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Extrapolation: extending predictions outside the range of observations. In regulatory toxicology extrapolation means predicting an effect in such conditions that it is not possible to assess the effect experimentally. Extrapolation is used over dose, species, sex, age, or route. Dose extrapolation means predicting an effect (e.g. the likelihood of cancer) below the range of doses that can be tested experimentally. In a group of 50 animals in a two-year cancer study, it is possible to detect a 10 % additional cancer risk, i.e. five cancers in addition to the typical background incidence of e.g. ten cancers. Ten per cent risk would be clearly unacceptable in humans. We would barely accept a risk of one in ten thousand of contracting cancer from a chemical. However, an experiment that could detect an increase in cancer risk from 20 % (background) to 20.01 % (background + chemical-induced) would need more than 100,000 animals. This is clearly not feasible. Therefore the dose of the chemical is increased so that the effect is detectable, and the effect at the true level of human exposure is extrapolated mathematically. Because there is no obvious way to prove the correct formula for extrapolation, this is one of the most common sources of disputes in toxicology (see also Linear extrapolation). Another extrapolation is species extrapolation. If the chemical is studied in the mouse, one need to know what dose in the mouse is equivalent to a dose in humans. This is one of the sources of confusion in dioxin risk assessment, because TCDD kills a guinea pig at a dose of 0.001-0.002 mg/kg, but a hamster only at a dose of several mg/kg. So it is important to know, which is a better model for human being, the guinea pig or the hamster. Some effects of TCDD, such as developmental toxicity, are seen at low doses both in guinea pigs and hamsters, however. 
A wide range of extrapolation methods is available, of varying complexity and statistical rigour (see links to left). In each case, however, extrapolation may be subject to a number of uncertainties and errors. In particular, care is needed to ensure that:
- the observed trends in the data are valid and unbiased: biases tend to occur, especially, when the data set is small or clustered either in space or time;
- the possibility of non-linearity (including thresholds or step-changes) is allowed for;
- allowance is made for the influence of external factors (e.g. social or environmental determinants) which may modify the observed trends;
- extrapolation remains within the range of plausible values and extrapolated estimates have plausible distributions (e.g. do not show large and unexpected skew or outliers).
- Jouko Tuomisto, Terttu Vartiainen and Jouni T. Tuomisto: Dioxin synopsis. Report. National Institute for Health and Welfare (THL), ISSN 1798-0089 ; 14/2011 
- Transferring results from other studies
- Temporal extrapolation methods
- Spatial interpolation and extrapolation methods