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What is a Practical Threshold?RIVM, Bilthoven, Netherlands The recently published article by Wanibuchi et al. (2006) is another attempt to find experimental evidence for the existence of a dose-threshold in the dose-response for a genotoxic carcinogen, in this case 2-amino-3,8-dimethylimidazol[4,5-f ]quinoxaline (MeIQx). I will use the same data to illustrate that such is actually impossible in general. At the same time, this example illustrates some of the benefits of dose-response modeling (the Benchmark Dose, or BMD approach) compared to pairwise statistical testing (the NOAEL approach). Wanibuchi and coworkers performed a study, in which rats were fed diets containing MeIQx concentrations ranging from 0.001 to 100 ppm, with 10 fold dose spacing, in addition to a control group. Each dose group consisted of 40 animals, half of which concurrently received 10% ethanol in the drinking water. Three potential effects were considered: induction of GST-P-positive foci in the liver, hepatocyte proliferation (PCNA labeling indices) and formation of (8-OHdG) adducts in hepatocyte DNA. For the foci, numerical results were reported (for the other two, graphical results only), and the present discussion will focus on this endpoint. For this endpoint the reported numerical results allow for a dose-response analysis: a model was fitted to these observations, as shown in Figure 1. Note that in this dose-response analysis the co-administration of ethanol was taken into account, resulting in two curves (visible only at the higher doses; to be further discussed below). Wanibuchi et al. conclude from these data that 1 ppm would constitute a "practical" threshold, based on the fact that this and all lower doses do not significantly differ from the controls. Indeed, Figure 1 strongly suggests the existence of a threshold: effects can be seen only at doses above (or equal to) 10 ppm (denoted as 1 in the plot, due to the log10-scale). So, it seems obvious that Wanibuchi’s conclusion of a "practical" threshold at around 1 ppm (denoted as 0 in the plot) is correct.
However, consider Figure 2, which represents exactly the same data (and the same fitted curves), but now dose is plotted as such, and not on log-scale as in Figure 1. The threshold has completely vanished. In fact, the shape of the dose-response curve(s) is nearly linear (slightly "sublinear"). Yet another possibility to plot these data is by having the number of foci on log-scale. It might be argued that this would be a more appropriate scale for interpreting the data, since changes in biological parameters are normally appraised in a relative way (e.g. a 10% decrease in body weights in rats would be considered similar to a 10% decrease in body weights in mice). The result is shown in Figure 3. In this plot the shape of the dose-response is strongly "supralinear."
Finally, Figure 4 shows the same data plotted on double log-scale. This is actually the best way to present the data, as well as the two dose-response models fitted to the data. It is now visible that the data do not exclude the possibility that there is a steady increase in the number of foci with dose—without any threshold. Further, the dose-response analysis showed that the (overall) response in the animals with co-administration of ethanol was significantly higher than the response without the co-administration. This implies that ethanol has an effect at all doses, including at zero dose of MeIQx. Further, the dose-response analysis showed that the slope of the dose-response significantly depended on ethanol co-administration (the slope being somewhat larger in the non-ethanol subpopulation).
The main lesson from this analysis is that there is no evidence whatsoever for a dose-threshold. A non-threshold dose-response curve is perfectly in agreement with the data. According to this fitted model there would be a more than 2 fold increase in the number of foci at the earlier assessed "practical" threshold. It is hard to defend the position that a 2 fold increase in the number of preneoplastic lesions cannot possibly result in an increased cancer risk. On the other hand, this analysis does not "prove" that a threshold does not exist; it rather shows that it is just impossible to assess if a dose-threshold exists from observed dose-response data. But even if it could be "proven" or made highly plausible, based on biological (mechanistic) arguments, that a threshold must exist, we will not be able to estimate it from any dose-response data that one may think of. Therefore, the concept of a dose-threshold is totally impractical. The only practical thing to do is to appoint a particular nonzero effect size, one that may be small, but still large enough to be within the range of observation. This effect size is usually called a Benchmark Response (BMR), and the associated dose is the Benchmark Dose (BMD). For this dose we can say that the associated size of the effect is (most likely) smaller than the specified effect size. It must be concluded that the concept of a dose-threshold as a dose below which the effect is assumed to be zero is impractical by definition: zero effects simply cannot be measured. Ignoring this simple fact may lead to human exposure limits allegedly without any risk at all, while in reality the risk might be quite large. Acknowledging this simple fact leads to the only practical (i.e., measurable) threshold that can be defined: the BMD, i.e. a dose where the effect is below some (nonzero) effect size.
Toxicologic Pathology, Vol. 35, No. 6,
848-849 (2007)
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