Summary
The dose-response model concerns to establish a relationship between a dose and the magnitude of the response produced by the dose. A common complication in the dose-response model for jejunal crypts cell surviving data is overdispersion, where the observed variation exceeds that predicted from the binomial distribution. In this study, two different methods for analyzing jejunal crypts cell survival after regimens of several fractions are contrasted and compared. One method is the logistic regression approach, where the numbers of surviving crypts are predicted by the logistic function of a single dose of radiation. The other one is the transform-both-sides approach, where the arcsine transformation family is applied based on the first-order variance-stabilizing transformation. This family includes the square root, arcsine, and hyperbolic arcsine transformations, which have been used for Poisson, binomial, and negative binomial count data, as special cases. These approaches are applied to a data set from radiobiology. Simulation study indicates that the arcsine transformation family is more efficient than the logistic regression when there exists moderate overdispersion.
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References
Anscombe, F. J. The transformation of Poisson, binomial and negative binomial data. Biometrika 35:246–254; 1948.
Box, G. E. P.; Cox, D. R. An analysis of transformations. J. R. Stat. Soc. B 26:211–246; 1964.
Breslow, N. E. Extra-Poisson variation in log-linear models. Appl. Stat. 33:38–44; 1984.
Carroll, R. J.; Ruppert, D. Power transformations when fitting theoretical models to data. J. Am. Stat. Assoc. 79:321–328; 1984.
Carroll, R. J.; Ruppert, D.: Transformation and weighting in regression. New York: Chapman and Hall; 1988.
Cox, D. R. Some remarks on overdispersion. Biometrika 70:269–274; 1983.
Govindarajulu, Z. Statistical techniques in bioassay. New York: Karger; 2001.
Haseman, J. K.; Kupper, L. L. Analysis of dichotomous response data from certain toxicological experiments. Biometrics 35:281–293; 1979.
Johnson, N. L.; Kotz, S. Discrete distributions. New York: John Wiley and Sons; 1969.
Kim, D. K. Estimating doubling time of cells in vitro. In Vitro Cell. Dev. Biol. 31A:419–420; 1995.
Kim, D. K. Statistical methods for estimating doubling time in in vitro cell growth. In Vitro Cell. Dev. Biol. 33:289–293; 1997.
Kim, D. K.; Taylor, J. M. G. Transform-both-sides approach for overdispersed binomial data when N is unobserved. J. Am. Stat. Assoc. 89:833–845; 1994.
McCullagh, P.; Nelder, J. A. Generalized linear models, 2nd ed. New York: Chapman and Hall; 1989.
Williams, D. A. Extra-binomial variation in logistic linear models. Appl. Stat. 31:144–148; 1982.
Withers, H. R.; Mason, K. A.; Taylor, J. M. G.; Kim, D. K.; Smathers, J. R. Dose-survival causes, Alpha/Beta ratios, RBE values and equal effect per fraction for neutron irradiation of jejunal crypts cells. Radiat. Res. 134:295–300; 1993.
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Kim, D.K. Regression models for overdispersed jejunal surviving crypts data. In Vitro Cell.Dev.Biol.-Animal 38, 242–245 (2002). https://doi.org/10.1290/1071-2690(2002)038<0242:RMFOJS>2.0.CO;2
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DOI: https://doi.org/10.1290/1071-2690(2002)038<0242:RMFOJS>2.0.CO;2