Comments on Papers on U-Shaped Dose-Respone Relationships for Carcinogens

Suresh H. Moolgavkar, M.D.

Fred Hutchinson Cancer Research Center

Division of Public Health Sciences

110 Fairview Avenue, N, MP-665

P.O. Box 19024

Seattle, WA 98109-1024

Tel: (206) 667-4145

Fax: (206) 667-7004


Radiation hormesis, the notion that low levels of radiation may actually protect against cancer (possibly by inducing repair), is not a new concept. Although I have not encountered the concept of chemical hormesis, the idea that there might be a threshold for chemical carcinogens has been hotly debated. A U-shaped dose-response relationship for chemical or radiation carcinogenesis obviously has profound implications for quantitative cancer risk assessment. The principal issues are: 1) How good is the experimental or epidemiological evidence that such a relationship exists? 2) Are there biologically reasonable models of carcinogenesis that can explain such a relationship?

Ken Bogen presents a model for lung cancer induced by radon and claims that it 'predicts' a U-shaped exposure-response relationship. Since this model, which is an extension of the two stage clonal expansion model, was specifically formulated to explain a U-shaped exposure response, it can hardly be claimed that the model 'predicts' this relationship. For radon, the existence of a U-shaped exposure-response relationship is inferred from combined evidence from cohort studies among heavily exposed miners and Cohen's ecologic studies of the relationship between U.S. county-level lung cancer mortality and mean radon levels in the counties. While the miner data clearly indicate a monotonically increasing risk with radon exposure, the ecologic studies exhibit a negative correlation between radon levels and lung cancer mortality. Ecologic studies are well known to be susceptible to various types of bias and are generally looked upon with disfavor by epidemiologists. Nevertheless, in response to critics, Cohen (e.g., Cohen, 1995) has done a credible job of investigating various possible sources of bias in his analyses, and I am loath to dismiss his findings purely on the grounds that they are based on ecologic correlations.

Bogen's CD2 model introduces two new cell compartments into the two stage clonal expansion model (see his figure 1). The ultimate result of Bogen's additional assumptions is to introduce a U-shaped exposure-response relationship in the net proliferation rate of initiated (intermediate) cells. This U-shape is then reflected in a U-shaped exposure-response relationship for the hazard function for lung cancer mortality. One might as well have started out with the assumption of a U-shaped exposure-response relationship for the net proliferation of initiated cells. For example, one could posit that low levels of radon exposure result primarily in cell killing of initiated cells. At higher levels, there would be both cell killing and cell division stimulated by radon, with cell division predominating. There is no more direct biological support for Bogen's assumptions than for these (simpler) assumptions.

Bogen suggests that it is better to fit models to incidence (hazard) rates than to lifetime probabilities. This is certainly true. But then he makes the rather amazing claim that 'typical MVK-type' model applications involve fitting lifetime rather than age-specific risks of cancer mortality. In fact, the first stochastic cancer models introduced more than 40 years ago were fitted to hazard (incidence) rates rather than lifetime probabilities. More recently, most publications that I have seen (e.g., Little, 1995, 1996; Kai et al., 1997) including our two papers (Moolgavkar et al., 1993; Luebeck et al., 1996) referenced by Bogen, are based on analyses of hazard data. In fact, when information has been available on individual members of a cohort, as in uranium miners, we (Moolgavkar et al., 1993) have used statistical methods for time-to-tumor analyses. One of the strengths of methods of analyses based on stochastic cancer models is that individual level information can explicitly and easily be incorporated. Individual level information for the cohorts of miners was presumably available to Bogen, and I believe that his analysis would be improved by explicitly taking this information into account. By categorizing the data, Bogen does not exploit fully the power of biologically-based analyses.

Finally, on a technical note, recent publications (e.g., Heidenreich et al., 1997) have discussed identifiability of parameters of the two stage clonal expansion model. Similar considerations probably apply to Bogen's extension of this model and should be addressed. It is important also to use the so-called exact hazard functions for analyses, rather than commonly used approximations that do not properly account for the inherent stochasticity of the models. Exact hazard functions for multistage cancer models quite generally approach a finite asymptote with time (age). This phenomenon may explain, at least partially, the leveling off of age-specific incidence at higher ages commented on by Bogen. In lung cancer birth cohort effects may also contribute to the leveling off because of the cohort-wise introduction of smoking in populations.

