Approaches to Intraspecies Dose Extrapolation

  • Charles C. Brown
Part of the Life Science Monographs book series (LSMO)


In recent years, as the serious long-range health hazards of environmental toxicants have become recognized, the need has arisen for quantitative estimates of their effects on humans exposed to low levels. Often inherent in this estimation procedure is the necessity to extrapolate evidence observed under one set of conditions in one population group or biological system to arrive at an estimate of the effects expected in the population of interest under another set of conditions.


Dose Level Toxic Agent Weibull Model Lower Confidence Limit Quantal Response 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abbott, W. S. 1925. A method of computing the effectiveness of an insecticide.J. Econ. Entomol. 18:265–267.Google Scholar
  2. Albert, R., and B. Altshuler. 1973. Considerations relating to the formulation of limits for unavoidable population exposures to environmental carcinogens. Pp. 233–253 in J. Ballou, R. Busch, D. Mahlum, and C. Sanders, eds.Radionuclide Carcinogenesis. AEC Symposium Series, Conference 720505, National Technical Information Service, Springfield, Virginia.Google Scholar
  3. Altshuler, B. 1977. A Bayesian approach to assessing population risks from environmental carcinogens. Pp. 31–45 in A. Whittemore, ed.Environmental Health, Quantitative Methods. Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
  4. Anderson, M. W., D. G. Hoel, and N. L. Kaplan. 1980. A general scheme for the incorporation of pharmacokinetics in low-dose risk estimation for chemical carcinogenesis; example-vinyl chloride.Toxicol. Appl. Pharmacol. 55:154–161.CrossRefGoogle Scholar
  5. Armitage, P., and R. Doll. 1954. The age distribution of cancer and a multistage theory of carcinogenesis.Br. J. Cancer8:1–12.CrossRefGoogle Scholar
  6. Armitage, P., and R. Doll. 1961. Stochastic models for carcinogenesis. Pp. 19–38 in J. Newman, ed.Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability,Vol-ume 4. University of California Press, Berkeley.Google Scholar
  7. Berkson, J. 1944. Application of the logistic function to bioassay. J.Am. Stat. Assoc. 39:134–167.Google Scholar
  8. Bliss, C. I. 1934. The method of probits.Science79:38–39.CrossRefGoogle Scholar
  9. Bliss, C. I. 1935. The calculation of the dosage-mortality curve.Annu. Appl. Biol. 22:134–167.CrossRefGoogle Scholar
  10. Brown, C. 1976. Mathematical aspects of dose-response studies in carcinogenesis-The concept of thresholds.Oncology33:62–65.CrossRefGoogle Scholar
  11. Brown, C. 1978a. Statistical aspects of extrapolation of dichotomous dose response data.J. Natl. Can cer Inst. 60:101–108.Google Scholar
  12. Brown, C. C. 1978b. Variability of risk extrapolation in dose-response experiments [Abstract].Envi ron. Health Perspect. 22:183–184.Google Scholar
  13. Brown, C., T. R. Fears, M. H. Gail, M. Schneiderman, R. E. Tarone, and N. Mantel. 1978. Letter to the editor. Reply by J. Cornfield.Science202:1105–1108.Google Scholar
  14. Burch, P. R. J. 1960. Radiation carcinogenesis: A new hypothesis.Nature185:135–142.CrossRefGoogle Scholar
  15. Busvine, J. R. 1938. The toxicity of ethylene oxide toCandra oryzae c. granaria, Tribolium casta neum,andClimex lectularis. Ann. Appl. Biol. 25:605–632.CrossRefGoogle Scholar
  16. Cairns, T. 1980. The ED01 study: Introduction, objectives, and experimental design.J. Environ. Pathol. Toxicol. 3:1–8.Google Scholar
