Fully Bayesian Experimental Design for Pharmacokinetic Studies

Ryan, Elizabeth G.; Drovandi, Christopher C.; Pettitt, Anthony N.

doi:10.3390/e17031063

Cited by 39 publications

(57 citation statements)

References 42 publications

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“…The applied statistician's default approach to analysing data in a Bayesian framework is to use uninformative priors. When designing an experiment, it is reasonable to assume that, generally, there is historical and/or expert opinion available to formulate an informative prior (e.g., Clyde et al, 1996, Stroud et al, 2001, Ryan et al, 2015. Therefore, the prior predictive distribution gives ranges of data values that the experimenter believes to be plausible.…”

Section: Bayesian Optimal Design Theorymentioning

confidence: 98%

Simulation-based fully Bayesian experimental design for mixed effects models

Ryan

Drovandi

Pettitt

2015

Computational Statistics & Data Analysis

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a b s t r a c tBayesian inference has commonly been performed on nonlinear mixed effects models. However, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models, especially those that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. Fully Bayesian experimental designs for nonlinear mixed effects models are presented, which involve the use of simulation-based optimal design methods to search over both continuous and discrete design spaces. The design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and can be addressed using the methods presented.

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Section: Bayesian Optimal Design Theorymentioning

confidence: 98%

Simulation-based fully Bayesian experimental design for mixed effects models

Ryan

Drovandi

Pettitt

2015

Computational Statistics & Data Analysis

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“…Results obtained from a two compartment analysis of data from Ryan et al (2014) The prior predictive distribution of this two-compartment model is shown in Fig. 8.…”

Section: Example 2: Bayesian A-optimality For One and Two Compartmentmentioning

confidence: 99%

“…We propose to re-design this study to minimise the uncertainty about population PK parameters such that differences between PK profiles for ECMO versus non-ECMO sheep can be investigated. The general form of the models considered in Ryan et al (2014) and in this paper are as follows. Let the time of blood …”

Section: Examplesmentioning

confidence: 99%

“…Data have been collected on sheep which have been treated with ECMO, and have been modelled previously by Ryan et al (2014). Each sheep was subjected to ECMO for 24 hours and infused with various antibiotic drugs.…”

Section: Examplesmentioning

confidence: 99%

“…However, unlike conventional CPB, ECMO is utilised in already critically ill patients, and lasts for days rather than hours increasing the likelihood of complications. Nonlinear random effect models for data from such trials have been considered recently (Ryan et al 2014). As the likelihood based on a value of the random effects is available analytically, these models are, in principle, straightforward to estimate, for example, via MCMC.…”

Section: Introductionmentioning

confidence: 99%

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A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

et al. 2015

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Motivated by the need to sequentially design experiments for the collection of data in batches or blocks, a new pseudo-marginal sequential Monte Carlo algorithm is proposed for random effects models where the likelihood is not analytic, and has to be approximated. This new algorithm is an extension of the idealised sequential Monte Carlo algorithm where we propose to unbiasedly approximate the likelihood to yield an efficient exact-approximate algorithm to perform inference and make decisions within Bayesian sequential design. We propose four approaches to unbiasedly approximate the likelihood: standard Monte Carlo integration; randomised quasi-Monte Carlo integration, Laplace importance sampling and a combination of Laplace importance sampling and randomised quasi-Monte Carlo. These four methods are compared in terms of the estimates of likelihood weights and in the selection of the optimal sequential designs in an important pharmacological study related to the treatment of critically ill patients. As the approaches consid-B J. M. McGree ered to approximate the likelihood can be computationally expensive, we exploit parallel computational architectures to ensure designs are derived in a timely manner.

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Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design

Beck

Dia

Espath

et al. 2020

Numerical Meth Engineering

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An optimal experimental set-up maximizes the value of data for statistical inferences and predictions. An optimal set-up is particularly important for experiments that are time consuming or expensive to perform. In the context of partial differential equations (PDEs), multilevel methods have been proven to dramatically reduce the computational complexity of their single-level counterparts. Here, two multilevel methods, which efficiently compute the expected information gain using a Kullback-Leibler divergence measure in simulation-based Bayesian optimal experimental design, are proposed. The first method is a multilevel double loop Monte Carlo (MLDLMC) with importance sampling that greatly reduces the computational work of the inner loop. The second proposed method is a multilevel double loop stochastic collocation (MLDLSC) with importance sampling, which performs a high-dimensional integration by deterministic quadrature on sparse grids. In both methods, the Laplace approximation is used as an effective means of importance sampling, and the optimal values of the method parameters are determined by minimizing the average computational work, subject to a desired error tolerance. The computational efficiencies of the methods are demonstrated by computing the expected information gain from an electrical impedance tomography experiment where the fiber orientation in composite laminate materials are inferred through Bayesian inversion. MLDLSC performs better than MLDLMC when the regularity of the underlying computational model, with respect to the additive noise and the unknown parameters, can be exploited.

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Fully Bayesian Experimental Design for Pharmacokinetic Studies

Cited by 39 publications

References 42 publications

Simulation-based fully Bayesian experimental design for mixed effects models

Simulation-based fully Bayesian experimental design for mixed effects models

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design

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