Mechanistic models such as the one-hit, the multihit, and the multistage are mathematical in structure, whereas time-to-tumor or tolerance distribution models such as the Probit, the Logit, and the Weibull are statistical (see, e.g., Faustman and Omenn, 1996; Rees and Hattis, 1994). All these models are used or have been attempted by various regulatory agencies to extrapolate toxic response to the low-dose region. The mechanistic models are designed typically for carcinogenic and mutagenic effects that assume a non-threshold mechanism. The time-to-tumor or tolerance distribution models, on the other hand, are used primarily for the rest (adverse) health effects that assume a threshold mechanism.

The applications of these mathematical and statistical models are built upon biological considerations which are ever evolving. As a matter of fact, the multistage model has been shown to be generally consistent with human epidemiology data for lung cancer resulting from occupational exposure to coke oven emissions (Dong, 1984; Dong et al., 1988).

The dose-response relationship used for curve fitting can be afforded only at high doses. Such a relationship is likely to be different from that at low doses, thus making the use of the above mathematical or statistical models vulnerable. PB-PK models can and hence should be used to more accurately characterize the dose-response relationship at low doses (Beck et al., 1994). Again, more metabolism and pharmacokinetics data are needed if a PB-PK model is used for low dose extrapolation.