Discrimination Criteria

There are three schools of thought on selection of models frequentist, information-theoretic, and Bayesian. The Bayesian paradigm for model selection has not yet penetrated the pharmacokinetics arena and as such will not be discussed here. The reader is referred to Hoeting et al., (1999) for a useful review paper. Frequen-tists rely on using probability to select a model and model development under this approach looks like the branches of a tree. A base model is developed and then one or more alternative models are developed. The alternative models are then compared to the base model and if one of the alternative models is statistically a 

Frequentist model selection is based on two models being nested. A nested model is where one model can be written as a simplification of another model. For example, 

Given two nested models, the full model having f-parameters with residual sum of squares SSEf and the reduced model having r-parameters with residual sum of squares SSEr, such that f r, then the F-test 

If the maximum likelihood estimates of the full and reduced models are normally distributed then for large n, — 2Ln( ) is distributed as a chi-squared random variable with f-r degrees of freedom. An approximate size a test then is to declare the full model the superior model if 

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The apparent orientation of insect stylets to the vascular bundles caused by hydrogen ion concentrations was first reported by Fife and Frampton ( ). The leafhoppers fed mainly in the phloem tissue, which had a substantially higher pH than the surrounding plant cells. Other discriminating criteria for phloem-feeding insects have been indicated, including carbohydrate concentration (10) and positive hydrostatic pressure (11). 

Although this chapter is focused on model estimation and model discrimination criteria, other criteria may also be useful. For example, Lewis and Dean (2001) proposed a new strategy for using group screening to estimate both main effects and key two-factor interactions. Their criteria minimise the expected total number of observations, the probability that the size of the experiment exceeds a prespecified target, and the proportion of active effects that are not detected (see also Chapter 9). 

A Posteriori Modei Discrimination. Several discrimination criteria can be used in the case no additional experimental information can be acquired. A first criterion has already been discussed in Section 3.1.2, that is, investigating the total pressure effect on the initial reaction rate potentially allows identifying the RDS in a reaction mechanism. Similar tests can be defined in which the rate equation is rearranged into a particular form to give a linear relationship between dependent and independent variables. 

Present all calculations, if done, for the discriminative criteria of cost, convenience, and so on, made in choosing one technique over another. 

These common elements are highlighted for products considered borderline, for which the discriminating criteria between being an MD or a drug often reside exclusively in the mechanism of action whereby the product reaches its intended use, not by the methods of development, production, and validation. 

This chapter is aiming to systematically present an overview of some recent advances in this very active field of research. For a better understanding, the information was structured in sections using basic discriminating criteria such as the nature of matrix and filler, the scale of interactions (micro- or nanoscale), the processing approach, etc. 

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