- ArmitageP. and DollR. (1961). Stochastic models for carcinogenesis. Fourth Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, pp. 19–38.
- ArmitageP. and DollR. (1975). A two-stage theory of carcinogenesis in relation to the age distribution of human cancer. British Journal of Cancer, 11,161–169.
- BrownC.C. (1976). Mathematical aspects of dose-response studies in carcinogenesis - the concept of thresholds. Oncology, 33, 62–65.
- CairnsT. (1979). The ED01 study: introduction, objectives, and experimental design. Journal of Environmental Pathology and Toxicology, 3,1–8.
- CasarettA.P. (1968). Radiation Biology. Prentice Hall, Inc., Englewood CliffsNew Jersey.
- CarlborgF.W. (1981a). Dose-response functions in carcinogenesis and the Weibull model. Food and Cosmetics Toxicology, 19,255–263.
- CarlborgF.W. (1981b). 2-Acetylaminofluorene and the Weibull model. Food and Cosmetics Toxicology, 19, 367–371.
- ChuK.C., CiprianoC.Jr. and WardJ.M. (1981). Factors in the evaluation of 200 National Cancer Institute carcinogen bioassays. Journal of Toxicology and Environmental Health, 8, 251–280.
- CieckaJ., FabianR. and MerilattD. (1979). A statistical model for small lake water quality management. Water Resources Bulletin, 15, 1318–1330.
- CookP.J., DollR. and FellinghamS.A. (1969). A mathematical model for the age distribution of cancer in man. International Journal of Cancer, 4, 93–112.
- CornfieldJ., RaiK. and Van RyzinJ. (1980). Procedures for assessing risk at low levels of exposure. Quantitative Aspects of Risk Assessment in Chemical Carcinogenesis. Archives of Toxicology Supplement, 3,295–303.
- CrouchE. and WilsonR. (1979). Interspecies comparison of carcinogenic potency. Journal of Toxicology and Environmental Health, 5, 1095–1118.
- CrowtherJ.A. (1924). Some considerations relative to the action of X-rays on tissue cells. Prodeedings of the Royal Society (London) Series B, 96,207–211.
- CrumpK.S., HoelD.G., LangleyC.H. and PetoR. (1976). Fundamental carcinogenic processes and their implications for low dose risk assessment. Cancer Research, 36,2973–2979.
- CrumpK.S. (1977). Theoretical problems in the modified Mantel-Bryan procedure. Biometrics, 33, 752–755.
- CrumpK.S., GuessH.A. and DealK.H. (1977). Confidence intervals and tests of hypothesis concerning dose response relations inferred from animal carcinogenicity data. Biometrics, 33,437–451.
- CrumpK.S. (1979). Dose response problems in carcinogenesis. Biometrics, 35,157–167.
- DorvloA., EnsleinS.K. and SalsburgD. (1980). A test of the hypothesis that time-to-tumor in humans fits the “one-hit” model. Journal of Environmental Pathology and Toxicology, 4, 139–143.
- DruckreyH. (1967). Quantitative aspects of chemical carcinogenisis. Potential Carcinogenis Hazards from Drugs (Evaluation of Risks). UICC Monograph Series, Vol. 7, (TruhautR., ed.) Springer-Verig, New York, pp. 60–78.
- EyringH. and StoverB.J. (1970). The dynamics of life, II. The steady-state theory of mutation rates. Proceedings of the National Academy of Sciences, 66, 441–444.
- FarmerJ.H., KodellR.L., GreenmanD.L. and ShawG.W. (1980). Dose and time response models for the incidence of bladder and liver neoplasms in mice fed 2-acetylaminofluorene continuously. Journal of Environmental Pathology and Toxicology, 3, 55–68.
- FishbeinL. (1979). Potential Industrial Carcinogens and Mutagens. Elsevier Scientific Publishing Company, New York, pp. 42–78.
- GaylorD.W. (1980). The ED01 study: summary and conclusions. Journal of Environmental Pathology and Toxicology, 3, 179–186.
- GrahamS.L., DavisK.J., HansenW.H. and GrahamC.H. (1975). Effects of Prolonged ethylene thiourea ingestion on the thyroid of the rat. Food and Cosmetics Toxicology, 13, 493–499.
- GuessH. and CrumpK. (1976a). Carcinogenicity experiments - analysis of a new statistical technique. Mathematical Biosciences, 32, 15–36.
- GuessH.A. and CrumpK.S. (1976b). Can we use animal data to estimate “safe” doses for chemical carcinogens?. Environmental Health: Quantitative Methods (WhittemoreA., ed.), Society for Industrial and Applied Mathematics, PhiladelphiaPennsylvania, pp. 13–30.
- HarrisR., PageH.T. and ReichesN.A. (1977). Carcinogenesis hazard of organic chemicals in drinking water. Origins of Human Cancer (HiattH. H., ed.) Cold Spring Harbor Laboratory, Cold Spring HarborNew York. pp. 309–330.
- HartleyH.O. TolleyH.D. and SielkenR.L.Jr. (1981). One product form of the hazard rate in carcinogenic testing. Statistics and Related Topics (CsorgoM., DawsonD., RaoJ.N.K. and SalehE., eds.) North Holland, New York, pp. 185–200.
- HasemanJ. K., HoelD.G. and JennrichR.I. (1981). Some practical problems arising from the use of the gamma multihit model for risk estimation. Journal of Toxicology and Environmental Health, 8, 379–386.
- JanardanK.G. and SchaefferD.J. (1977). Models for the analysis of chromosomal aberrations in human leukocytes. Biometrical Journal, 19,599–612.
