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Benchmark Dose Software (BMDS)

Choice of Model

Dose-response models are expressed as functions of dose, possibly covariates, and a set of constants, called parameters, that govern the details of the shape of the resulting curve. They are fitted to a data set by finding values of the parameters that adjust the predictions of the model for observed values of dose and covariates to be close to the observed response. Dose-response models for toxicology data are usually of the type called "nonlinear" in mathematical terminology. In a linear model, the value the model predicts is a linear combination of the parameters. For example, in a linear regression of a response y on dose, the predicted value is a linear combination of a and b, namely aX1 + bXdose. Note that quadratic or other polynomial models are linear models because, despite having quadratic or cubic terms, they are still a linear combination of parameters. Nonlinear models are usually more difficult to fit to data, requiring more complicated calculations, and statistical inference is more typically approximate than with linear models.

At the present, although biological models may often be expressed as nonlinear models (e.g., Michaelis-Menten curves), nonlinear models do not necessarily have a biological interpretation. Thus, criteria for final model selection will be based solely on whether various models describe the data, conventions for the particular endpoint under consideration, and, sometimes, the desire to fit the same basic model form to multiple data sets. Since it is preferable to use special purpose modeling software, EPA has developed software that includes several models and default processes as described in this tutorial.

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