Toxicological Sciences 75, 223 (2003)
Copyright © 2003 by the Society of Toxicology
Letter
Department of Toxicology, University of Wuerzburg, 9 Versbacher St., D-97078 Wuerzburg, Germany, Phone: +49 931 201 48402, Fax: +49 931 201 48446, E-mail: lutz{at}toxi.uni-wuerzburg.de
To the Editor:
I agree with Crump and Clewell (2003)
that Waddell’s representation of the tumor incidence data of the ED01 study is strongly misleading (Waddell, 2003b). The logarithmic transformation of the dose axis makes it impossible to include the control group (dose 0) in the figures because log 0 is undefined. This is a major shortcoming because any discussion of dose-response relationships and extrapolation in chemical carcinogenesis should include the background process that may result in spontaneous tumor incidence. Waddell "avoids" this problem by subtracting the control tumor incidence and plotting net increases only. An example taken from Table 1 of Waddell (2003b) illustrates the consequences: The spontaneous tumor incidence in the liver at the 33-month time point is 34.8 percent. Feeding 30 ppm 2-acetylaminofluorene (AAF) resulted in an increase by 13 percent; 60 ppm gave an increase by 28.8 percent above control. This indicates proportionality between exposure concentration and induced tumor incidence, and nobody would think about a threshold. Figure 9, which shows the same data after background subtraction and logarithmic transformation of the dose axis, gives a completely different impression. A threshold is implied because the dose axis is stretched by 19 orders of magnitude to one molecule, and because the incidence axis only shows net increases in tumor incidence. That is, the linear dose response for the chemically induced tumors breaks at the dose axis. Note also that the incidence axis is falsely described as "Percent of Animals with Tumors," concealing that the very important data point at dose 0 with its spontaneous tumor incidence cannot be shown in this type of representation.
Waddell’s strong statement in the reply to Crump and Clewell that "a log-linear plot ... is the only plot that is consistent with fundamental principles of chemistry" is definitely beyond my understanding (Waddell, 2003a, p. 486). Taking enzyme kinetics as an example, the substrate dependence of a reaction rate is approximately proportional to the substrate concentration for concentrations that are much lower than the Michaelis-Menten constant, i.e., indicate a linear relationship at concentrations close to zero. Only upon stretching low dose to the infinite by log-transformation of the concentration axis does a sigmoidal shape appear, which is often erroneously interpreted as being indicative of a threshold.
I am not only concerned about obvious misconceptions, but also about the fact that such strongly misleading representations of dose-tumor incidence relationships passed the review process of Toxicological Sciences twice (Waddell, 2002; Waddell, 2003b). I have shown with my publications that I am open to discuss many types of shapes of dose-response curves, including non-monotonic behavior (Lutz, 1998) and practical thresholds (Lutz et al., 2002). I am afraid that the analyses of Waddell are counterproductive to an unbiased discussion of such an important issue in toxicology.
REFERENCES
Crump, K. S. and Clewell, H. J. (2003). Letter to the Editor. Toxicol. Sci. 74, 485.
Lutz, W. K. (1998). Dose-response relationships in chemical carcinogenesis: Superposition of different mechanisms of action, resulting in linear-sublinear curves, practical thresholds, J-shapes. Mutat. Res. 405, 117–124.[Web of Science][Medline]
Lutz, R. W., Stahel, W. A., and Lutz, W. K. (2002). Statistical procedures to test for linearity and estimate threshold doses for tumor induction with nonlinear dose response relationships in bioassays for carcinogenicity. Regul. Toxicol. Pharmacol. 36, 331–337.[CrossRef][Web of Science][Medline]
Waddell, W. J. (2003a). Reply. Toxicol. Sci. 74, 485–486.
Waddell, W. J. (2002). Thresholds of carcinogenicity of flavors. Toxicol. Sci. 68, 275–279.
Waddell, W. J. (2003b). Thresholds of carcinogenicity in the ED01 study. Toxicol. Sci. 72, 158–163.
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