- JanardanK.G., KersterH.W. and SchaefferD.J. (1979). Biological applications of the Lagrangian Poisson distribution. BioScience, 29, 599–602.
- KellererA.M. and RossiH.H. (1972). The theory of dual radiation action. Current Topics in Radiation Research, 8:85–158.
- KrewskiD. and Van RyzinJ. (1981). Dose response models for quantal response data. Statistics and Related Topics (CsorgoM., DawsonD. A., RaoJ.N.K. and SalehE., eds.) North Holland, New York, pp. 201–231.
- LeaD.E. (1955). Actions of Radiations on Living Cells (Second Edition). Cambridge University Press, CambridgeEngland.
- LeeP.N. and O'NeillJ.A. (1971). The effect of both time and dose applied on tumor incidence rate in benzopyrene skin painting experiments. British Journal of Cancers, 25, 759–770.
- LeeW.R. (1978). Dosimetry of chemical mutagens on eukaryote cells. Chemical Mutagens, V. 5 (HollaenderA. and DeSerresF.J., eds.), Plenum Press, New York, pp. 177–202.
- MantelN., BohidarN.R., BrownC.C., CimineraJ.L., and TukeyJ.W. (1975). An improved Mantel-Bryan procedure for “safety” testing of carcinogens. Cancer Research, 35,865–72.
- MantelN. and BryanW.R. (1961). “Safety” testing of carcinogenic agents. Journal National Cancer Institute, 27,455–70.
- National Council on Radiation Protection and Measurements (1980). Influence of Dose and Its Distribution in Time on Dose-Response Relationships for Low LET Radiations. WashingtonD. C.
- NormanA. and SasakiM.S. (1966). Chromosome exhange aberrations in human lymphocytes. International Journal of Radiation Biology, 11,321–8.
- OserB.L. (1981). The rat as a model for human toxicological evaluation. Journal of Toxicology and Environmental Health, 8,521–542.
- PetoR. and LeeP.N. (1973). Weibull distributions for continuous–carcinogenesis experiments. Biometrics, 29,457–70.
- PikeM.C. (1966). A method of analysis of a certain class of experiments in carcinogensis. Biometrics, 22, 142–61.
- PrenticeR.L. (1976). A generalization of the probit and logit methods for dose response curves. Biometrics, 32,761–768.
- RaabeO., BookS.A. and ParksN.J. (1980). Bone cancer from radium canine dose response explains data for mice and humans. Science, 208,61–64.
- RaiK. and Van RyzinJ. (1979). Risk assessment of toxic environmental substances using a generalized multi-hit dose response model. Energy and Health (BreslowN. E. and WhittemoreA. S. eds.), Society for Industrial and Applied Mathematics, PhiladelphiaPennsylvania, pp. 99–117.
- RaiK. and Van RyzinJ. (1981). A generalized multihit dose-response model for low-dose extrapolation. Biometrics, 37, 341–352.
- SchaefferD.J. and JanardanK.G. (1980). Threshold and dose response estimation using the “Filter Model”. Environment International, 6, 151–162.
- SchaefferD.J., JanardanK.G., and KersterH.W. (1980). Development and applications of an equilibrium dose response model. Environmental Mutagenesis, 2,314.
- SchaefferD.J., JanardanK.G., and KersterH.W. (1981). Threshold estimation from the linear dose-response model: Method and radiation data. Environmental Management, 5, 515–520.
- SchaefferD.J. (1981). Is “No-Threshold” a “Non-Concept”?. Environmental Management, 5, 475–481.
- SchaefferD.J., JanardanK.G., KersterH.W. and ClarkeA.C. (1982). Statistically estimated free energy. Biometrical Journal, in press.
- SchererE. and EmmelotP. (1979). Multihit kinetics of tumor cell formation and risk assessment of low doses of carcinogens. Carcinogens; Identification and Mechanisms of Action (GriffenA. C. and ShawC. R. eds.). Raven Press, New York, pp. 337–364.
- SchneidermanM.A., Decoufle'P., and BrownC.C. (1979). Thresholds for environmental cancer: biologic and statistical considerations. Public Control of Environmental Health Hazards. HammondE. C. and SelikoffI. J. (eds.). New York Academy of Sciences, New York, pp. 92–130.
- Scientific Committee of the Food Safety Council (1978). Proposed system for food safety assessment. Food and Cosmetics Toxicology Supplement 2, 16, 1–136.
- Society of Toxicology ED01, Task Force (1981). Re-examination of the ED01 study - risk assessment using time. Fundamental and Applied Toxicology, 1, 88–123.
- StaffaJ.A. and MehlmanM.A., (eds.) (1979). Innovations in cancer risk assessment (ED01 study). Pathotox Publishers, Park Forest SouthIllinois.
- StevensR.H., ColeD.A. and RandR.S. (1980). Radiation equivalency of 1,2-dimethylhydrazine in rats. Archives of Environmental Health, 35,69–74.
- TotterJ.R., and WeinbergA.M. (1977). Repair and dose-response at low doses. Report ORAU/IEA (0)-77-ll. Oak Ridge Associated Universities, Oak Ridge Tennessee.
- TurnerM.E.Jr. (1975). Some classes of hit-theory models. Mathematical Biosciences, 23, 219–235.
- USEPA 1980. Water quality criteria documents; availability. Federal Register, November 28, 1980 Part V, pp. 79318–79379.
- USEPA 1979. Water quality criteria. Federal Register, March 15, 1979, part V, pp. 15926–15980.
The Low Dose Extrapolation Problem: A Review and A New Model
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