Threshold models

Carcinogens, 21 837. See afeo Cancer agency lists of, 23 113-114 Category I, 10 580 DEHP as, 25 674-675 formaldehyde, 12 121 nonlinear and threshold models for, 25 244... 

Linear, no-threshold model (extrapolated upper bound on low-dose risk)... 

Figure 8.1 Dose-response curves for carcinogens and illustration of low-dose extrapolation using linear, no-threshold model. Benchmark dose (BMD) is also illustrated.

A simple example might make this clearer. Suppose it were known that a 100 mg dose of chemical Z produced an extra 10% incidence of liver tumors in rats. Suppose further that we studied the pharmacokinetics of compound Z and discovered that, at the same 100 mg dose, 10 mg of the carcinogenic metabolite of Z was present in the liver. The usual regulatory default would instruct us to select the 100 mg dose as the point-of-departure for low dose extrapolation, and to draw a straight line to the origin, as in Figure 8.1. We are then further instructed to estimate the upper bound on risk at whatever dose humans are exposed to - let us say 1 mg. If the extra risk is 10% at 100 mg, then under the simple linear no-threshold model the extra risk at 1 mg should be 10% 100 = 0.1% (an extra risk of... 

Denoble VJ, Schrack LM, Reigel AL, et al Visual recognition in squirrel monkeys effects of serotonin antagonists on baseline and hypoxia induced performance deficits. Pharmacol Biochem Behav 39 991-996, 1991 Depue RA, Karuss SP, Spoont MR A two-dimensional threshold model of seasonal bipolar affective disorder, in Psychopathology An Interactional Perspective. Edited by Magnusson D, Ohman A. Orlando, FL, Academic Press, 1987, pp 95-123... 

Also M. Gough and D. Turnbull, Use of a Threshold Model for the Estimation of Risk Associated with Exposure to Chlorinated Dibenzo-p-di-oxins and Dibenzofurans, in H. A. Hattemer-Frey and . C. Travis, eds., Health Effects of Municipal Waste Incineration (Boca Raton, Fla. CRS Press, 1989), pp.20151-46. 

Although the straightforward threshold model of the dose-response relationship as described here is the one originally conceived and the one for which there is clear mechanistic justification, other dose-response relationships have been suggested. The other dose-response relationships are substantially different and lead to different predictions in relation to toxicity. This becomes particularly important in risk assessment (see below). 

Linear, No-Threshold Model. This simplest model is based on the assumption that risk is directly proportional to the dose P(d) = ad. When it is assumed that the true dose-response curve is convex, linear extrapolation in the low-dose region may overestimate the true risk. However, it is not known if the experimental dose is in the convex region of the curve. 

The two-threshold model, i.e. a model with distinct values for E+ and Er, can account for the data, notably that the pulsed field spectrum is identical to that at zero field until a time At = rc — ra when the distribution begins to reach ER. Figure 6.14 shows pulsed field spectra (and also an example with a constant field) taken at different times ra... 

Fig. 6.13. Superimposed zero field and pulsed field (81 V cm-1 peak amplitude) positron lifetime spectra. The pulsed field spectrum has been decomposed into heated components (broken line) and unheated components (crosses) to illustrate how the electric field splits up the positron ensemble. This is also illustrated by the inset, which shows, schematically, the energy distribution p(E,t) of the positron ensemble in the two-threshold model (see text). Reprinted from Physical Review Letters 56, Tawel and Canter, Observation of a positron mobility threshold in gaseous helium, 2322-2325, copyright 1986 by the American Physical Society.

Downs, S.G. and Ratnieks, F.L.W. (2000). Adaptive shifts in honey bee (Apis mellifera L.) guarding behavior support predictions of the acceptance threshold model. Behav. Ecol., 11, 326-333. 

Starks, P.T., Fischer, D. J., Watson, R.E., Melikian, G.L. and Nath, S.D. (1998). Context-dependent nestmate discrimination in the paper wasp, Polistes dominulus a critical test of the optimal acceptance threshold model. Anim. Behav., 56, 449—158. 

The individual tolerance concept has some unrealistic properties (Kooijman 1996 Newman and McCloskey 2000). Most importantly, if there is a distribution in sensitivities, this would imply that the survivors from an experiment are the less sensitive individuals. Experiments with sequential exposure show that this prediction fails (at least as the dominant mechanism) (Newman and McCloskey 2000 Zhao and Newman 2007). There is sufficient reason to conclude that the individual threshold model is not sufficient to explain the observed dose-response relationships, and that mortality is a stochastic process at the level of the individual... 

Avoidance of arbitrary thresholds Model builders should avoid arbitrary thresholds for continuous variables because categorization discards potentially useful information... 

Another line of thinking suggests that there may be no adverse effects at all from exposure to low levels of radiation that there may be a threshold, below which we see no risk. Under threshold models, there is a certain level of exposure that is completely safe, and it is only above that threshold that we begin to see an increase in cancer risk. Virtually all known harmful agents exhibit threshold effects. 

Saccharin is not metabolized and does not react with DNA. Although it was mutagenic in vitro, this was only at high concentrations. It was concluded that saccharin was not a genotoxic carcinogen. Assuming that there was no threshold was, therefore, not appropriate. A threshold model could be applied to the dose-response data from these safety evaluation studies. 

In distributed pharmacokinetics, threshold models, in which a biological response is associated with the increase of concentration above a threshold value, are likewise dependent on spatial location. 

There is considerable controversy over the shape of the dose-response curve at the chronic low dose levels important for environmental contamination. Proposed models include linear models, nonlinear (quadratic) models, and threshold models. Because risks at low dose must be extrapolated from available data at high doses, the shape of the dose-response curve has important implications for the environmental regulations used to protect the general public. Detailed description of dosimetry models can be found in Cember (1996), BEIR IV (1988), and Harley (2001). 

A corollary is that almost all stressors leave lasting impacts and that the information is located in a variety of biotic and abiotic components. The hypothesis states that ecological structures are historical, unique, and complex. The hypothesis explicitly recognizes the importance of indirect effects in retention of information within systems and in impacting the outcomes of future stressor events. These features place community conditioning in opposition to equilibrium-based or threshold models prevalent in ecological risk assessment and environmental toxicology. 

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