Afterword: Some Thoughts on What was Learned and Some Science Policy Issues

  • James D. Wilson


This symposium marked a significant change in the use of mathematical modelling to understand carcinogenesis. Within the last two years, experimentalists in carcinogenesis have begun to recognize the power for testing hypotheses offered by expressions of the new theory first described by Moolgavkar and Knudson in 1981. We have already seen significant change in our understanding as a result.

Any new field of scientific investigation develops its own language adapted to communicate concepts peculiar to its investigators’ needs. This new field of carcinogenesis modelling borrowed from pathology the concept of “stage” to describe discrete steps in the process by which normal cells are transformed into cancer cells. Because its use evolved, communication between mathematicians and biologists became difficult: the mathematical models became focussed on the events which cause transition from one biological “stage” to the next, and the usage changed as a result. We suggest that modellers adopt “event” instead of “stage” to describe their expressions, in order to clarify communications.

The models explored here are potentially useful for regulatory purposes — sometimes referred to as “risk assessment”. Their use for hypothesis-testing is clear. However, it seems likely that unavailability of data will preclude widespread use of these models to predict hazard functions far outside the observable range; that is, their direct usage for regulation will not soon be common. In addition, the uncertainty associated with estimating all the parameters which enter these calculations means that the final estimates of the hazard function cannot be very precise. A means is needed for altering the present regulatory methodology so as to take into account the information developed by application of the models discussed at this symposium to the experimental data whose generation they suggest.


Hazard Function Cancer Risk Assessment Regulatory Purpose Urinary Bladder Cancer Carcinogenesis Modelling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    P. Armitage and R. Doll, “The age distribution of cancer and a multi-stage theory of carcinogenesis”. Brit. J. Cancer 8:1–12 (1954).CrossRefGoogle Scholar
  2. 2).
    K. S. Crump, D. G. Hoel, C. H. Langley and R. Peto, “Fundamental carcinogenic processes and their implications for low dose risk assessment”. Cancer Research 36:2673–2679 (1976).Google Scholar
  3. 3).
    R. E. Greenfield, L. B. Ellwein and S. M. Cohen, “A general probabilistic model for carcinogenesis: analysis of experimental urinary bladder cancer”. Carcinogenesis 5:437–445 (1984) .CrossRefGoogle Scholar
  4. 4).
    S. H. Moolgavkar, A. Dewanji, and D. J. Venzon, “A stochastic two-stage model for cancer risk assessment. I. The hazard function and the probability of tumor.” Risk Anal. 8:383–392 (1988).CrossRefGoogle Scholar
  5. 5).
    S. H. Moolgavkar and A. G. Knudson Jr., “Mutation and cancer: a model for human carcinogenesis”. J. Nat. Cancer Inst. 66:1037–1052 (1981).Google Scholar
  6. 6).
    T. W. Thorslund, C. C. Brown and G. Charnley, “Biologi cally motivated cancer risk models”. Risk Anal. 7:109–119 (1987).CrossRefGoogle Scholar
  7. 7).
    C. C. Travis, ed., Biologically Based Methods for Cancer Risk Assessment. New York and London: Plenum Press (in cooperation with NATO Scientific Affairs Division), 1989.Google Scholar
  8. 8).
    J. D. Wilson, “Biological bases for cancer doseresponse extrapolation procedures”. Env. Health Perspectives, (in press) .Google Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • James D. Wilson

There are no affiliations available

Personalised recommendations