Anderson and Conolly present a model that explains a U-shaped response of number of altered hepatic foci and focal volume as functions of administered TCDD in rats. The development of this model was apparently stimulated by an experiment performed by Pitot et al (1987), which reported such a U-shaped relationship. The interpretation of the shape of the exposure-response relationship in this experiment is difficult, however, because the control animals were apparently sacrificed later than the animals on TCDD. Thus, the evidence for the existence of a U-shaped exposure-response relationship is far from convincing. Neither is there evidence of such a relationship for enzyme induction (Kohn et al., 1993) or receptor binding (Portier et al., 1993) by TCDD. A recent analysis, which took time until sacrifice explicitly into account (Portier et al., 1996), of two distinct data sets, one of them the data of Pitot et al., found no evidence of a U-shaped relationship. This analysis arrived at some rather unexpected conclusions, however. In particular, the analysis found that the data were consistent with TCDD having some initiating activity. In analyses of a completely different data set from the two analyzed by Portier et al., we (Moolgavkar et al., 1996) arrived at a similar conclusion.

Anderson and Conolly suggest that the Pitot data can be explained on the basis of a 'two-cell' model of initiation. In this model, DEN-initiation together with partial hepatectomy is posited to produce two distinct types of initiated cells, both of which are capable of clonal growth leading to enzyme altered foci. The model assumes that one of these cell types responds to the negative growth environment associated with TCDD treatment. The net proliferation rate of this cell type decreases with increasing TCDD concentration. The other type of initiated cell is unresponsive to the mito-inhibitory environment associated with TCDD exposure. For these cells, the net proliferation rate increases with increasing concentration of TCDD. Anderson and Conolly show by simulation that this model is capable of explaining some features of the Pitot data without requiring that TCDD have initiating activity, and produces a U-shaped exposure-response relationship. I would like to note here, however, that the data used for our analysis referred to above (Moolgavkar et al., 1996) did not contain groups of animals exposed to different doses of TCDD, although it did contain groups of animals sacrificed at different time points. Thus, we arrived at the conclusion that TCDD has initiating activity on the basis of data that have no exposure-response information, i.e., our conclusion is not based on the shape of an exposure-response relationship.

Even if a U-shaped exposure-response relationship is unequivocally demonstrated for TCDD-induced liver foci, it is not necessary to posit a 'two-cell' model for initiation. For example, any model leading to decreased net proliferation rates of initiated cells at low levels of TCDD and increased net proliferation rates at higher levels would predict a U-shaped relationship. It is plausible that rates of division and apoptosis may depend not only on concentration of TCDD but also on the time course of TCDD exposure. In recent analyses of small foci (not yet published) we find that rates of division and apoptosis of focal cells in TCDD treated animals are not constant with time but exhibit a complex temporal pattern over the course of TCDD administration.

Anderson and Conolly are to be commended for a model that takes explicit account of liver architecture. Clearly, such models will have to be developed in parallel with our understanding of the biological properties endowed by the architecture of organs. I find the details of their model and their simulations unsatisfactory, however. Despite the ample evidence that an important mechanism of TCDD-induced promotion may be inhibition of apoptosis (e.g., Stinchcombe et al., 1995), their model focuses on mitosis and their simulations appear to be based on the concept of net proliferation. When considering stochastic processes in which both cell death and cell division are taking place it is important to simulate each of these separately and explicitly. One consequence of a positive rate of apoptosis in initiated cells is that these cells can die off with a high probability without giving rise to initiated foci. This has profound implications for both the number of non-extinct foci and the size distribution of foci.

The evidence of U-shaped exposure-response relationships for radon and TCDD is tenuous at best. On balance, despite the ecologic nature of the evidence, I believe that the case for radon is stronger than that for TCDD. Models developed for such possibly ephemeral observations could make important contributions if the observations are shown to be logical consequences of basic biological principles. Neither of the models I have discussed here would appear to satisfy this criterion and, to be fair, very few models do. The models are also useful if they lead to testable biological hypotheses. Certainly, the Anderson-Conolly two-cell hypothesis should be amenable to experimental verification. With respect to radon, recently reported observations (e.g., Hickman et al., 1994) on gene regulation by low levels of radiation suggest that irradiation by alpha particles may stimulate cell proliferation by up or down regulation of critical genes. A direct effect of radon on promotion in lung tissue would appear to be difficult to demonstrate, however. That the dose-response curve for such an effect is U-shaped would be even more difficult to establish.


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