Fully Bayesian Experimental Design for Pharmacokinetic Studies

Elizabeth Gabrielle Ryan, Christopher Drovandi, Anthony Pettitt

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)
135 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)1063-1089
JournalEntropy
Volume17
Issue number3
DOIs
Publication statusPublished - 5 Mar 2015

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