Background Response

For the probit model any toxic response in zero dosage control is usually subtracted from all the data. Thus, what is used in the calculations is the excess mortality or toxic effect. For stochastic biological models, where a hit can be caused by natural background causes, the response can be adjusted for the probability of that occurring. In this case, P(d) is interpreted as the additional risk over background, which can be attributed to the dose d:

where P* (d) is the observed response and p is the probability of a spontaneous hit. The value of p may be so small that it cannot be measured directly in laboratory animals. In such a case, it could be estimated by extrapolating dose-response data to zero dose, as described in the next section.

19.3.1 Low-Dose Extrapolation

For many toxic effects, especially carcinogenesis, the goal is to control environmental exposures to keep the risk at an extremely low level. A typical regulatory goal for a

TABLE 19.5 Data and Model Results for Dieldrin

Dose (ppm)

Fraction Having Tumors

Excess Risk

Predicted P

Predicted Excess Risk

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