  17. Chand, N., and D. Hoel. 1974. A comparison of models for determining safe levels of environmental agents. Pp. 681–700 in F. Proschan and R. J. Serfling, eds.Reliability and Biometry. Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
  18. Cornfield, J. 1977. Carcinogenic risk assessment.Science198:693–699.CrossRefGoogle Scholar
  19. Crump, K. S. 1977. Low dose extrapolation utilizing the age distribution of cancer. Presented at Joint Statistical Meeting, Chicago, Illinois, August 15–18.Biometrics34:155.Google Scholar
  20. Crump, K. S. 1979. Dose response problems in carcinogenesis.Biometrics35:157–167.CrossRefGoogle Scholar
  21. Crump, K. S., D. Hoel, C. Langley, and R. Peto. 1976. Fundamental carcinogenic processes and their implications for low dose risk assessment.Cancer36:2973–2979.Google Scholar
  22. Day, N. E., and C. C. Brown. 1980. Multistage models and primary prevention of cancer.J. Natl. Cancer Inst. 64:977–989.Google Scholar
  23. Doll, R. 1971. The age distribution of cancer. Implications for models of carcinogenesis.J. R. Stat. Soc. 134:133–155.CrossRefGoogle Scholar
  24. Doll, R., and R. Peto. 1978. Cigarette smoking and bronchial carcinoma: Dose and time relationships among regular smokers and lifelong non-smokers.J. Epidemiol. Commun. Health32:303–313.CrossRefGoogle Scholar
  25. Druckrey, H. 1967. Quantitative aspects of chemical carcinogens. Pp. 60–78 inPotential Carcinogen Hazards from Drugs,U.I.C.C. Monograph series, Volume 7. Springer-Verlag, New York.Google Scholar
  26. Falk, H. L. 1978. Biologic evidence for the existence of thresholds in chemical carcinogenesis.Environ. Health Perspect. 22:167–170.Google Scholar
  27. Farmer, J. H., R. L. Kodell, D. L. Greenman, and G. W. Shaw. 1980. Dose and time response models for the incidence of bladder and liver neoplasms in mice fed 2-acetylaminofluorene continuously. J.Environ. Pathol. Toxicol. 3:55–68.Google Scholar
  28. Finney, D. J. 1949. The choice of a response metameter in bio-assay.Biometrics5:261–272.CrossRefGoogle Scholar
  29. Finney, D. J. 1952.Statistical Methods in Biological Assay. Griffin &Co., London. 661 Pp.Google Scholar
  30. Finney, D. J. 1971.Probit Analysis,3rd ed. Cambridge University Press, London. 333 Pp.Google Scholar
  31. Fisher, J. C., and J. H. Holloman. 1951. A new hypothesis for the origin of cancer foci.Cancer4:916–918.CrossRefGoogle Scholar
  32. Food and Drug Administration Advisory Committee on Protocols for Safety Evaluation. 1971. Panel on carcinogenesis report on cancer testing in the safety evaluation of food additives and pesticides.Toxicol. Appl. Pharmacol. 20:419–438.CrossRefGoogle Scholar
  33. Freese, E. 1973. Threshold in toxic, teratogenic, mutagenic and carcinogenic effects.Environ. Health Perspect. Experimental Issue6:171 -178.Google Scholar
  34. Gaddum, J. H. 1933.Reports on Biological StandardsIII.Methods of Biological Assay Depending on a Quantal Response. Special Report Series 183. Medical Research Council, London.Google Scholar
  35. Gaylor, D. W., and R. L. Kodell. 1980. Linear interpolation algorithm for low dose risk assessment of toxic substances. J.Environ. Pathol. Toxicol. 4:305–312.Google Scholar
  36. Gahring, P. J., and G. E. Blau. 1977. Mechanisms of carcinogenesis: Dose response. J.Environ. Pathol. Toxicol. 1:163–179.Google Scholar
  37. Gehring, P. J., P. G. Watanabe, and J. D. Young. 1977. The relevance of dose dependent pharmacokinetics in the assessment of carcinogenic hazard of chemicals. Pp. 187–203 in H. H. Hiatt, J. D. Watson, and J. A. Winston, eds.Origins of Human Cancer,Book A:Incidence of Cancer in Humans. Cold Spring Harbor Laboratory, Cold Spring Harbor ,New York.Google Scholar
