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How Biologically Based Models May Help Extrapolating Cancer Risk to Low Doses by E. Georg Luebeck Fred Hutchinson Cancer Research Center, Public Health Sciences Division, MP-665 1124 Columbia Street, Seattle WA 98104 Prepared for the International Center for a Scientific Ecology Is the concept of linear relationship between dose and effect still a valid model for assessing risk related to low doses of carcinogens? April 7, 1993

1 The Problem Much has been written about the subject of low dose and species extrapolation in the context of quantitative cancer risk assessment (e.g see the provocative discussion by D.A. Freedman and H.Zeisel, 1988). It would be presumptuous to attempt another in depth discussion of the subject, its problems and potential pitfalls, that wouldn't simply reiterate what many in the field are already well aware of. However, a new paradigm in quantitative cancer risk assessment has emerged over the last 5 to 10 years, that is based upon a better understanding of carcinogenesis in terms of the underlying genetic processes, in particular the role of oncogene activation and anti-oncogene (tumor suppressor gene) inactivation in the cell. Further, the ability to quantitate molecular changes due to carcinogenic exposures, to identify metabolic pathways and interactions of metabolites with the cellular machinery, have made it possible to include such information into the risk assesment process. With a steady stream of new information on cancer biology and the biochemistry of the processes involved we are challenged to develop better and more realistic cancer models that can be descriptive as well as predictive. The use of bioassays, and rodent experiments in particular, to test putative carcinogens for their carcinogenicity in humans, has proven to be quite problematic. Aside from the formidable problem of translating results form one species to another, many experiments are also performed with relatively high doses (often near the maximally tolerated dose (MTD)), the reason being, of course, mostly one of economy. Thus, an extrapolation of relevant risk quantities (hazard or incidence functions, relative or excess risks) to much lower doses is necessary to quantify the cancer risk to human populations exposed to levels many orders of magnitude lower than those used in typical bioassays. On the other hand, epidemiologic information is sparse, unavailable, or is terribly confounded with certain lifestyle factors, like diet, smoking or occupational hazards so that the animal experiment represents the next best source of in vivo information. Other advantages are obvious: The experimental protocol may very closely monitor carcinogen uptake, use specific age groups and a homogenous population (strain) of animals. Often serial sacrifices are performed to monitor intermediate endpoints. 2 Model Dependency of Low Dose Behaviour The traditional assumption of low dose linearity for bioassays that employ high doses of a carcinogen is primarily one of convenience. It has been shown that a variety of models, some of them biologically motivated, can actually lead to linear, convex or concave low dose behaviour in the response function, depending on the choice of dose response in the available model parameters (Van Ryzin, 1982). Since in most statistical analyses the dose response is fitted at the range of dose where the induced carcinogenic response is relatively high, it is doubtful whether the estimated relationships of model parameters and dose actually continue to hold when going to very low doses. It is our fundamental belief that a model should properly reflect real physical processes that may be too complex to be described explictly. Can we really assume that the cell biology that works at high levels of chemical exposure is still the same at much lower levels? What about threshold N uN 2 0 N i A ~ a ~ ~

