Abstract
Maximum likelihood procedures for fitting the probit, logit, Weibull and gamma multi-hit dose response models with independent, additive or mixed independent/additive background to quantal assay toxicity data are reviewed. In addition to parameter estimation, the use of the above models for low dose extrapolation is indicated with both point estimates and lower confidence limits on the “safe” dose discussed. A computer program implementing these procedures is described and two sets of toxicity data are analyzed to illustrate its use.
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References
Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. (1975). Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, Mass.
Crump, K.S., Hoel, D.G., Langley, C.H. & Peto, R. (1976). Fundamental carcinogenic processes and their implications for low dose risk assessment. Cancer Research 36,2973–2979.
Crump, K.S. (1979). Dose response problems in carcinogenesis. Biometrics 35, 157–167.
Fletcher, R. and Powell, M.J.D. (1963). A rapidly convergent descent method for minimization. Computer Journal 6, 163–168.
Food Safety Council (1980). Proposed system for Food Safety Assessment. Food Safety Council, Washington, D.C.
Gaylor, D.W. & Kodell, R.L. (1980). Linear interpolation algorithm for low dose risk assessment of toxic substances. Journal of Toxicology and Environmental Health (to appear).
Guess, H.A. & Crump, K.S. (1976). Low dose extrapolation of data from animal carcinogenicity experiments - analysis of a new statistical technique. Mathematical Bioscience 32, l5–36.
Guess, H.A. & Crump, K.S. (1978). Maximum-likelihood estimation of dose-response functions subject to absolutely monotonic constraints. Annals of Statistics 6, 101–111.
Hoel, D.G. (1980). Incorporation of background in dose-response models. Federation Proceedings 39, 73–75.
Hartley, H.O. & Sielken, R.L. (1977). Estimation of “safe doses” in carcinogenic experiments. Biometrics 33, 1–30.
Interagency Regulatory Liaison Group. (1979). Scientific bases for identification of potential carcinogens and estimation of risks. Journal of the National Cancer Inst. 64, 241–268.
Krewski, D., & J. Van Ryzin. (1981). Dose response models for quantal response toxicity data. In Current Topics in Probability and Statistics, Csorgo, M., D. Dawson, J.N.K. Rao, and E. Saleh (eds.), North-Holland, New York. (in press).
Rai, K. & Van Ryzin, J. (1979). Risk assessment of toxic environmental substances based on a generalized multi-hit model. In Energy and Health. N. Breslow & A. Whittemore (eds.), SIAM, Philadelphia, 99–117.
Rai, K. & Van Ryzin, J. (1981). A generalized multi-hit dose response model for low-dose extrapolation. Biometrics (to appear).
U.S. Environmental Protection Agency (1980). Water quality criteria documents: availability. Federal Register 45, 79318- 79319.
Van Ryzin, J. (1980). Quantitative risk assessment. Journal of Occupational Medicine 22, 321–326.
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© 1981 Springer-Verlag New York Inc.
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Kovar, J., Krewski, D. (1981). Statistical Procedures for Low Dose Extrapolation of Quantal Response Toxicity Data. In: Eddy, W.F. (eds) Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9464-8_61
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DOI: https://doi.org/10.1007/978-1-4613-9464-8_61
Publisher Name: Springer, New York, NY
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