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Bayesian Modeling

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Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Abstract

Sometimes a scientist has prior information regarding the parameters in a model. Previous studies may have already reported a drug’s clearance or an expert may have an estimate for some pharmacodynamic parameter. Bayesian models take into account this prior information to provide new estimates that balance the prior information and the likelihood of the observed data. Modeling within Bayesian framework is introduced in this chapter, as are topics unique to Bayesian modeling: stochastic estimation via Markov Chain Monte Carlo, choosing the prior, model selection, and model averaging. Two examples are provided: development of a Bayesian pharmacokinetic model for quinidine and development of a model for time to steady state of pharmacokinetic data.

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Notes

  1. 1.

    If both the prior probability density and the posterior probability density are of the same family (e.g., the normal distribution, which is technically a member of the exponential family of distributions), the prior is said to be conjugate to the likelihood. Conjugate priors were often used to facilitate a closed-form solution to the posterior. For example, a Poisson likelihood with a gamma prior results in a gamma posterior.

  2. 2.

    Named after Andrei Markov, a Russian mathematician (1856–1922), whose Master’s degree thesis was once credited by Chebyshev as being one of the finest achievements of his school and perhaps even all of Russian mathematics.

  3. 3.

    David Spiegelhalter, one of the creators of the BUGS software, writes in the BUGS User Manual for the user to “Beware – Gibbs sampling can be dangerous!”

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Recommended Reading

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    Google Scholar 

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Authors and Affiliations

  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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Appendix

Appendix

SAS code to implement the random walk Metropolis algorithm as shown in Fig. 6

SAS code to implement the bivariate normal Gibbs sampler as shown in Fig. 9

WinBUGS code to implement the time-to-steady-state model in (58)

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Bonate, P.L. (2011). Bayesian Modeling. In: Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9485-1_10

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