PRINCIPLES OF TOXICOLOGY

Generating Cancer Risk Estimates Estimating the lifetime cancer risk associated with a particular
dose is a relatively simple mathematical process. Because most regulatory agencies such as the USEPA
use the conservative assumption that cancer risk should be modeled via a linear, nonthreshold model
like the LMS model, the risk associated with a particular dose is calculated by the following formula:
R = D × CSF or R = LADD × CSF
where R = risk
D = dose [normally expressed as the lifetime average daily dose (LADD)
(mg/kg⋅day)]
CSF = cancer slope factor [the slope of the dose–response curve in units of
(mg/kg⋅day) –1 ]
With this equation, the total dose the individual or population has accumulated during their entire
exposure interval is first converted into a lifetime average daily dose (LADD), a dose that if received
everyday for a lifetime would be equivalent to the total dose accumulated during the actual exposure
period. For example, if the exposure assessment projected a daily dosage of 70 mg/kg⋅day for a 30-year
exposure interval, then the LADD assuming a 70-year lifespan, would be 30 mg/kg⋅day (i.e., 70
mg/kg⋅day × 30 years ÷ 70 years = 30 mg/kg⋅day). The dose is expressed in units of mg/kg⋅day and
the CSF is in units of reciprocal mg/kg⋅day or (mg/kg⋅day) –1 . Thus, the product of dose × CSF is
unitless, and is intended to represent the excess probability of cancer associated with the dose. For
example, assume that the CSF for a chemical is 0.001 (mg/kg⋅day) –1 (in scientific notation a value of
1.0 × 10 –3 (mg/kg⋅day) –1 ) and that the LADD derived during the exposure assessment was 0.03
mg/kg⋅day (3.0 × 10 –2 mg/kg⋅day). The risk would be as follows:
which can also be written as
R =
R = 0.001 × 0.03 = 0.00003
3
100,000
18.4 DOSE–RESPONSE ASSESSMENT 459
or R = 3.0 × 10–5
In this example the risk estimate represents a 3 / 100,000 chance or mathematical probability that a
cancer will develop from exposure. It should also be noted, however, that because regulatory agencies
strive for conservative, health protective risk calculations, the CSF used is statistically an upper-bound
estimate of the dose–cancer relationship. The true cancer risk of the chemical at this dose may be much
less than that calculated, and in fact, could be as low as zero.
Dose Metrics
A common issue for both threshold and nonthreshold dose–response relationships is the metric used
to express dose. The dose metric is important because animal data must often be used as a surrogate
for dose–response information in humans. Humans are, of course, much different in size than most
laboratory animals. How then should doses be scaled between one animal species and another, and
between animals and humans?
One can improve the accuracy of SHD calculations by starting with the best “dose metric” (measure
of the dose) for the actual amount of chemical required to induce toxicity in the most sensitive target
organ. Most dose information in animal studies is reported in terms of the “applied dose” (the dose
administered to the whole animal). Remember, however, that it is only the “absorbed dose” (the amount
of the chemical actually absorbed into the body) that is eligible for inducing toxicity. Further, from the
dose that is absorbed, it is the dose that reaches the target tissue that is most important in determining
the extent of response. The relationship between applied dose and target organ dose can be different
among species, due to differences in metabolism and/or distribution of the chemical within the body,