Abstract
It is often assumed that the probability of observing a specific cancer-related response by time t under constant dose rate d depends on d and t only through the product dt,the “total dose.” Loosely attributable to Haber from another context, it is shown here that for several classes of time/dose response curves, Haber’s rule implies severe model restrictions for mathematical consistency. A generalized-Haber’s rule (G-H rule) is suggested instead that is calculated from the specific time/dose-response model used to describe the data. This approach requires only a change in dose and time metameters, from d to D(d) and from t to T(t), respectively. Determination of the functions D and T is demonstrated for several models, for some corresponding expressions of extra risk, and for assumptions of additive and independent background mechanisms.
The G-H rule is of the form D(d)T(t) = C, for C a constant (C > 0), and defines the “tradeoff” between changes in d and t that give the same change in risk (the probability the event will occur by time t),or in extra risk, which is often the measure of interest.
This work was initiated under U.S. EPA Contract 68–01–6826. The views expressed are those of the authors. Agency policy should not be inferred. The authors gratefully acknowledge the support provided by Environmental Monitoring and Services, Inc., Chapel Hill, NC, toward completion of this work.
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© 1989 Plenum Press, New York
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Brown, K.G., Beliles, R.P. (1989). On Basing Extrapolation of Risk for a Chemical Carcinogen on Total Dose (Constant Dose Rate × Continuous Exposure Duration): Implications and an Extension. In: Bonin, J.J., Stevenson, D.E. (eds) Risk Assessment in Setting National Priorities. Advances in Risk Analysis, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5682-0_5
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