PRINCIPLES OF TOXICOLOGY

458 RISK ASSESSMENT
TABLE 18.1 Expected Risk (Cancer Incidence) Calculated by Three Models When a Relative Dose of
1.0 is Assumed to Cause a 50% Tumor Incidence in Test Animals
Modeled Tumor Incidence (%)
Relative Dose Lognormal Loglogistic One-Hit
16 98 96 100
4 84 84 94
1 a
50 a
50 a
50 a
1
4
16 16 16
1
16
2 4 4
1
100 th
1
1000 th
1
10,000 th
0.05 0.4 0.7
0.00035 0.026 0.07
0.0000001 0.0016 0.007
Source: Adapted from Office of Technology Assessment (1981).
a
Boldface numbers represent the only data assumed for each model; all other tumor incidences were calculated from this single
dose–response point.
the critical point for extrapolating responses in the low-dose range. For dose–response relationships
assumed to have no threshold, the simplest extrapolation model is used: a straight line drawn between
the point of departure and zero. The second proposed change is to allow for the consideration and use
of nonlinear and threshold models for carcinogens where empirical and mechanistic evidence argues
strongly that this type of dose–response model is appropriate for a particular chemical. In this situation,
risk of cancer would be evaluated in a manner entirely analogous to noncancer health effects, such as
through calculation of a margin of exposure.
TABLE 18.2 The Estimated Impact of Six Conservative USEPA Assumptions on Agency Risk
Assessments
Factor
Range of Possible Overstatement in Estimated Cancer
Risk a
Body weight vs. surface area as a scalar for an
interspecies extrapolation
2–12
MLE b vs. 95% UCL c for the cancer slope factor 2–3
Malignant tumors only vs. malignant + benign 1–2
Average species sensitivity vs. most sensitive species 2–5
Pharmacodynamics vs. effective dose 1–6
Risks at shorter than equilibrium buildup time 2–5
Total risk exaggeration 15–10,800
Source: Adapted from Barnard (1994) and based on information supplied by Dr. E. Anderson.
a Note: Instead of presenting ranges of possible overstatement in cancer risk, the Barnard paper presents ranges of possible reduction
in estimated cancer risk if the alternative factors to the current default factors are applied.
b Maximum likelihood exposure.
c Upper confidence limit.