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Program Set-Up - General approach

Model Visualization

The first step in the running a nonlinear regression problem is to visualize the model. The two factors which need to be considered are the route of drug administration and the data that has been collected. (Designing the experiment and planning the samples involves identifiability and optimal sampling, here we are concerned with modeling data already collected).

From the route of administration the modeler can include details in the model that describe the administration. This might be single or multiple dose regimens. Drug may be given by IV bolus injection, IV infusion, or an extravascular route such as oral, topical or inhalation. The extravascular routes may include multiple steps such dissolution and absorption in the case of oral administration or diffusion from a patch and through the skin in the case of a topical dose. The structure of this part of the model may be derived from an understanding of the dosage form and prior knowledge however certain parameter values may need to be determined by nonlinear regression. Dissolution rate constants, absorption rate constants or extent of absorption may be among the parameters to be estimated (example diagrams).

Consideration of the data plotted on linear and semi-log graph paper will provide more information about a suitable model. Distribution may be described with more than one compartment (example diagrams). More data types, such drug excreted in urine or metabolite concentrations, provide information useful in extending the model to better describe drug metabolism or excretion (example diagrams).

With some nonlinear programs it is possible to draw a sketch of a proposed models (SAAM II) or select a pre-drawn model from a library (WinNonlin). Users of other programs such as Boomer or ADAPT II may wish to draw this visualization by hand. Having a clear idea of what the model 'looks' like can be very useful in correctly defining the model with any nonlinear regression program.

Derive the Mathematical Model

A number of nonlinear regression program relieve the modeler from the chore of deriving the equations needed to describe the pharmacokinetic model. These programs include Boomer, SAAM II and WinNONLIN, although further model definition is possible if the equations are known. ADAPT II users and users of WinNONLIN with models that go beyond the built-in library will need to use equations to define the model. Differential equations can be derived directly from the model diagram. Integrated equation for most pharmacokinetic models can be derived using Laplace transforms. This method was discussed earlier in Chapter 2 and Chapter 7.

Defining the Model within the Nonlinear Regression Program

Each program is somewhat different in the way one defines the model but there are three different approaches. Details of how models are define within any given program should be available within the program manual.

Selection from a library Some programs have a collection of predefined models within a library. The user simply selects the appropriate model from this library. WinNonlin is an example of this approach. It is probably the easiest for the user IF their model is in the library. WinNonlin also allows the user to define more complicated models using a computer language (Phoenix Modeling Language [PLM]) or graphically.

Selection of Model Parameters Programs like Boomer, WinNonlin and SAAM II provide the user with a collection of parameters, rate constants, volumes, components (compartments), etc. (toolbox) from which the user can build their model. This provides the user with considerable flexibility without the need to derive the equations required for the model. SAAM II users have the added flexibility of modifying the form of some parameters. If the parameter toolbox is contains all the required parts this can be very convenient.

Describe the Model within a Computer Program For maximum flexibility the modeler can describe their model using a computer language. ADAPT II (using Fortran code) and WinNonlin (using Phoenix Modeling Language [PLM]) (and to some extent SAAM II) are computer programs that provide this flexibility. Although while this approach is flexible it does require more of the modeler.

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