  38. Gehring, P. J., P. G. Watanabe, and C. N. Park. 1978. Resolution of dose response toxicity data for chemicals requiring metabolic activation: Example-vinyl chloride.Toxicol. Appl. Pharmacol. 44:581–591.CrossRefGoogle Scholar
  39. Gillette, J. R. 1976. Application of pharmacokinetic principles in the extrapolation of animal data to humans.Clin. Toxicol. 9:709–722.CrossRefGoogle Scholar
  40. Guess, H. A., and K. S. Crump. 1976. Low dose extrapolation of data from animal carcinogenicity experiments-Analysis of a new statistical technique.Math. Biosci. 32:15–36.CrossRefGoogle Scholar
  41. Guess, H. A., and K. S. Crump. 1978. Best-estimate low-dose extrapolation of carcinogenicity data.Environ. Health Perspect. 22:149–152.CrossRefGoogle Scholar
  42. Guess, H. A., and D. G. Hoel. 1977. The effect of dose on cancer latency period. J.Environ. Pathol. Toxicol. 1:279–286.Google Scholar
  43. Hartley, H. O., and R. L. Sielken. 1977. Estimation of “safe doses” in carcinogenic experiments.Bio metrics33:1 -30.Google Scholar
  44. Hoel, D. G. 1980. Incorporation of background response in dose-response models.Fed. Proc. 39:67–69.Google Scholar
  45. Hoel, D. G., D. Gaylor, R. Kirschstein, U. Saffiotti, and M. Schneiderman. 1975. Estimation of risks of irreversible delayed toxicity.J. Toxicol. Environ. Health1:133–151.CrossRefGoogle Scholar
  46. Hoel, D. G., N. L. Kaplan ,and M. W. Anderson. 1983. The implication of nonlinear kinetics on risk estimation in carcinogenesis.Science219:1032–1037.CrossRefGoogle Scholar
  47. Jones ,H. B., and A. Grendon. 1975. Environmental factors in the origin of cancer and estimation of the possible hazard to man.Food Cos met. Toxicol. 13:251–268.CrossRefGoogle Scholar
  48. Krewski ,D., and J. Van Ryzin. 1981. Dose response models for quantal response toxicity data. Pp. 201–231 in M. Csorgo ,D. Dawson ,J. N. K. Rao ,and E. Saleh ,eds.Current Topics in Probability and Statistics. Elsevier/North-Holland ,New York.Google Scholar
  49. Lepkowski ,W. 1978. Extrapolation of carcinogenesis data.Environ. Health Perspect. 22:173–181.CrossRefGoogle Scholar
  50. Mantel ,N. 1963. The concept of threshold in carcinogenesis.Clin. Pharmacol. Ther. 4:104–109.Google Scholar
  51. Mantel ,N. 1978. Letter to the editor and reply by K. S. Crump.Cancer38:1835–1838.Google Scholar
  52. Mantel ,N., and W. Bryan. 1961. “Safety” testing of carcinogenic agents. J.Natl. Cancer Inst. 27:455–470.Google Scholar
  53. Mantel ,N., W. Heston ,and J. Gurian. 1961. Thresholds in linear dose-response models for carcinogenesis. J.Natl. Cancer Inst. 27:203–215.Google Scholar
  54. Mantel ,N., N. Bohidar ,C. Brown ,J. Ciminera ,and J. Tukey. 1975. An improved Mantel-Bryan procedure for ’safety’ testing of carcinogens.Cancer Res. 35:865–872.Google Scholar
  55. Marshall, J. H., and P. G. Groer. 1977. A theory of the induction of bone cancer by alpha radiation.Radiat. Res. 71:149–192.CrossRefGoogle Scholar
  56. National Research Council. 1980a.The Effects on Populations of Exposure to Low Levels of Ionizing Radiation. A report of the Committee on the Biological Effects of Ionizing Radiation. National Academy of Sciences ,Washington ,D.C.Google Scholar
  57. National Research Council. 1980b.Drinking Water and Health,Volume 3. A report of the Safe Drinking Water Committee. National Academy of Sciences ,Washington ,D.C.Google Scholar
  58. Nordling ,C. O. 1953. A new theory on the cancer industry mechanism.Br. J. Cancer7:68–72.CrossRefGoogle Scholar
  59. Peto, R., P. Lee, and W. Paige. 1972. Statistical analysis of the bioassay of continuous carcinogens.Br. J. Cancer26:258–261.CrossRefGoogle Scholar
