Non-linear dose-response functions in carcinogenesis have long been debated especially with respect to the degree of over-estimation of risk that the linear no-threshold assumption may bring. Limited cancer data for a given agent are usually found to be reasonably consistent with linearity and then argued that the data are linear. For example, gamma radiation induced solid cancers in the A-bomb survivor cohort are considered to have linear responses for each radiogenic cancer type although simple models with non-linearities at about 5 mSv provides equivalent or improved descriptions of the observed data (Hoel and Li 1998). General low-dose non-linear behavior with chemical carcinogens can be easily described using simple pharmacokinetics (e.g. Hoel et al. 1983). The current three papers go much further by considering several observed "U shaped" dose-response functions and provide possible biologically based models which could possibly explain this observed behavior. These proposed dose-response models are very speculative and will require biological justification.
The paper by Andersen and Conolly provides an interesting approach to explaining and modelling the "U shaped" response of the TCDD promoted liver foci in Pitot's rat model. The idea of two different cell types both of which can develop into the enzyme-altered foci is a key assumption, which to my mind is very speculative. Further, one cell type's net division rate increases with TCDD dose while the other cell type's division rate decreases with dose. Clearly this system would easily allow for non-monotonic responses in altered foci. If these two types of cells really do exist have we seen similar dose response behavior in this rat liver system for other promoters or is this unique to TCDD? Secondly, for risk assessment purposes there has been a focus on human studies and lung cancer. If so then there probably is no carry-over of the liver foci non-linearity to human risk estimation. With regard to the model simulations I found the choice of the dose response for the death rates of A-type cells (20x, 40x, 50x, 70x for doses increasing at 10x per dose) curiously uneven. This is, however, of minor note. Since the biologically based models that are usually applied cannot adequately describe the TCDD data clearly the biology is more complex and so the models necessarily need more complexity. I find the approach offered by Andersen and Conolly most intriguing and they should be encouraged to further develop and test their hypotheses.
Non-linear Michaelis-Menton kinetics has been applied for some time in risk assessment. Downs and Frankowski add a speculated background substance that competes for the activating enzyme. The effective dose is still monotonic until DNA repair is added to the model. By allowing the repair rate to be determined by the administered dose through Michaelis-Menton kinetics non-monotonicity of effect is clearly possible. The argument in support of hormesis has long been the initiation of repair at low exposure. Whether repair rates should be viewed as following simple Michaelis-Menton kinetics of exposure is an open issue. When these processes are all combined into a single model the number of parameters will in many cases exceed the experimental data points. Therefore considerable supplemental assumptions and measurements will be required in order to apply these models in risk estimation.
The paper by Bogen on combining miner data with ecological county data on radon and lung cancer involves two issues. First, whether the use of ecological data at the county level is reasonable and the second is the biological realism of the CD2 model. The issue of ecological bias as it applies to the Cohen county analysis at the county level of lung cancer rates and radon exposure have been published in a series of papers in the July 1998 issue of Health Physics (Lubin pg 4-10 and pg 29-30, Smith et al. pg 11-17, Field et al. pg 31-33, and Cohen pg 18-22 and 23-28). The general criticism is that unless lung cancer risk factors for individuals are not correlated with indoor radon levels within counties estimated exposure response relationships for individuals are not valid. Lubin (pg 30) also presents the relative risk estimates from eight indoor radon studies (low exposure) which are consistent with the extrapolated lung cancer risks from the miner studies and are not consistent with the negative slope lung cancer response estimates from Cohen's ecological correlation study. These issues clearly apply to Bogen's analysis using female lung cancer rates and county radon levels adjusting as Cohen did for demographic variables. Although the arguments for and against the negative slope estimates from Cohen's ecological analysis are primarily theoretical, careful attention must be given to the many completed and ongoing case-control studies of radon exposure in the home with and without cigarette smoking. From an epidemiological standpoint the case-control study is much more persuasive than the ecological study. The addition of the reservoir of unexposed cells to the CD2 model needs biological justification as it relates to lung cancer. As with the proposed mechanistic cell model of Andersen and Conolly experimental data is needed before the implications of their mathematical descriptions can receive acceptance. This line of research should be encouraged.
Hoel DG, Li P. Threshold models in radiation carcinogenesis. Health Physics, 75(3):241-50, 1998.
Hoel DG, Kaplan N and Anderson MW. Implications of
nonlinear kinetics on risk estimation in carcinogenesis.
Science, 219:1032-1037, 1983.