effects, saturation effects due to a finite number of receptors, hidden toxicity, competition of metabolic pathways etc ? These questions cannot be answered by curve fitting exercises or by using purely phenomenological models that contain parameters which are not amenable to biological interpretation. It is imperative that we use biologically based models if the results are to be meaningful. To illustrate the dilema the statistician would usually arrive at, let us consider the multistage model, a model that has increasingly been considered for cancer risk analysis because it seems biologically motivated. It assumes that cancer is a multistep process with rates a;(d), i.e. the malignant tumor is the outcome of k transformations, starting with a normal cell that undergoes k progressive changes, turning into a malignant cell at the 04 step. The shortcomings of this naive picture will be discussed below. Further, assume that a;(d) = a; + Q;dN with powers p; > 0 and i = 1, 2,.., k. The dose-response function of this model may be written as k P(d) = 1 - exp [- JI(a: + (3tdP' )) • (1) .=r This can be rewritten as k P(d) = I -exp[-E(B:dn')]. (2) ._o where we defined po - 0. Obviously, at low doses the terms with smallest powers will be most important in the Taylor series expansion of P(d). The excess risk, over background, usually defined as ER(d) =(P(d)-P(0))/(1-P(0)) can then be seen to have the limiting behaviour dlim ER(d) = Bjd"i with 0< Pi < P:#i • .(3) If 0< pj < 1 then the low-dose behaviour of ER is concave and estimates of the vir- tually safe dose (VSD) are more conservative (smaller) compared to VSDs derived from a linear low-dose response model with pj = 1. This sublinear dose response was found for vinyl chloride in several analyses (see e.g. Krewski and Van Ryzin 1981). It is an often cited example where low-dose linearity is not a conservative assumption. When pj > 1 the low-dose response is convex and the VSD can be larger. See Figure 1 for a schematic representation of these scenarios and the determination of VSD. Clearly, the low-dose be- haviour of the response function should not be deduced from remote measurements alone- Not only may the estimates of the powers p; in our model be very uncertain, the biology may also be quite different at the lower dose levels. Without additional information on empirically derived responses at the lower dose levels and on intermediate endpoints and other mechanistic considerations on the action of a particular compound, low-dose extrap- olation remains guesswork and cannot be trusted. To conclude this section, quantitative risk assessment is not an impossible undertaking but should be based upon, may be com- peting, mathematical implementations of current knowledge of the fundamental processes. Consequently it needs to be a collaborative effort among basic scientists, biochemists, epi- demiologists and the risk modeler. 3

Fig.1 0.100 i.ono dose(arbitrary unils) 10.000 ioo.ooo Figure 1: Log-Log plot of a typical dose response scenario together with sublinear (slope p=.5), linear (slope p=l) and quadratic (slope p=2) low-dose fits. The 3 VSD points are defined by a response of .001. In this hypothetical case the VSDs roughly differ by factors of 10. 4

3 BB Models at Low Dose Among the many models that have been used for dose response modeling in the past only the multistage model, first proposed by Armitage and Doll, can be considered a BB model since its parameters can be equated with rate limiting mutational events on the pathway to cancer- Nethertheless, it stops short of incorporating another important aspect of carcinogenesis, namely the cell kinetics of intermediate cell populations. That this is an important point has been shown in a number of initiation-promotion (IP) experiments in the mouse skin (DMBA/TPA treatment) and in the rat liver where enzyme altered lesion are promoted with a variety of non-genotoxic substances (Phenobarbital, AAF, PCBs, Dioxin). The most parsimonious model that incorporates the transformation of normal cells into premalignant cells and also describes the clonal expansion of such cell populations is the two-event clonal expansion model formulated by Moolgavkar and colleagues (see Figure 2 for a graphical representation). The model has been shown to be consistent with a number of experimental and epidemiologic data sets (see e.g. Moolgavkar et al. 1992, 1993). It also relates fundamental biological processes at the cellular level to the incidence of benign and malignant tumors in specific tissues in human or animal populations. The parameters in the model are interpretable in biological terms and can be made functions of dose and time to allow for the varying influence of the carcinogen on tell transformation and cell kinetics. Because of this feature the problem of low-dose extrapolation is shifted form the macroscopic level of the (observable) tumor to a microscopic one where the problem of low-dose extrapolation emerges anew in a different light. In order to relate the parameters of the model to the specific agent under investigation it is first necessary to identify the metabolic pathway(s) and to determine the dose of the active metabolite responsible for the carcinogenic response in the tissue of interest. Thus, the BB models used should be combined with a pharmacokinetic front-end, that allows one to infer the tissue level of the metabolite from knowledge of the level of the agent in the environment_ The importance of pharmacokinetic modeling in qunatitative risk assessment is now widely appreciated. What do we hope to gain from such refinement for the task of risk assessment? The cellular mechanisms considered by the model are obviously intermediate (on the pathway to cancer) in character and may be more sensitive to low dose stimuli. Since the occurrence of a large number of premalignant lesions is likely to precede the formation of malignancies an amplification of the dose effect can be achieved provided the correlation of precursor lesions and malignant tumors is understood (at least in a statistical way). In the rodent liver, for instance, many thousand enzyme altered foci (EAF) can be seen on histological sections before animals die of liver cancer. The correlation between hepatocellular carcinomas and appearance of EAF is well established empirically. What would the amplification be? Assuming, very conservatively, that the first malig- nant transformation leads inevitably to an observable tumor, the number of non-extinct intermediate clones that appear at time t would roughly amount to vX(1 - Q/a)t. Here, the product vX is the number of initiated premalignant progenitor cells and the factor (1 - f3/a) is the asymptotic probability of survival of the generated clone. Of course, some intermediate clones may give rise to malignant tumors before they become extinct. To 5

