Sublinear dose-response relationship

Sublinear dose-response relationship is a dose-response relationship in which the probability of a specified adverse health effect is either not increasing at all or increasing slower than linearly (i.e., slower than in direct proportion to the increase in dose). 

The proportion of female Sprague-Dawley rats developing mammary tumors decreases very rapidly as the dose decreases (American Biogenics Corporation, 1986 McCormick, 1988 Thakur, 1991, 1992). The observed dose-response relationship is sublinear. Furthermore, the biological mechanism by which atrazine and simazine cause this response is most likely a threshold mechanism thus, the sublinear dose-response relationship contains a range of positive doses for which the frequency of the response is not increased above the background frequency at zero dose (Andersen et al., 1998 Connor et al., 1998 Eldridge et al 1998 Simpkins et al, 1998). 

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 manner in which the proportion of animals developing a response changes as the dose level changes is the dose-response relationship. If the proportion decreases in parallel with decreasing dose (e.g., halving the dose halves the proportion), then the dose-response relationship is linear. However, if the proportion decreases faster than linearly (e.g., halving the dose results in either one-fourth the proportion or no occurrences of the adverse effect), then the dose-response relationship is sublinear (one type of nonlinearity). 

Potency estimates derived from such animal studies help to characterize the dose-response relationship at the low-exposure levels to which humans are likely to be exposed and to predict the quantitative estimate of the risks that humans are likely to encounter at ambient exposures. Experimental evidence for various shapes of the dose-response curve for carcinogens showed that reliable high-dose data from human studies contain examples of superlinearity, linearity, and sublinearity. These are also seen in animal studies. But there are no data to indicate the shape of the dose-response relationship corresponding to lifetime risk of one in a million, the insignificant risk level generally used by the regulatory agencies. 

BELLE founders noted that risks at low levels are estimated by various means, frequently utilizing assumptions about which there may be considerable uncertainty. BELLE is committed to the enhanced understanding of low-dose responses of all types, whether of an expected nature (e.g., linear, sublinear) or of a so-called paradoxical nature. Paradoxical dose-response relationships might include U-shaped dose-response curves and biphasic dose-response curves. The focus of BELLE now encompasses dose-response relationships to toxic agents, pharmaceuticals, and natural products over wide dosage ranges in in vitro and in vivo systems, including human populations. 

Although there is no consensus on the matter, most scientists believe that models showing even higher risks than the linear model, so-called superlinear models, are not likely to be correct. They see the linear, nothreshold model as a kind of upper limit on the dose-response relationship, and admit that the actual but unknown dose—response relation may be sublinear or may even take the threshold form for some carcinogens. 

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