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The Art of Modeling

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Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Abstract

There is more to modeling than the act of modeling. To be an effective modeler requires understanding the different types of models and when one type of model is more appropriate than another, how to select a model from a family of similar models, how to evaluate a model’s goodness of fit, how to present modeling results both verbally and graphically to others, and to do all these tasks within an ethical framework. This chapter lays the groundwork for the rest of the book and covers these topics with an eye toward applying these concepts across the other chapters.

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Notes

  1. 1.

    Superposition was developed in physics to explain the behavior of waves that pass simultaneously through the same region in space. In pharmacokinetics, superposition states that concentration–time profiles passing through the same relative region in time are additive. For example, if two doses are taken 24 h apart and the concentration 6 and 30 h after the first dose was 100 and 10 ng/mL, respectively, then the concentration 6 h after the second dose (which is 30 h after the first dose) would be equal to 110 ng/mL (100 + 10 ng/mL). Thron (1974) presents a comprehensive review of linearity and the meaning of superposition.

  2. 2.

    Defining degrees of freedom in a simple manner is difficult. First consider that there are n “pieces of information” contained within a data set having n-observations. From these n pieces of information, either a parameter or variability can be estimated with each item being estimated decreasing the information in the data set by one degree of freedom. The degrees of freedom then is the number of pieces of information less all the estimated items. For example, given a data set in which the mean was estimated, the degrees of freedom then is n – 1. With a model having p-estimable parameters, the degrees of freedom is n – p.

  3. 3.

    The p-value is sometimes mistaken as the probability that the null hypothesis is true or as evidence against the null hypothesis, both of which are incorrect. Formally, a p-value is defined as probability of observing data at least as contradictory to the null hypothesis H0 as the observed data given the assumption that H0 is true. The reader is referred to Hubbard and Bayarri (and commentary) (2003) for a very interesting discussion on p-values and critical levels from Fisher’s and Neyman–Pearson’s point of view.

  4. 4.

    Akaike is often mispronounced by pharmacokineticists as “Ah-chi-key” but the correct pronunciation is “Ah-kay-e-kay.”

  5. 5.

    AIC and AICc will be used interchangeably hereafter.

  6. 6.

    A perturbed compartment is one in which material is added to the compartment to push the system from steady state, following which the system returns to steady state (Jacquez 1996).

  7. 7.

    Asterisks and plus signs (+) are examples of line endings or terminators. Asterisks contain eight line endings, whereas + symbols contain four line endings. The larger the number of terminators, the greater the distinguish ability between symbols.

  8. 8.

    The data to ink ratio is the ratio of the ink used to show data to the ink used to print the graphic.

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  1. Astellas Pharma Global Development Pharmacokinetics, Modeling, and Simulation, Deerfield, IL, USA

    Peter L. Bonate Ph.D.

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  1. Peter L. Bonate Ph.D.
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Bonate, P.L. (2011). The Art of Modeling. In: Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9485-1_1

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