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Open AccessArticle

Fully Bayesian Experimental Design for Pharmacokinetic Studies

1
Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane 4001, Australia
2
Biostatistics Department, Institute of Psychiatry, King's College London, London SE5 8AF, UK
3
ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane 4001, Australia
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Entropy 2015, 17(3), 1063-1089; https://doi.org/10.3390/e17031063
Received: 22 December 2014 / Revised: 9 February 2015 / Accepted: 27 February 2015 / Published: 5 March 2015
(This article belongs to the Special Issue Entropy in Experimental Design, Sensor Placement, Inquiry and Search)
Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future dataset drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature, which rapidly obtains samples from the posterior, is importance sampling, using the prior as the importance distribution. However, importance sampling from the prior will tend to break down if there is a reasonable number of experimental observations. In this paper, we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study, which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times that produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions. View Full-Text
Keywords: Bayesian design; pharmacokinetics; utility function; importance sampling; Laplace approximation Bayesian design; pharmacokinetics; utility function; importance sampling; Laplace approximation
MDPI and ACS Style

Ryan, E.G.; Drovandi, C.C.; Pettitt, A.N. Fully Bayesian Experimental Design for Pharmacokinetic Studies. Entropy 2015, 17, 1063-1089.

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