  60. Peto, R., M. C. Pike, N. E. Day, R. G. Gray, P. N. Lee, S. Parish, J. Peto, S. Richards, and J. Wah-rendorf. 1980. Guidelines for simple, sensitive significance tests for carcinogenic effects in long-term animal experiments. Pp. 311–425 inLong-Term and Short-Term Screening Assays for Car cinogens: A Critical Appraisal. IARC Monographs on the Evaluation of the Carcinogenic Risk of Chemicals to Humans, Annex to Supplement 2. International Agency for Research on Cancer, Lyon.Google Scholar
  61. Pike, M. C., M. D. Krailo, B. E. Henderson, J. T. Casagrande, and D. G. Hoel. 1983. ’Hormonal’ risk factors, ’breast tissue age,’ and the age-incidence of breast cancer.Nature303:767–770.CrossRefGoogle Scholar
  62. Rai, K., and J. Van Ryzin. 1979. Risk assessment of toxic environmental substances using a generalized multi-hit dose response model. Pp. 99–117 in N. Breslow and A. Whittemore, eds.Energy and Health. Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
  63. Rai, K., and J. Van Ryzin. 1981. A generalized multi-hit dose-response model for low-dose extrapolation.Biometrics37:341–352.CrossRefGoogle Scholar
  64. Rall, D. P. 1978. Thresholds.Environ. Health Perspect. 22:163–165.CrossRefGoogle Scholar
  65. Riggs, D. S. 1963.The Mathematical Approach to Physiological Problems. MIT Press, Cambridge, Massachusetts.Google Scholar
  66. Schneiderman, M. A. 1974. Safe dose? Problems of the statistician in the world of trans-science.J. Wash. Acad. Sci. 64:68–78.Google Scholar
  67. Schneiderman, M. A., N. Mantel, and C. C. Brown. 1975. From mouse to man-or how to get from the laboratory to Park Avenue and 59th Street.Ann. N. Y. Acad. Sci. 246:237–246.CrossRefGoogle Scholar
  68. Schneiderman, M. A., P. Decoufle, and C. C. Brown. 1979. Thresholds for environmental cancer: Biologic and statistical considerations.Ann. N. Y. Acad. Sci. 329:92–130.CrossRefGoogle Scholar
  69. Scientific Committee, Food Safety Council. 1978. Proposed system for food safety assessment.Food C osmet. Toxicol. 16(Suppl. 2): 1–136.Google Scholar
  70. Scientific Committee, Food Safety Council. 1980. Quantitative risk assessment. Pp. 137–160 inPro posed System for Food Safety Assessment. Food Safety Council, Washington, D.C.Google Scholar
  71. Tomatis, L., V. Turusov, N. Day, and R. T. Charles. 1972. The effects of long term exposure to DDT on CF-1 mice.Int. J. Cancer10:489–506.CrossRefGoogle Scholar
  72. Turner, M. 1975. Some classes of hit theory models.Math. Biosci. 23:219–235.CrossRefGoogle Scholar
  73. Van Ryzin, J. 1980. Quantitative risk assessment.J. Occup. Med. 22:321–326.CrossRefGoogle Scholar
  74. White, J. 1972. Studies of the mechanism of induction of pulmonary adenomas in mice. Pp. 287–307 in L. E. Lecam, J. Neyman, and E. L. Scott, eds.Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability,Volume 4. University of California Press, Berkeley.Google Scholar
  75. Whittemore, A. S. 1977. The age distribution of human cancers for carcinogenic exposures of varying intensity.Am. J. Epidemiol. 106:418–432.Google Scholar
  76. Whittemore, A. S., and J. B. Keller. 1978. Quantitative theories of carcinogenesis.Soc. Ind. Appl. Math. Rev. 20:1–30.Google Scholar
  77. Worcester, J., and E. B. Wilson. 1943. The determination of LD50 and its sampling error in bioassay.Proc. Natl. Acad. Sci. USA29:79–85.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Charles C. Brown
    • 1
  1. 1.National Cancer InstituteNational Institutes of HealthBethesdaUSA

Personalised recommendations