Bayesian Analysis of Population PK/PD Models: General Concepts and Software

Markov chain Monte Carlo (MCMC) techniques have revolutionized the field of Bayesian statistics by enabling posterior inference for arbitrarily complex models. The now widely used WinBUGS software has, over the years, made the methodology accessible to a great many applied scientists, in all fields of research. Despite this, serious application of MCMC methods within the field of population PK/PD has been comparatively limited. We appreciate that for many applied pharmacokineticists the prospect of conducting a Bayesian analysis will require numerous alien concepts to be taken on board and it may be difficult to justify investing the time and effort required in order to understand them (especially since the approach is so computer-intensive). For this reason we provide here a thorough (but often informal) discussion of all aspects of Bayesian inference as they apply specifically to population PK/PD. We also acknowledge that while the WinBUGS software is general purpose, model specification for some types of problem, population PK/PD being a prime example, can be very difficult, to the extent that a specialized interface for describing the problem at hand is often a practical necessity. In the latter part of this paper we describe such an interface, namely PKBugs. A principal aim of the paper is to offer sufficient technical background, in an easy to follow format, that the reader may develop both the confidence and know-how to make appropriate use of the PKBugs/WinBUGS framework (or similar software) for their own data analysis needs, should they choose to adopt a Bayesian approach.

[1]  Adrian F. M. Smith,et al.  Bayesian Analysis of Linear and Non‐Linear Population Models by Using the Gibbs Sampler , 1994 .

[2]  K. Cowles,et al.  CODA: convergence diagnosis and output analysis software for Gibbs sampling output , 1995 .

[3]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[4]  David J. Lunn,et al.  The Pharmacokinetics of Saquinavir: A Markov Chain Monte Carlo Population Analysis , 1998, Journal of Pharmacokinetics and Biopharmaceutics.

[5]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[6]  David J. Spiegelhalter,et al.  Bayesian analysis in expert systems , 1993 .

[7]  Philip C. Spector.  Introduction to S and S-Plus , 1995 .

[8]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[9]  G. Grimmett,et al.  Probability and random processes , 2002 .

[10]  R. Kass,et al.  Reference Bayesian Methods for Generalized Linear Mixed Models , 2000 .

[11]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[12]  Walter R. Gilks,et al.  Full conditional distributions , 1995 .

[13]  David J. Lunn,et al.  Markov Chain Monte Carlo Techniques for Studying Interoccasion and Intersubject Variability: Application to Pharmacokinetic Data , 1997 .

[14]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[15]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[16]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[17]  M. O. Karlsson,et al.  The importance of modeling interoccasion variability in population pharmacokinetic analyses , 1993, Journal of Pharmacokinetics and Biopharmaceutics.

[18]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[19]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[20]  G. B. Smith,et al.  Preface to S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images” , 1987 .

[21]  L Aarons,et al.  Software for Population Pharmacokinetics and Pharmacodynamics , 1999, Clinical pharmacokinetics.

[22]  Dani Gamerman,et al.  Statistical inference : an integrated approach , 1999 .

[23]  Stuart L. Beal,et al.  Ways to Fit a PK Model with Some Data Below the Quantification Limit , 2001, Journal of Pharmacokinetics and Pharmacodynamics.

[24]  M. Kenward,et al.  Informative Drop‐Out in Longitudinal Data Analysis , 1994 .

[25]  Adrian Dunne,et al.  Analysis of Nonrandomly Censored Ordered Categorical Longitudinal Data from Analgesic Trials , 1997 .

[26]  A. Gelfand,et al.  Inequalities between expected marginal log‐likelihoods, with implications for likelihood‐based model complexity and comparison measures , 2003 .

[27]  J. E. Bennett,et al.  A comparison of a bayesian population method with two methods as implemented in commercially available software , 1996, Journal of Pharmacokinetics and Biopharmaceutics.

[28]  Radford M. Neal.  Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function , 1997 .

[29]  Christian P. Robert,et al.  MCMC Convergence Diagnostics : A « Reviewww » , 1998 .

[30]  A. P. Dawid,et al.  Independence properties of directed Markov fields. Networks, 20, 491-505 , 1990 .

[31]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[32]  H. Akaike.  A new look at the statistical model identification , 1974 .

[33]  David J. Spiegelhalter,et al.  Estimation of population pharmacokinetics using the Gibbs sampler , 1995, Journal of Pharmacokinetics and Biopharmaceutics.

[34]  Radford M. Neal,et al.  Suppressing Random Walks in Markov Chain Monte Carlo Using Ordered Overrelaxation , 1995, Learning in Graphical Models.

[35]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[36]  J. Q. Smith,et al.  1. Bayesian Statistics 4 , 1993 .

[37]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[38]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[39]  D. Spiegelhalter,et al.  Bayesian Analysis of Realistically Complex Models , 1996 .

[40]  A W Kelman,et al.  Population pharmacokinetics of gentamicin in neonates. , 1988, Developmental pharmacology and therapeutics.

[41]  Jon Wakefield,et al.  An Expected Loss Approach to the Design of Dosage Regimens Via Sampling‐Based Methods , 1994 .

[42]  Adelchi Azzalini,et al.  Statistical Inference: An Integrated Approach. Helio S. Migon and Dani Gamerman, Arnold, London, 1999. No. of pages: ix+262. Price: £24.99. ISBN 0‐340‐740590 , 2001 .

[43]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[44]  Kerrie Mengersen,et al.  [Bayesian Computation and Stochastic Systems]: Rejoinder , 1995 .

[45]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .