Middle Ground

The “Low Dose” Problem

Evidence of potential harm from arsenic and other contaminants usually comes from epidemiology studies exposures that are much higher than those that occur in the diet.  Because these exposures are both statistically significant and there is strong evidence that the association is causally related to exposure to the contaminant, this “high-dose” region is the only part of the curve where the data are good enough to empirically characterize the shape of a dose-response curve.   Potential effects at lower doses necessarily involve extrapolation from high doses to the “low-dose” region where exposures from the U.S. diet actually occur.  There is also often a substantial “intermediate-dose” part of the curve that is in between the high- and low-dose regions. 

The inevitable question underlying most toxicological assessments is this:  What effects in the low dose region can be inferred from the demonstrable effects in the high dose region?  Since effects in the low-dose-region are not within the limits of detection, by definition, any claim of an effect or lack there of must be theoretical.  The scientific debate typical revolves around whether or not the shape of dose response is “linear” or “nonlinear”.  If it is “linear”, then it is supposed that the risk at low doses is proportional to the risk at high doses.  If it is nonlinear, then it is supposed that the risk at low doses is negligible, and therefore, no quantification of the risk is necessary.  But, there are many other plausible alternatives.   In particular, the risk at low doses may be linear without being proportion to the effect at high doses.  As a result, a risk assessment isn’t just about what happens at high doses and low doses; it is about what happens in the middle as well.

Some Theoretical Alternatives

A comparison of some of the mathematical models used for benchmark dose modeling is illustrative.  The behavior of these models when used to describe the relationship between exposure to inorganic arsenic in NE Taiwan (Chen et al, 2010; Carrington et al, 2013) are illustrated in the following three figures that show four different models in three different dose ranges. 

The High-Dose Region

The Intermediate-Dose region

The Low-Dose Region

At high doses, all four of the models are nonlinear.  Even the Weibull model, which appears to be linear in Figure 1, becomes nonlinear at doses that result in incidence rates that exceed 50%.  However, near the transition point between the high and intermediate dose ranges there is a large discrepancy in the models.  While the Weibull model is almost completely linear, the Probit model is somewhat nonlinear, while the Logprobit and Quantal Hill models are highly nonlinear.   As a result of their nonlinearity in the intermediate dose range, the latter two models are nearly flat at low doses, which is indicative of an incremental risk that is very close to zero .  Although the increase is very small relative to background, the other two models exhibit a noticeable slope in the range of dietary exposure.

No Dichotomy

Given the complexity of biological reality, none of these simple models are likely to be entirely correct:  They are approximations at best.  Nonetheless, they serve to demonstrate that the shape of the curve really does matter.  Just about all plausible curves are non linear at some point, yet are still approximately linear at very low doses.  Nonlinearity does not imply that there is a threshold.  Linearity does not imply that the risk is of any significance.  It all depends on how and where the nonlinearities occur, and in the intermediate region theoretical justification is the only game in town. 

References

Carrington CD, Murray C, and Tao, S. (2013). A Quantitative Assessment of Inorganic Arsenic in Apple Juice. 

Chen CL, Chiou HY, Hsu LI, Hsueh YM, Wu MM, and Chen CJ (2010).  Ingested arsenic, characteristics of well water consumption and risk of different histological types of lung cancer in northeastern Taiwan.  Environ Res. 110:455-62.

Official Post Soundtrack

Fixx, The (2003).   Straight 'Round the Bend.  In: Want That Life, Track 7.

Post Notes

Thesis Post #46.  First post in almost a month.  That mostly because my manfesto is pretty much manifested - I've already covered most of the main ideas I wanted to cover when I set out.