Chem. Res. Toxicol. 2009, 22, 1493–1494
Response to the Waddell et al. Letter Received August 4, 2009
To the Editor: An important goal of our ultralow dose project (1) was to provide a unique cancer dose-response data set that the risk assessment community might find useful for modeling and future experimental inquiry. The commentary by Dr. Waddell and his colleagues is a welcome response that begins to meet our goal. However, their assertion that we, the authors, could have saved much time and effort in our analysis if we had recognized and simply applied the laws of nature causes us to carefully evaluate their claims. After doing so, we must disagree with their assessment of our data analysis, as follows. A Flawed Basic Premise. Dr. Waddell et al. argue that, “Dose must be plotted on a logarithmic scale with effect on a linear scale to conform to the laws of chemistry.” This argument is founded on their belief that chemical carcinogenesis, like any simple chemical reaction, can be properly described in terms of the Gibbs free energy change for reactions in equilibria,
∆G ) ∆G° - RT log Keq a relationship that would force a semilog plot of tumor dose-response data. We strongly disagree that a process as multifaceted as cancer can be so described. Although carcinogenesis certainly involves many biochemical reactions such as the metabolic activation of pro-genotoxins that can tend toward a measurable equilibrium, many other steps from exposure to development of cancer do not meet this test. Mutagenic loss of tumor suppressor gene function through large-scale deletion is but one such example. Dysregulation of tissue homeostasis through apoptotic imbalance, angiogenesis for growth to detectable tumors, and multiple chromosomal deletions and rearrangements are additional biological hallmarks of tumor progression that are not processes best described as equilibria. Apoptosis, like deletion of a gene, is unidirectional. In our opinion, Dr. Waddell et al.’s long-standing assertion that carcinogenesis data must be plotted as response versus log dose simply lacks a convincing foundation in basic cancer biology. Inadequate Graphical and Statistical Considerations for Model Assessment. Even if the Waddell et al. semilogarithmic analysis were accepted by some as a valid approach, significant procedural issues invalidate their conclusions. For each tissue (liver and stomach). Waddell et al.’s evidence for their threshold model consists of a graph of pooled and adjusted data with a fitted line and correlation coefficients. It is our contention that, although this graphic may be useful for some purpose, it is largely useless for visual assessment of the fit of their or other models due to serious data compression problems. Furthermore, the fact that the correlation coefficients are close to 1.0 cannot be used for assessment of the fit for two important reasons: (1) Simple linear regression is highly inappropriate for background-corrected proportions involving wide ranges of incidences and sample sizes, and (2) nothing in their analysis uses the observed variation between replicate quartiles as part of the assessment. Use of an analytic approach that ignores the within-group variation among the four quartiles at each dose and uses only between-group variation of the mean response values among (selected) exposure doses also underserves the richness of the study design and the resultant data setsby Dr. Waddell et al.’s approach, cancer data sets based on a single experiment using a few animals distributed over a range of doses
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are accorded the same statistical utility as studies performed in quadruplicate with many thousands of animals distributed over the same dose range. This fails the common sense test. The following expands on these points. Dr. Waddell et al. have previously recognized (2) that, “The low dose range is critical for the determination of a threshold and for extrapolating animal studies at high doses to doses which humans are ordinarily exposed.” It is ironic, therefore, that their Figures 1 and 2 draw conclusions regarding thresholds based largely on our high dose/high incidence data, while the animalrich data at lower doses are either discounted (both visually and analytically) or arbitrarily assigned a value of zero. As we and others have previously noted (see ref 1 and references therein), the visual discounting of low incidence data is in part due to the compression inherent in using a linear response scale when showing all of the doses. Dr. Waddell et al.’s use of a linear 0-100% incidence axis guarantees that all responses below a few percent will appear to be zero, even when they are not. The choice of horizontal scaling is also problematic for any visual model assessment. Waddell and colleagues have chosen to present figures displaying DPB exposures over 23 log units, even though the doses used to generate the tumor responses covered less than 3 log units. This choice generates a fitted higher dose line with a very steep slope and, consequently, a visual impression of good proximity of the largesized data symbols to their least-squares line. This is easily shown to be an artifact. Without changing the type of axis, but reducing the range, one can focus in on the actual doses used and responses observed to more reasonably assess the fit. For example, by reducing the range of the axes in Figure 2 to only