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.
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.