Linear dose-response

When the effect of exposure to a chemical is the production of a cancer, it is sometimes assumed, for instance, by regulatory agencies such as the U.S. Environmental Protection Agency (EPA) that the dose-response curve passes through zero. Thus, it is not like the dose-response curve we have been discussing above where there is a threshold. The zero threshold dose response is predicated on the belief that the causation of cancer by a genotoxic mechanism is a stochastic (chance) event, in which a reactive chemical binds to and damages or alters DNA (see chap. 6). 

Therefore, it is argued, there is no safe dose of such a chemical because one molecule could theoretically interact with the DNA in one cell, which could then become a tumor. 

Therefore, the curve is not an S shape but the lowest portion is linearized and extrapolated to the origin (Fig. 2.10). 

Now in practice it seems very likely that this is not the case and that an effective threshold exists. This can be justified on the following grounds  

the chemical must gain access to a cell. This requires, at the least, crossing biological membranes and entering an aqueous environment in which substances such as glutathione and vitamin C are present, which can detoxify reactive chemicals. 

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An inadequate intake in the diet of those food chemicals that are essential nutrients results in health risks. Indeed these risks are by far the most important in terms of the world s population where malnutrition is a major public health problem. But, unlike the toxic chemicals, they would show a very different dose-response if they were subject to similar animal bioassays. At very low doses there would be a high risk of disease that would decrease as the dose was increased, the curve would then plateau until exposure was at such a level that toxicity could occur. Figure 11.2 shows this relationship which is U- or J-shaped rather than the essentially linear dose-response that is assumed for chemicals that are only toxic. The plateau region reflects what is commonly regarded as the homeostatic region where the cell is able to maintain its function and any excess nutrient is excreted, or mechanisms are induced that are completely reversible. 

Differences of opinion are common among epidemiologists based on what appears to be similar, if not comparable, data. In spite of the numerous large-scale and long-term investigations, the debate eontinues over whether there is a safe (threshold) level for asbestos or other fibrous materials, or if there is a linear dose-response relationship in the induction of cancer. Conclusions and interpretations of this body of data usually reflect personal philosophy and tolerance of risk. 

The T25 is dehned as the chronic daily dose (in mg/kg body weight per day), which will give 25% of the animal s tumors at a specihc tissue site, after correction for spontaneous incidence, within the standard lifetime of that species. It is a value calculated from a single observed dose-response and based upon the assumphon of a linear dose-response relationship over the entire dose range. 

Eor compounds with presumed linear dose-response curves, such as genotoxic and carcinogenic compounds for which it is assumed that a no-effect level does not exist and for which the mechanism of action may be regarded as similar, response addition and dose addition will provide identical results (Konemann and Pieters 1996). 

Fig. 3. The way in which an envelope of additivity may be calculated for two pairs of cytotoxic agents (A + B and C + D) where one of each pair gives a non-linear dose-response curve (isobologram analysis from Peckham and Steele ref. 27).

The dose of propofol should be reduced in older patients however, it does have a relatively linear dose-response characteristic, and patients generally can be... 

There was a log-linear dose-response relationship for DEF and CHE, particularly for birds in the acute, one day study (Figure 5)-... 

Figure 11.3 The dose-response relationship, (a) Five segments of the sigmoidal dose-response curve as described in the text, (b) Linearized dose-response relationship through log (dose)-probit (effect) transformations. Locations of the LD50 and LD05 are depicted.

Stochastic Responses. A basic principle of health protection for both radionuclides and hazardous chemicals is that the probability of a stochastic response, primarily cancers, should be limited to acceptable levels. For any substance that causes stochastic responses, a linear dose-response relationship, without threshold, generally is assumed for purposes of health protection. However, the probability coefficients for radionuclides and chemicals that induce stochastic responses that are generally assumed for purposes of health protection differ in two potentially important ways. 

Establishing Allowable Risks or Doses of Substances That Cause Stochastic Responses. Given the assumption of a linear dose-response relationship for substances that cause stochastic responses without threshold, either risk or dose may be used to calculate the risk index. The following two sections discuss suitable approaches to establishing negligible and acceptable risks or doses of substances that cause stochastic responses. 

Linear dose-response relationship is a dose-response relationship in which the probability of a specified response changes as a linear function of the dose. 

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