include the three points modeled and adding the replicate quartile-corrected incidences to provide the variation at each dose, one finds that Waddell et al.’s fitted line is not even within the range of the four replicate responses for any of the doses and is proportionately quite far from that range for the data at 28.4 ppm. By comparison, the fitted curve for, say, an appropriately modeled logistic regression dose response [linear in log(dose)] visually fits much better to the same data and is well within the range of the four quartiles at all three doses. A formal goodness-of-fit F test1 agrees with the visual assessment in that the logistic model fits well (p > 0.3) while even the bestfitting linear model using appropriate weighting (so that it fits somewhat better than the Waddell et al. linear model) reveals strong evidence of lack of fit (p < 0.002). Note that the evidence against a Waddell et al. threshold model would become even greater if one included the data for the next dose down (10.1) rather than arbitrarily setting it to zero. In contrast, models such as the logistic model would continue to fit well when the fourth dose is added. Consequently, Dr. Waddell et al.’s assertion that “...a linear fit for incidence of tumors (indicating the presence of a threshold) is better than an exponential fit...” on his semilogarithmic scale is simply not useful because both of his models actually fit quite poorly while other standard models fit quite well. 1 This is an approximate test that uses the empirical variation in total incidence between replicate quartiles at each dose to account for possible overdispersion relative to binomial variation (the quasilikelihood approach in ref 4). To include the variation due to background estimation, the total incidences for the three highest doses and the zero dose were modeled as background plus a dose-response function (mean response linear in log of dose on either the incidence scale or the logit of incidence scale) using maximum likelihood within the Nlmixed procedure in SAS version 9.2.
10.1021/tx900269j CCC: $40.75 2009 American Chemical Society Published on Web 08/20/2009
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Chem. Res. Toxicol., Vol. 22, No. 9, 2009
Incorrect consideration of low incidence data also occurs in the analysis due to the inappropriate use of simple linear regression methods (including correlation coefficients) designed for data with equal variances, when in actuality the variances for our data strongly decrease with incidence on the background-corrected p scale used for the response in Waddell et al.’s modeling.2 The usual statistical standard of weighting inversely to the variance (3) gives increasingly larger weights to our lower dose data on that scale, whereas simple linear regression as is done by Waddell et al. gives too much weight to higher dose data. This problem is compounded by arbitrarily setting low dose data to zero so that they are not even used in the modeling. Indeed, for their Figure 2, Dr. Waddell et al. use curious circular reasoning to set the stomach tumor response at the 10.1 ppm dose at zero (“...the lowest four doses are considered as zero since the linear fit for the three highest doses gives the best fit”), when in fact at this dose the responses for all four quartiles are above zero. In our opinion, these analytical problems, coupled with failure to conduct any valid goodness-of-fit analyses for the models used, render the Waddell et al. analysis of our data set uninformative. We are not arguing that our data do not suggest a possible threshold response but that it is not legitimately assessed or proven by the Waddell et al. approach. We respectfully suggest that valid statistical and graphical procedures must be used in the model fitting and model assessment for cancer dose-response data and that a more convincing, biologically plausible case must be put forward if we are all to 2
This is based on the empirical variation in corrected incidences between replicate quartiles as well as the empirical variation in total incidences in Table 2 of the manuscript, which is generally consistent with being proportional to binomial variation (i.e., proportional to p × (1 - p)/n as discussed in refs 3 and 4).
accept that cancer dose-response data are best expressed in simple chemical thermodynamic terms.
References (1) Bailey, G. S., Reddy, A. P., Pereira, C. B., Harttig, U., Baird, W., Spitsbergen, J. M., Hendricks, J. D., Orner, G. A., Williams, D. E., and Swenberg, J. A. (2009) Nonlinear cancer response at ultra-low dose: A 40,800-animal ED001 tumor and biomarker study. Chem. Res. Toxicol. 22 (7), 1264–1276. (2) Waddell, W. J. (2006) Critique of dose response in carcinogenesis. Hum. Exp. Toxicol. 25, 413–436. (3) Collett, D. (2003) Modeling Binary Data, 2nd ed., pp 53-56, Chapman and Hall/CRC: Boca Raton, FL. (4) Ramsey, F., and Schafer, D. (2002) The Statistical Sleuth: A Course in Methods of Data Analysis, 2nd ed., Chapters 20 and 21, Duxbury Press, Pacific Grove, CA.
George S. Bailey,* Distinguished Professor Emeritus Linus Pauling Institute Oregon State University Gayle A. Orner, Assistant Professor Senior Research Linus Pauling Institute Oregon State University Clifford B. Pereira, Research Associate Department of Statistics Oregon State University James A. Swenberg, Distinguished Professor of Environmental Sciences University of North Carolina at Chapel Hill TX900269J
