# An empirical comparison of low-dose extrapolation from points of departure (PoD) compared to extrapolations based upon methods that account for model uncertainty

**ABSTRACT** Experiments with relatively high doses are often used to predict risks at appreciably lower doses.A point of departure (PoD) can be calculated as the dose associated with a specified moderate response level that is often in the range of experimental doses considered. A linear extrapolation to lower doses often follows.An alternative to the PoD method is to develop a model that accounts for the model uncertainty in the dose-response relationship and to use this model to estimate the risk at low doses.Two such approaches that account for model uncertainty are model averaging (MA) and semi-parametric methods.We use these methods, along with the PoD approach in the context of a large animal (40,000+ animal) bioassay that exhibited sub-linearity. When models are fit to high dose data and risks at low doses are predicted, the methods that account for model uncertainty produce dose estimates associated with an excess risk that are closer to the observed risk than the PoD linearization.This comparison provides empirical support to accompany previous simulation studies that suggest methods that incorporate model uncertainty provide viable, and arguably preferred, alternatives to linear extrapolation from a PoD.

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- Journal of environmental pathology and toxicology 02/1980; 3(3 Spec No):1-7.
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**ABSTRACT:**Quantitative risk assessment proceeds by first estimating a dose-response model and then inverting this model to estimate the dose that corresponds to some prespecified level of response. The parametric form of the dose-response model often plays a large role in determining this dose. Consequently, the choice of the proper model is a major source of uncertainty when estimating such endpoints. While methods exist that attempt to incorporate the uncertainty by forming an estimate based upon all models considered, such methods may fail when the true model is on the edge of the space of models considered and cannot be formed from a weighted sum of constituent models. We propose a semiparametric model for dose-response data as well as deriving a dose estimate associated with a particular response. In this model formulation, the only restriction on the model form is that it is monotonic. We use this model to estimate the dose-response curve from a long-term cancer bioassay, as well as compare this to methods currently used to account for model uncertainty. A small simulation study is conducted showing that the method is superior to model averaging when estimating exposure that arises from a quantal-linear dose-response mechanism, and is similar to these methods when investigating nonlinear dose-response patterns.Risk Analysis 03/2012; 32(7):1207-18. DOI:10.1111/j.1539-6924.2011.01786.x · 1.97 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Quantitative risk assessment involves the determination of a safe level of exposure. Recent techniques use the estimated dose-response curve to estimate such a safe dose level. Although such methods have attractive features, a low-dose extrapolation is highly dependent on the model choice. Fractional polynomials, basically being a set of (generalized) linear models, are a nice extension of classical polynomials, providing the necessary flexibility to estimate the dose-response curve. Typically, one selects the best-fitting model in this set of polynomials and proceeds as if no model selection were carried out. We show that model averaging using a set of fractional polynomials reduces bias and has better precision in estimating a safe level of exposure (say, the benchmark dose), as compared to an estimator from the selected best model. To estimate a lower limit of this benchmark dose, an approximation of the variance of the model-averaged estimator, as proposed by Burnham and Anderson, can be used. However, this is a conservative method, often resulting in unrealistically low safe doses. Therefore, a bootstrap-based method to more accurately estimate the variance of the model averaged parameter is proposed.Risk Analysis 03/2007; 27(1):111-23. DOI:10.1111/j.1539-6924.2006.00863.x · 1.97 Impact Factor