Optimal Design for Nonlinear Response Models

Fedorov, Valerii V.; Leonov, Sergei

doi:10.1201/b15054

Cited by 172 publications

(258 citation statements)

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“…The lift-one algorithm is much faster than commonly used optimization techniques (Table 2), including Nelder-Mead, quasi-Newton, conjugate-gradient, simulated annealing (for a comprehensive reference, see Nocedal and Wright (1999)), as well as popular design algorithms for similar purposes including the Fedorov-Wynn (Fedorov (1972), Fedorov andHackl (1997), Fedorov and Leonov (2014)), Multiplicative (Titterington (1976(Titterington ( , 1978, Silvey, Titterington, and Torsney (1978)), and Cocktail (Yu (2010)) algorithms. We utilized the function constrOptim in R to implement Nelder-Mead, quasi-Newton, conjugategradient, and simulated annealing algorithms.…”

Section: Lift-one Algorithm For Maximizing F (P) = |X ′ W X|mentioning

confidence: 99%

“…Theorem 1 is essentially a specialized version of the general equivalence theorem on a pre-determined finite set of design points. Unlike the usual form of the equivalence conditions (for examples, see Kiefer (1974), Pukelsheim (1993), Atkinson, Donev, and Tobias (2007), Yang (2012), Fedorov andLeonov (2014)) where the inverse matrix of X ′ W X needs to be calculated, Theorem 1 is expressed in terms of the quantities f (p), f i (1/2) and f i (0) only. These expressions are critical for the algorithms proposed later.…”

Section: Characterization Of Locally D-optimal Designsmentioning

confidence: 99%

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Optimal designs for 2k factorial experiments with binary response

Yang¹,

Mandal²,

Majumdar³

2017

STAT SINICA

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Abstract:We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and k qualitative factors each at two levels. We obtain a characterization of locally D-optimal designs. We then develop efficient numerical techniques to search for locally D-optimal designs. Using prior distributions on the parameters, we investigate EW D-optimal designs that maximize the determinant of the expected information matrix. It turns out that these designs can be obtained easily using our algorithm for locally D-optimal designs and are good surrogates for Bayes D-optimal designs. We also investigate the properties of fractional factorial designs and study robustness with respect to the assumed parameter values of locally D-optimal designs.Key words and phrases: D-optimality, EW D-optimal design, fractional factorial design, full factorial design, generalized linear model, uniform design.

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Section: Lift-one Algorithm For Maximizing F (P) = |X ′ W X|mentioning

confidence: 99%

Section: Characterization Of Locally D-optimal Designsmentioning

confidence: 99%

Optimal designs for 2k factorial experiments with binary response

Yang¹,

Mandal²,

Majumdar³

2017

STAT SINICA

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“…The predicted M F after linearisation is a block matrix with a block corresponding to derivatives of the log-likelihood with respect to the fixed effects, a block for derivatives with respect to the standard derivation terms and a block containing mixed derivatives with respect to all parameters. In our work, the block of mixed derivatives was set to 0 for linearisation, based on publications showing the better performance of the block diagonal expression compared with the full one (Mielke and Schwabe, 2010;Fedorov and Leonov, 2014;Nyberg et al, 2014).…”

Section: Fisher Information Matrixmentioning

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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“…The added value of the Bayesian approach in optimal experimental design has been demonstrated convincingly by Woods et al (2006) for generalized linear models in an industrial context and by Sándor and Wedel (2001) for binary choice models in a marketing context. In the context of the optimal design of biopharmaceutical experiments, Fedorov and Leonov (2014) mention the main advantage of Bayesian optimal designs, namely that they take into account prior uncertainty about the unknown parameters. However, they also indicate that this leads to computationally demanding optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Quadrature Methods for Bayesian Optimal Design of Experiments With Nonnormal Prior Distributions

Goos

Mylona

2017

Journal of Computational and Graphical Statistics

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Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques in order to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for non-normal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients and any other parameters that are strictly positive or have 1 upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well.

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Optimal Design for Nonlinear Response Models

Cited by 172 publications

References 0 publications

Optimal designs for 2k factorial experiments with binary response

Optimal designs for 2k factorial experiments with binary response

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

Quadrature Methods for Bayesian Optimal Design of Experiments With Nonnormal Prior Distributions

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