Cancer Modeling with Intermittent Exposures

  • Daniel Krewski
  • Duncan J. Murdoch


In this article we consider the application of both the classical Armitage-Doll multi-stage model and the Moolgavkar-Venzon-Knudson two-stage birthdeath-mutation model in situations in which carcinogen exposure is not constant over time. In particular, novel representations of the cumulative hazard function are used to describe the relative effectiveness of dosing at different times, and to establish an equivalent constant dose which leads to the same risk as time-dependent dosing. The relative effectiveness function may be used to establish the degree to which the use of a simple time-weighted average dose may underestimate (or overestimate) risk. Both the Armitage-Doll and Moolgavkar-Venzon-Knudson models are applied to bioassay data on B(a)P with variable dosing patterns, using equivalent constant doses to facilitate maximum likelihood estimation of the model parameters.


Relative Effectiveness Cumulative Hazard Cancer Risk Assessment Constant Dose Intermittent Exposure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Armitage, P. (1985). Multistage models of carcinogenesis Environmental Health perspectives 63, 195–201.CrossRefGoogle Scholar
  2. 2.
    Brown, K.G. & Hoel, D.G. (1986). Statistical modeling of animal bioassay data with variable dosing regimens: example — vinyl chloride. Risk Analysis 6, 155–166.CrossRefGoogle Scholar
  3. 3.
    Chen, C.W. & Moini, A. (1989). On cancer dose response models with clonal expansion. In: Scientifíc Issues in Quantitative Cancer Risk Assessment (S.H. Moolgavkar, ed.). Birkhauser Boston, New York. In Press.Google Scholar
  4. 4.
    Chen, J.J., Kodell, R.L. & Gaylor, D. (1988). Using the biological two-stage model to assess risk from short-term exposures. Risk Analysis 6, 223–230.CrossRefGoogle Scholar
  5. 5.
    Clifton, K-H. (1989) The clonogenic cells of the rat mammary and thyroid glands: their biology, frequency of initiation, and promotion/progression to cancer. In: Scientific Issues in Quantitative Cancer Risk Assessment (S.H. Moolgavkar, ed.). Birkhauser Boston, New York. In Press.Google Scholar
  6. 6.
    Crump, K.S. & Howe, R.B. (1984). The multistage model with a timedependent dose pattern: applications to carcinogenic risk assessment. Risk Analysis 4, 163–176.CrossRefGoogle Scholar
  7. 7.
    Gart, J.J., Krewski, D., Lee, P.N., Tarone, R.L. & Wahrendorf, J. (1986). Statistical Methods in Cancer Research, Vol. II, The Design and Analysis of Long-Term Animal Experiments. IARC Scientific Publications No.79, International Agency for Research on Cancer, Lyon.Google Scholar
  8. 8.
    Kalbfleisch, J.D.; Krewski, D.R. and Van Ryzin, J. (1983). Doseresponse models for time-to-response toxicity data (with discussion by V.T. Farewell and J.F. Lawless). Canadian Journal of Statistics 11, 25–49.CrossRefGoogle Scholar
  9. 9.
    Kodell, R.L., Gaylor, D.W. & Chen, J.J. (1987). Using average lifetime dose rate for intermittent exposures to carcinogens. Risk Analysis 7, 339–345.CrossRefGoogle Scholar
  10. 10.
    Krewski, D., Murdoch, D. & Dewanji, A. (1986). Statistical modeling and extrapolation of carcinogenesis data. In: Modern Statistical Methods in Chronic Disease Epidemiology (S.H. Moolgavkar & R.L. Prentice, eds.). Wiley-Interscience, New York, pp. 259–282.Google Scholar
  11. 11.
    Moolgavkar, S.H. (1986). Carcinogenesis modeling: from molecular biology to epidemiology. Annual Review of Public Health 7, 151–169.CrossRefGoogle Scholar
  12. 12.
    Moolgavkar, S. & Dewanji, A. (1988). Biologically based models for cancer risk assessment: a cautionary note. Risk Analysis 8, 5–6.CrossRefGoogle Scholar
  13. 13.
    Murdoch, D.J. & Krewski, D. (1988). Carcinogenic risk assessment with time-dependent exposure patterns. Risk Analysis 8, 521 – 530.CrossRefGoogle Scholar
  14. 14.
    National Research Council (1988). Criteria and Methods for Preparing Emergency Exposure Guidance Level (EEGL), Short-Term Public Emergency Guidance (SPEGL), and Continuous Exposure Guidance Level (CEGL) Documents. National Academy Press, Washington, D.C.Google Scholar
  15. 15.
    Neal, J. & Rigdon, R.H. (1967). Gastric tumors in mice fed benzo[a]pyrene: a quantitative study. Texas Reports in Biology and Medicine 24, 553–557.Google Scholar
  16. 16.
    Thorslund, T. (1988). Comparative Potency Approach for Estimating the Cancer Risk Associated with Exposure to Mixtures of Polycyclic Aromatic Hydrocarbons. Clement Associates, Washington, D.C.Google Scholar
  17. 17.
    Thorslund, T.W., Brown, C.C. & Charnley, G. (1987). Biologically motivated cancer risk models. Risk Analysis 7, 109–119.CrossRefGoogle Scholar
  18. 18.
    U.S. Environmental Protection Agency (1986). Guidelines for carcinogen risk assessment. Federal Register 51, 33992–34003.Google Scholar

Copyright information

© Birkhäuser Boston 1924

Authors and Affiliations

  • Daniel Krewski
    • 1
    • 2
  • Duncan J. Murdoch
    • 3
  1. 1.Environmental Health Directorate, Health Protection BranchHealth and Welfare CanadaOttawaCanada
  2. 2.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada
  3. 3.Department of Statistics & Actuarial ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations