental cancer risk at the lowest positive dose. These data sets are also consistent with the predictions of incremental risk of 2% to 6% over background at the lowest positive dose, as shown in Tables 1 and 2. The shape of the dose-response relationship will be determined by assumptions about how the parameters in the model depend upon dose, supplemented by direct measurements of cell kinetics to the extent that such measurements are available. As the chlordane example illustrates, alternative functional forms that fit the data in the experimental range can lead to widely differing estimates of risk in the low dose range. Narrowing the uncertainty in the low dose range will require improved mechanistic understanding of how exposure to low doses of a toxicant affects the kinetics of cell transformation and proliferation.
DISCUSSION
Data Needs
The strength of the two-stage model is its ability to use information about cell division and differentiation. However, many of the discrete steps in those processes cannot be well characterized.
OCR for page 213
Issues in Risk Assessment
Among the problems is our relative inability to identify the cells in the several compartments. For many tissues, the stem cell populations are still unknown or structurally indistinguishable from related cell populations. It is probably not correct to assume that all cells that can divide or form adducts are necessarily at risk of transformation. We need biologic markers to identify the susceptible cell populations. The intermediate cell populations are also often difficult to identify. The many putative preneoplastic lesions associated with the carcinogenic process include few for which a causal association has been demonstrated. Malignant cells themselves might be difficult to identify until a tumor clone has grown enough for histopathologic diagnosis.
Measuring birth and death processes and transition rates requires identification of the cells in the several compartments. Birth processes are relatively easy to measure with existing methods, but methods for measuring programmed and unprogrammed cell death are still under development. In addition, the intermediate cell clones themselves are not always homogeneous, and cells can differ considerably from one another in biologic potential.
Those considerations and many others (including the doses to the target cells and interindividual differences in chemical metabolism) apply not only to laboratory animals, but also to humans, for whom similar information on cell kinetics is required. Humans pose the additional complication of greater heterogeneity (genetic and environmental) with individual variability in susceptibility to tumor formation at various body sites. To assess risk, one needs information not only about processes that take place in unexposed subjects, but also about the effect of various doses on the processes themselves. That is true, regardless of the dose-response modeling procedures used.
Criteria for Adoption
Before the two-stage model can be adopted for routine health risk assessments, chronic bioassay methods will have to be changed to generate the necessary data. It will be helpful, too, to evaluate the methods through a series of studies that use various agents in multiple animal strains or species. Prospective hypothesis-testing studies are preferable to retrospective model-fitting exercises.
OCR for page 214
Issues in Risk Assessment
The two-stage model can be used now to gain insights into the nature of induced carcinogenesis. The examples discussed illustrate the usefulness of two-stage models in characterizing the critical events. They also reveal the types and numbers of assumptions that might be made when data are incomplete or lacking. The models could be used as well to examine a range of assumptions.
The committee encourages diverse applications of the two-stage model to gain insight into its usefulness, particularly for risk assessment. However, the committee also recommends that, whenever the model is applied in formal risk assessment or hypothesis-testing, the reproducibility and scientific validity of the results be ensured by the application of optimal statistical methods (e.g., maximum-likelihood methods) to estimate values of parameters and to test goodness-of-fit. Critical assumptions (those with a major quantitative impact on risk estimates) should be clearly stated. And statistical confidence-interval methods, sensitivity analyses, and related quantitative methods should be applied as appropriate to determine the extent to which the resulting data are consistent with other mathematical representations and ranges of risk.
For the time being, the committee recommends that two-stage models be used primarily to promote research understanding; for health risk assessments, two-stage models can be used in conjunction with other models to add perspective to the evaluation process.
Prospects
Until recently, information about the stages of carcinogenesis has been largely limited to the descriptive and operational terms of ''early" and "late" effects in epidemiologic studies and "initiation" and "promotion" in animal studies. The current growth of concepts and information about molecular carcinogenesis in patients and in experimental systems, however, promises new opportunities for conceptual understanding and model development. As more mechanistic information becomes available, the results of some human and animal studies can be expected to converge and make extrapolations across species more precise. Moreover, the patterns of genetic alterations in preneoplastic and neoplastic cells will probably help to distinguish tumors induced by exposure to specific environmental agents from those in the background (of endogenous or
OCR for page 215
Issues in Risk Assessment
unknown origin) and so lead to better measures of attributable risks. Biologically based mathematical models will continue to evolve in concert with advances in biology and medicine.
CONCLUSIONS AND RECOMMENDATIONS
Mechanistic understanding of toxicity has strong implications for improvement in the development of low dose extrapolation for the regulation of chemical substances. Currently, low dose extrapolation uses a multistage model with data developed from human occupational exposures or from whole animal bioassays (Anderson et al., 1983). The newer two-stage model examined in this report attempts to use data related more to mechanisms of toxicity. Its potential utility (and the gathering of the data needed to use it) derives from the recent rapid development of biologic investigative techniques.
Understanding of and data on cell birth and death are required for the development and use of the two-stage model, but they do not exist for most chemicals. A better mechanistic understanding must be developed, if modeling efforts are to take advantage of cell birth and death data. If the mechanism of a toxic effect is not understood, inappropriate dose-response data are likely to be used in the extrapolation process, which could then produce an incorrect result. The committee recommends that when critical assumptions about mechanisms of toxicity are made, they must be clearly stated.
The two-stage model can be used as a basis for decision-making, if there is sufficient mechanistic understanding and if a sufficient data base is available. The committee recognizes that regulators face the question of how to determine when such understanding, data, and models are sufficient and appropriate; no hard and fast rules can be given. Complicating the issue is that there is a continuum in the extent of mechanistic understanding and data on any chemical. The risk management context need also be considered.
Scientific work on the two-stage model of carcinogenesis has proceeded sufficiently for it to be clear that its further development should be strongly encouraged. Regulatory agencies might review decisions and standards on materials with economic or public health importance to see whether enough data are available or can be rapidly collected to permit
OCR for page 216
Issues in Risk Assessment
application of the two-stage model for additional perspective. The judgment of scientists as to whether sufficient data are available or could be collected might be helpful to regulatory agencies before they decide to apply this newer model in risk assessment. Experience in conducting such reviews will probably lead to a set of criteria for determining when the two-stage model should be used. The proposed reviews should be conducted on only a narrowly limited number of materials. And they must not be allowed to substitute for or interfere with the prompt regulation of or setting of standards for materials currently or soon to be under examination.
The committee recommends exploratory applications of the two-stage model along with its testing and validation. A first stage in the testing requires mechanistic understanding and the gathering of sufficient data to permit its use. Comparative information on humans must be developed as a part of the validation process. The committee also recommends that statistical confidence-interval methods, sensitivity analyses and related quantitative methods as appropriate be applied to determine the extent that the data are consistent with other mathematical representations and ranges of risk. Although the committee recognizes that the simulation approach to model fitting can have very important uses, particularly for exploratory data analysis and when no closed-form solution of the two-stage model is available, the committee recommends that whenever the model is applied in formal risk assessment, formal statistical methods (e.g., maximum likelihood) should be employed.
Representative terms from entire chapter:
low doses
