Linear dose-response relationship

A potential pitfall with stop-time experiments comes with temporal instability of responses. When a steady-state sustained response is observed with time, then a linear portion of the production of reporter can be found (see Figure 5.15b). However, if there is desensitization or any other process that makes the temporal responsiveness of the system change the area under the curve will not assume the linear character seen with sustained equilibrium reactions. For example, Figure 5.16 shows a case where the production of cyclic AMP with time is transient. Under these circumstances, the area under the curve does not assume linearity. Moreover, if the desensitization is linked to the strength of signal (i.e., becomes more prominent at higher stimulations) the dose-response relationship may be lost. Figure 5.16 shows a stop-time reaction dose-response curve to a temporally stable system and a temporally unstable system where the desensitization is linked to the... 

Cohen, B.L., Surveys of Radon Levels in U.S. Homes as a Test of the Linear-No Treshold Dose-Response Relationship for Radiation Carcinogenesis, this volume (1987). 

A Test of the Linear-No-Threshold Dose-Response Relationship for Radiation Carcinogenesis... 

Burch, P.R.J., Problems With the Linear-Quadratic Dose-Response Relationship, Health Physics 44 411-413 (1983)... 

Note that in actuality, dose-response relationships are often not linear and instead we must use either a transform (to linearlize the data) or a nonlinear regression method (Gallant, 1975). 

Note (a) Recti linearity of the dose-response relationship, transformed or untransformed, is often obtained only over a very limited range. It is this range that must be used in calculating the activity and it must include at least three consecutive doses in order to permit rectilinearity to be verified,... 

Lipophilicity in particular, as reflected in partition coefficients between aqueous and non-aqueous media most commonly water (or aqueous buffer) and Z-octanol,has received much attention [105,141,152,153,176,199,232,233]. Logic )W for the octanol-water system has been shown to be approximately additive and constitutive, and hence, schemes for its a priori calculation from molecular structure have been devised using either substituent tt values or substructural fragment constants [289, 299]. The approximate nature of any partition coefficient has been frequently emphasized and, indeed, some of the structural features that cause unreliability have been identified and accommodated. Other complications such as steric effects, conformational effects, and substitution at the active positions of hetero-aromatic rings have been observed but cannot as yet be accounted for completely and systematically. Theoretical statistical and topological methods to approach some of these problems have been reported [116-119,175,289,300]. The observations of linear relationships among partition coefficients between water and various organic solvents have been extended and qualified to include other dose-response relationships [120-122,160,161,299-302]. 

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. 

For non-threshold mechanisms of genotoxic carcinogenicity, the dose-response relationship is considered to be linear. The observed dose-response curve in some cases represents a single ratedetermining step however, in many cases it may be more complex and represent a superposition of a number of dose-response curves for the various steps involved in the tumor formation (EC 2003). Because of the small number of doses tested experimentally, i.e., usually only two or three, almost all data sets fit equally well various mathematical functions, and it is generally not possible to determine valid dose-response curves on the basis of mathematical modeling. This issue is addressed in further detail in Chapter 6. 

Dose-response assessment today is generally performed in two steps (1) assessment of observed data to derive a dose descriptor as a point of departure and (2) extrapolation to lower dose levels for the mmor type under consideration. The extrapolation is based on extension of a biologically based model (see Section 6.2.1) if supported by substantial data. Otherwise, default approaches that are consistent with current understanding of mode of action of the agent can be applied, including approaches that assume linearity or nonlinearity of the dose-response relationship, or both. The default approach is to extend a straight line to the human exposure doses. 

The dose-response relationship is by default assumed to be linear in the absence of mechanistic evidence to the contrary, at least in the observable range of the response, and risks are often linearly extrapolated into the low-dose range. 

The linear component of the LMS model, qi (i.e., one of the parameters of the polynomial), is approximately equivalent to the slope at low doses of the dose-response relationship between the tumor incidence and the dose. This linearity at low dose is a property of the formulation developed for the multistage model and is considered by proponents to be one of its important properties. This linear component of the polynomial, qi, is used to carry out low-dose extrapolation. The linear response at low doses is considered to be conservative with regard to risk, as the dose-response relationship at low doses may well be sublinear. Although supralinearity at low doses cannot be excluded, it is usually considered to be unlikely. 

The 95% confidence limits of the estimate of the linear component of the LMS model, /, can also be calculated. The 95% upper confidence limit is termed qi and is central to the US-EPA s use of the LMS model in quantitative risk assessment, as qi represents an upper bound or worst-case estimate of the dose-response relationship at low doses. It is considered a plausible upper bound, because it is unlikely that the tme dose-response relationship will have a slope higher than qi, and it is probably considerably lower and may even be zero (as would be the case if there was a threshold). Lfse of the qj as the default, therefore, may have considerable conservatism incorporated into it. The values of qi have been considered as estimates of carcinogenic potency and have been called the unit carcinogenic risk or the Carcinogen Potency Factor (CPF). 

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. 

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