Bogen's Critique of Linear‐No‐Threshold Default Assumptions

Abstract

In an article recently published in this journal, Bogen concluded that an NRC committee's recommendations that default linear, nonthreshold (LNT) assumptions be applied to dose- response assessment for noncarcinogens and nonlinear mode of action carcinogens are not justified. Bogen criticized two arguments used by the committee for LNT: when any new dose adds to a background dose that explains background levels of risk (additivity to background or AB), or when there is substantial interindividual heterogeneity in susceptibility (SIH) in the exposed human population. Bogen showed by examples that SIH can be false. Herein is outlined a general proof that confirms Bogen's claim. However, it is also noted that SIH leads to a nonthreshold population distribution even if individual distributions all have thresholds, and that small changes to SIH assumptions can result in LNT. Bogen criticizes AB because it only applies when there is additivity to background, but offers no help in deciding when or how often AB holds. Bogen does not contradict the fact that AB can lead to LNT but notes that, even if low-dose linearity results, the response at higher doses may not be useful in predicting the amount of low-dose linearity. Although this is theoretically true, it seems reasonable to assume that generally there is some quantitative relationship between the low-dose slope and the slope suggested at higher doses. Several incorrect or misleading statements by Bogen are noted.

Linear‐No‐Threshold Default Assumptions are Unwarranted for Cytotoxic Endpoints Independently Triggered by Ultrasensitive Molecular Switches

“…In this issue of this journal, Crump concurs that my critique correctly disproved the substantial interindividual heterogeneity (SIH) argument for low‐dose linearity, as formulated by Lutz and cited by the 2009 Science and Decisions report of the National Research Council as a basis for applying default linear‐no‐threshold (LNT) assumptions for increased cytotoxic risks. By outlining a concise and elegant proof, Crump shows that “the SIH argument for linearity is generally false” and further claims that, consequently, the SIH argument is false “not just in the special cases considered by Bogen.” However, one of the “special cases” I considered (in Appendix D of my critique) was a finite mixture of n specified lognormal distributions.…”

“…Crump's Fig. is also superfluous because it merely illustrates a tautologous discrepancy between his LNT “true linear fit” and an S‐shaped (i.e., threshold‐like) mixed bi‐lognormal type of response that I showed (as he conceded) can be impossible to distinguish statistically from an LNT relationship fit to the same set of data that appear to have a linear dose response. The key point is that, absent extraordinarily detailed dose–response data that typically are unavailable, experimentally and mechanistically based theoretical considerations are crucial for meaningful low‐dose, dose–response extrapolation.…”

“…were first to propose the additive to background (AB) argument for low‐dose linearity, whereby if a toxicant operates by augmenting a process that is already producing adverse effects in background, then any additional response caused by exposure at low dose D is expected to vary approximately linearly with D. However, Crump concedes that “Bogen is technically correct … that additivity to background, without additional conditions, does not assure that the low‐dose slope guaranteed by AB, can be well‐predicted by data gathered at higher doses,” and explains that “AB is ‘not applicable’ if the background response occurs by a mechanism that is completely independent of that of the substance of interest.” Crump thus implies that his Fig. is superfluous because it simply rescales a portion of my Fig. to show a positive slope ( B ) at a dose ( D o ), where the corresponding unscaled dose–response function is extremely flat but nevertheless at which “ B > 0” as noted explicitly in my Fig.…”

“…Crump notes that Crump et al . showed that linear extrapolation must be quite accurate for any extra risk less than the spontaneous risk predicted by multistage somatic mutation (MSM) models of carcinogenesis, via which (by definition) the AB argument applies to cancer risk increased by exposure to a mutagenic carcinogen.…”

“…Crump is skeptical that chemical exposures can increase rates of any disease by mechanisms totally independent of those explaining its background rates. He asserts that I did not discuss such conditions, and asserts that because “it will generally be difficult to determine whether they exist,” to protect human health “it may be prudent to assume that a common mechanism is involved.” Crump thus recommends AB‐based LNT extrapolation of increased risk for all endpoints as a prudent default because “it seems plausible that in general there would be some relationship [between] low‐dose slope and the responses at higher doses.” Crump moreover claims my descriptions of cytotoxic endpoint and associated mechanistic dose–response data as exhibiting nonlinear low‐dose, dose–response relationships were misleading because, as he previously pointed out, “any set of dose–response data will be consistent with both a threshold and a low‐dose linear response” such that “distinguishing between a low‐dose linear dose response and a threshold dose response on the basis of dose–response data is impossible—it is something that science is incapable of doing.”…”