h M 14 conv D progression ~ promotion Figure 2: Pictorial representation of the two-event clonal expansion model. In the parlance of chemical carcinogenesis, the first rate-limiting event can be identified with initiation (rate v), the second rate-limiting event with malignant conversion (rate u.), and the clonal expan- sion of intermediate cells with promotion. Thus, a promoter increases the net proliferation rate, a-(i, of initiated cells, either by increasing a, the cell division rate, or decreasing Q, the cell death (or differentiation) rate, or both. Increased cell division rates and decreased cell death rates have both been implicated in promotion. X is the number of normal susceptible target cells. After malignant transformation, relatively rapid changes lead to tumor progression. These are not explicitly modelled. be specific, let me give an example (see Moolgavkar et al. 1990). From an analysis of the number and size distribution of EAF in rat liver of rats treated with various levels of N-nitrosomorpholine (NNM) in their trinking water we have estimated that vX , 200 per day per liver at the 1 ppm dose level. The parameter p/a, measuring clonal extinction, was estimated to be near .99. Thus after 100 days of treatment with I ppm NNM, we have an amplification factor 200x(1-.99)x100 = 200. This is likely a lower bound since none of the animals that were not sacrificed for the EAF ascertainment developed hepatocellular. carcinomas in this dose group. Furthermore, it is unlikely that the first malignant occur- rence leads to the tumor, so that many more intermediate clones may be needed on average to yield a tumor during the animals life span. This example is very crude but exemplifies the idea. Because of recent advances in DNA amplification and the use of molecular markers many intermediate level cellular responses can be measured. It also has become possible to quantitate a number of proposed mechanisms of action of the carcinogen under investigation over a wide range of doses. For instance, an agent may simply act as an initiatior, increasing the number of transformed progenitor cells of premalignant lesions without increasing cell proliferation. Such agents are generally described as mutagenic or genotoxic. On the other hand, some agents act as promoters and stimulate cell turnover in existing (pre)malignant clones without being directly mutagenic. Strong initiators in the rat liver, for instance, are N-nitrosomorpholine (NNM) and diethylnitrosamine (DEN) while a large number of 6

PCB congeners and dioxins (TCDDs and HCDDs) are shown to act mainly as promoters. The distinction between the different modes of action has profound consequneces for the infered tumor risk. It is important to assess the relative potencies of agents with respect to their initiating and promoting action and to relate them to tumor outcome. The two-event clonal expansion model provides a unified framework to do this in a rational manner. References D.A. Freedman and H.Zeisel (1988). Frout Mouse-to-Man: The Quantitative Assessment of Cancer Risks. Statistical Science, Vol.3, No.1,3-56. J. Van Ryzin (1982). Discussion. In Current Topics in Biostatistics and Epidemiology, Biometrics Supplement, 130-139. . D. Krewski and J. Van Ryzin (1981). Dose response models for quantal response toxicity data. In Statistics and Related Topics, M. Csbrgo, D. Dawson, J.N.K. Rao and E. Saleh (eds), 201-231, New York: North Holland. S.H. Moolgavkar, E.G Luebeck, M. de Gunst., ILE. Port and M. Schwarz (1990). Quan- titative analysis of enzyme-altered foci in rat hepatocarcinogenesis experiments I: Single agent regimen. Carcinogenesis, 11, 8, 1271-1278. S.li. Moolgavkar and E.G Luebeck. (1992). Multistage Carcinogenesis: Population-Based Model for Colon Cancer. J Natl Cancer Inst 84: 610-618. S.H. Moolgavkar, E.G Luebeck, D. Krewski and J.M. Zielinski (1993). Radon, Cigarette Smoke, and Lung Cancer: A Reanalysis of the Colorado Plateau Uranium Miners' Data. American Journal of Epidemiology, in press. N N O N i A 7 01 O V tfl