Optimum Design of Experiments for Enzyme Inhibition Kinetic Models

Bogacka, Barbara; Patan, Maciej; Johnson, Phylis; Youdim, Kuresh A.; Atkinson, Anthony C.

doi:10.1080/10543406.2010.489979

Cited by 21 publications

(28 citation statements)

References 13 publications

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“…The model parameters are V, K m , K ic , K iu , and Bogacka et al (2011) found locally D-optimal designs for these four enzyme inhibition kinetic models. The locally Doptimal designs do not depend on V because this parameter enters the four models linearly.…”

Section: Standardized Maximin Optimal Designs For Enzyme Inhibition Kmentioning

confidence: 99%

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Minimax optimal designs via particle swarm optimization methods

et al. 2014

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Particle swarm optimization (PSO) techniques are widely used in applied fields to solve challenging optimization problems but they do not seem to have made an impact in mainstream statistical applications hitherto. PSO methods are popular because they are easy to implement and use, and seem increasingly capable of solving complicated problems without requiring any assumption on the objective function to be optimized. We modify PSO techniques to find minimax optimal designs, which have been notoriously challenging to find to date even for linear models, and show that the PSO methods can readily generate a variety of minimax optimal designs in a novel and interesting way, including adapting the algorithm to generate standardized maximin optimal designs.

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Section: Standardized Maximin Optimal Designs For Enzyme Inhibition Kmentioning

confidence: 99%

“…We follow the set up in Bogacka et al (2011) 4,5], which includes the nominal values used in their study for an application using the Competitive Inhibition model. The nested PSO-generated standardized maximin optimal designs are shown in Table 2 along with their efficiency lower bounds.…”

Section: Standardized Maximin Optimal Designs For Enzyme Inhibition Kmentioning

confidence: 99%

Minimax optimal designs via particle swarm optimization methods

et al. 2014

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“…In particular, we produce a standardized maximin optimal design with 4 points for a 3-parameter inhibition model, thereby invalidating the assumption made in Ref. [25] that locally D -optimal designs for the inhibition models are minimally supported. Section 4 offers conclusions.…”

Section: Introductionmentioning

confidence: 92%

“…[25] provided interpretation of the parameters in the 4 inhibition models, which all have two common parameters V max and km . The competitive model and the noncompetitive models has a common third parameter kic .…”

Section: Standardized Maximin Optimal Designs For Enzyme Inhibitiomentioning

confidence: 99%

“…[25], the nominal values for the parameters are ( V max , km, kic, kiu ) = (7.2975, 4.3859, 2.5822, 5) and the design space is X = S × I = [0,30] × [0,60]. They reported locally D -optimal designs for three 3-parameter inhibition models and a fourth for mixed-type inhibition, which has an additional parameter.…”

Section: Standardized Maximin D-optimal Designs For Inhibition Modelsmentioning

confidence: 99%

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Standardized maximim D -optimal designs for enzyme kinetic inhibition models

Chen

Tung

et al. 2017

Chemometrics and Intelligent Laboratory Systems

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Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters. An alternative is the maximin approach that allows the user to specify a range of values for each parameter of interest. However, the maximin approach is difficult because we first have to determine the locally optimal design for each set of nominal values before maximin types of optimal designs can be found via a nested optimization process. We show that particle swarm optimization (PSO) techniques can solve such complex optimization problems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae for standardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact and nonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibition models are not necessarily supported at a minimum number of points. To facilitate use of such designs, we create a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs.

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A design criterion for symmetric model discrimination based on flexible nominal sets

Harman

Müller

2020

Biometrical J

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Experimental design applications for discriminating between models have been hampered by the assumption to know beforehand which model is the true one, which is counter to the very aim of the experiment. Previous approaches to alleviate this requirement were either symmetrizations of asymmetric techniques, or Bayesian, minimax and sequential approaches.Here we present a genuinely symmetric criterion based on a linearized distance between meanvalue surfaces and the newly introduced tool of flexible nominal confidence sets. We demonstrate the computational efficiency of the approach using the proposed criterion and provide a Monte-Carlo evaluation of its discrimination performance on the basis of the likelihood ratio. An application for a pair of competing models in enzyme kinetics is given.

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Optimum Design of Experiments for Enzyme Inhibition Kinetic Models

Cited by 21 publications

References 13 publications

Minimax optimal designs via particle swarm optimization methods

Minimax optimal designs via particle swarm optimization methods

Standardized maximim D -optimal designs for enzyme kinetic inhibition models

A design criterion for symmetric model discrimination based on flexible nominal sets

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