Bayesian Experimental Design for Nonlinear Mixed‐Effects Models with Application to HIV Dynamics

Han, Cong; Chaloner, Kathryn

doi:10.1111/j.0006-341x.2004.00148.x

Cited by 72 publications

(91 citation statements)

References 29 publications

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“…Alternatives, such as adaptive designs (Leonov and Miller, 2009;Foo and Duffull, 2012) or robust designs based on Bayesian criteria (Han and Chaloner, 2004;Dette and Pepelyshev, 2008;Gotwalt et al, 2009;Abebe et al, 2014) would be interesting to explore.…”

Section: Discussionmentioning

confidence: 99%

Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature

Nguyễn

2014

Computational Statistics & Data Analysis

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. Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature. Computational Statistics and Data Analysis, Elsevier, 2014, 80, pp.57 -69 AbstractNonlinear mixed effect models (NLMEM) are used in model-based drug development to analyse longitudinal data. To design these studies, the use of the expected Fisher information matrix (M F ) is a good alternative to clinical trial simulation. Presently, M F in NLMEM is mostly evaluated with first-order linearisation. The adequacy of this approximation is, however, influenced by model nonlinearity. Alternatives for the evaluation of M F without linearisation are proposed, based on Gaussian quadratures. The M F , expressed as the expectation of the derivatives of the log-likelihood, can be obtained by stochastic integration. The likelihood for each simulated vector of observations is approximated by Gaussian quadrature centred at 0 (standard quadrature) or at the simulated random effects (adaptive quadrature). These approaches have been implemented in R. Their relevance was compared with clinical trial simulation and linearisation, using dose-response models, with various nonlinearity levels and different number of doses per patient. When the nonlinearity was mild, three approaches based on M F gave correct predictions of standard errors, when compared with the simulation. When the nonlinearity increased, linearisation correctly predicted standard errors of fixed effects, but over-predicted, with sparse designs, standard errors of some variability terms. Meanwhile, quadrature approaches gave correct predictions of standard errors overall, but standard Gaussian quadrature was very time-consuming when there were more than two random effects. To conclude, adaptive Gaussian quadrature is a relevant alternative for the evaluation of M F for models with stronger nonlinearity, while being more computationally efficient than standard quadrature.

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Section: Discussionmentioning

confidence: 99%

Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature

Nguyễn

2014

Computational Statistics & Data Analysis

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“…Previous approaches, such as Han and Chaloner [7], have used MCMC to approximate the posterior distribution for the utility function calculations. However, Han and Chaloner [7] only investigated fixed designs, and no optimisation was performed over the design space.…”

Section: Other Methodsmentioning

confidence: 99%

“…However, Han and Chaloner [7] only investigated fixed designs, and no optimisation was performed over the design space. Whilst MCMC is useful and often appropriate for Bayesian data analysis, it may not be suitable for optimal Bayesian experimental design, as it is computationally intensive to perform MCMC to approximate the posterior distribution for each of the thousands of iterations required in the Bayesian experimental design algorithms.…”

Section: Other Methodsmentioning

confidence: 99%

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Fully Bayesian Experimental Design for Pharmacokinetic Studies

Ryan

Drovandi

Pettitt

2015

Entropy

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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.

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“…Similar criteria for uncertainty in linear models have also been considered by Läuter (1974Läuter ( , 1976 and Dette and Studden (1995). When the approach is viewed from a Bayesian perspective as, for example, by Zhou et al (2003), it may exhibit the dichotomy discussed by Etzioni and Kadane (1993) and, most recently, by Han and Chaloner (2004), that different prior distributions are used for design and analysis.…”

Section: Compromise Design Selection Criteriamentioning

confidence: 99%

Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Woods¹,

Lewis²,

Eccleston³

et al. 2006

Technometrics

133

125

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Standard factorial designs may sometimes be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments which uses a criterion that allows for uncertainty in the link function, the linear predictor or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications and their advantages over factorial and central composite designs are demonstrated.

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Bayesian Experimental Design for Nonlinear Mixed‐Effects Models with Application to HIV Dynamics

Cited by 72 publications

References 29 publications

Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature

Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature

Fully Bayesian Experimental Design for Pharmacokinetic Studies

Designs for Generalized Linear Models With Several Variables and Model Uncertainty

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