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# Modeling

## Why model? - General Approach

### Student Objectives for this Chapter

• Understand the reasons why models are developed and used
• Understand how models can summarize or 'compress' data
• Understand how models can be used to study pharmacokinetic mechanisms
• Understand how models can be used to predict concentrations or dosage regimens

• Understand the use of formulas as 'Mathematical models'
• Understand the criteria of least squares
• Understand how parameter adjustment changes the fit to data
Why Model?

Summarize Data Pharmacokinetic models are very useful for summarizing data. A suitable model with good parameter value estimates and estimates of their uncertainty can be helpful. Thus, a model with population mean and standard deviation data could summarize pages and pages of data from many subject or patients.

Explore Mechanisms Developing models is an important step in understanding how drugs are absorbed, distributed, metabolized or excreted. After developing good models it possible to explore correlations between pharmacokinetic parameter values and clinical parameters such as measures of renal, hepatic, cardiac or other patient characteristics. Developing and testing pharmacokinetic (and other models) is an important basis of scientific enquiry.

Make Predictions Once a satisfactory pharmacokinetic model and parameter values have been determined we can make predictions such anticipated drug concentrations after a particular drug dosage regimen. Alternately we could calculate suitable dosage regimens to produce and maintain optimal drug concentrations.

General Approach

Mathematical models as equations What is a mathematical model, a pharmacokinetic model? It can be useful to describe a model as a diagram with components to represent drug amount and arrows to represent rate processes. However, every pharmacokinetic model needs to be represented as a formula or an equation. Understanding these equations and the parameters in these equations is important.

Criteria of least squares We need to decide on a criteria for a best fit when analyzing data and finding the best parameters values. If we put a line through data drawn on a piece of graph paper we can put the line where we think it looks best. However, if we want the computer program to find the best parameter values we need to have a well defined criteria. A commonly used criteria is the least squares criteria.

Changing parameters to fit to the data Once we have a suitable criteria we can have the computer program change the parameters value to achieve a best fit to the data. The computer program will systematically alter the each parameter until the least square criteria value is minimized.