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Selection of the "best" model

Student Objectives for this Chapter

Evaluate various graphical plots produced by non-linear regression program
Evaluate various output tables including parameter values and variability produced by non-linear regression program
Calculate and evaluate statistical parameters such as AIC and F-test
Evaluate various criteria and determine the best most appropriate model

Modeling of pharmacokinetic data does not mean a single run of a non-linear regression model and automatic acceptance of the output. The output must be evaluated carefully. There may be errors or there may be systematic deviations from a 'best'-fit. The wrong weighting scheme may have been used. [See Weighting Scheme for details about weighting schemes.] The chosen model may not be the best for the data set(s) under investigation. Certain systematic deviations in the graphical output from non-linear regression programs may support or refute a particular model. The reported parameter variability can provide useful information. There are a number of statistical 'tests', such as AIC and F-test, which can be very informative.

The Best Model

The best model may be developed from theoretical consideration of the system under study. In other case the model may be empirical, that is based on the data provided. In other case there may be a mixture such as a general theoretical description with the detail defined by the available data. Many pharmacokinetic models may be considered to be mixtures. 'Classical' compartmental models, such as the one compartment model, have some theoretical basis in terms of drug absorption, distribution, metabolism and excretion but the detail will depend on the data collected. Early data collected after an IV bolus may support a multi-compartment pharmacokinetic model (see Chapter 14 for more information). Without the early data or if the data had more error then a simpler model may be all that can be supported. Graphical, parameter variability and statistical criteria can be used to decide on the 'best' model.

Occam's razor, the principle of parsimony or the KISS principle suggest that the smaller model is better. The model with the least adjustable parameters. This is the basis of the statistical tests, AIC and F-test. Does the more complicated model provide statistically significant improvements in the fit?

Can the parameters be determined accurately, consistently? With insufficient data (samples/sites) or more complex models it may not be possible to identify, that is determine all the adjustable parameters in the model. Identifiability is described on more detail in Chapter 20.

The best model also depend on how it is to be used. A simple model may be satisfactory. A more complex model may be required so the detail can be explored. Is the model too big? Too small?

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