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Model Appropriateness and Population Pharmacokinetic Modeling

From Vertex Pharmaceutical, Inc., Cambridge, Massachusetts (Dr. Ette, Dr. Capparelli); Trials by Design, LLC, La Jolla and Stockton, California (Dr. Williams, Dr. Kim, Dr. Lane, Dr. Capparelli); University of the Pacific, Stockton, California (Dr. Williams, Dr. Kim); and Advanced Medicine, Inc., South San Francisco, California (Dr. Liu).

The purpose of this study was to define model appropriateness, identifying the individual elements thereof, and to set out a framework within which model appropriateness could be determined for population pharmacokinetic (PPK) models. Model appropriateness was defined by stating the problem to be solved, with the intended use of the model being the pivotal event. The elements of model appropriateness were identified with the type of model (descriptive vs. predictive) determining which elements of model appropriateness need to be executed. An example is presented to show how model appropriateness is determined for the optimal application of PPK models. It was determined that PPK models are developed to solve problems. Model appropriateness depends on identifying the problem, as well as stating the intended use of the model, and requires evaluation of the model for goodness of fit, reliability, and stability if intended for descriptive purposes; for predictive models, validation would be an additional requirement. Descriptive models are used to explain variability in the pharmacokinetics (PK) of a drug, while predictive models are developed to extrapolate beyond the immediate study population. For those models used for predictive purposes, strong assumptions are made about the relationship to the underlying population from which the data were collected. As an example of determining model appropriateness, a PPK model for 5-fluorocytosine was developed, using NONMEM, version IV. The model was evaluated and validated by the process of percentile bootstrapping. From the PPK model, the range of expected serum concentrations based on two widely used dosing methods (Sanford and the University of California at San Diego [UCSD]) was simulated (Pharsight Trial Designer software). These results indicated that the UCSD method performed well and has the advantage of recommending convenient dosing intervals. In conclusion, considering and applying the principles of model appropriateness to PPK models will result in models that can be applied for their intended use with confidence. Model appropriateness was efficiently established and determined to address the problem of comparing competing dosing strategies.

Key Words: Population pharmacokinetic models • model appropriateness • descriptive models • predictive models • bootstrapping

Address for reprints: Paul J. Williams, Trials by Design, LLC, 1918 Verdi Court, Stockton, CA.

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