2013
DOI: 10.1080/02331888.2013.839680
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Abstract: In this paper we investigate the problem of designing experiments for weighted least squares analysis in the Michaelis Menten model. We study the structure of exact D-optimal designs in a model with an autoregressive error structure. Explicit results for locally D-optimal are derived for the case where 2 observations can be taken per subject. Additionally standardized maximin D-optimal designs are obtained in this case. The results illustrate the enormous difficulties to find exact optimal designs explicitly f… Show more

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Cited by 7 publications
(3 citation statements)
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“…A plausible strategy in this situation is to show the algorithm generates the same optimal designs that are already worked out analytically for simple cases, and then use the algorithm to find optimal designs for more complicated cases where theoretical designs are no longer available. For example, Chen et al (2015b) used PSO to generate locally Doptimal exact designs for the Michaelis-Menten model with correlated errors and confirm their numerical results with the theoretical optimal designs available from Dette and Kunert (2014) when only a couple of time points are allowed for taking measurements. Chen et al (2015b) then used PSO to generate optimal designs for a longitudinal study with more time points than those considered in Dette and Kunert (2014), where theoretical results are not available.…”
Section: Discussionmentioning
confidence: 78%
“…A plausible strategy in this situation is to show the algorithm generates the same optimal designs that are already worked out analytically for simple cases, and then use the algorithm to find optimal designs for more complicated cases where theoretical designs are no longer available. For example, Chen et al (2015b) used PSO to generate locally Doptimal exact designs for the Michaelis-Menten model with correlated errors and confirm their numerical results with the theoretical optimal designs available from Dette and Kunert (2014) when only a couple of time points are allowed for taking measurements. Chen et al (2015b) then used PSO to generate optimal designs for a longitudinal study with more time points than those considered in Dette and Kunert (2014), where theoretical results are not available.…”
Section: Discussionmentioning
confidence: 78%
“…Here V and S denotes the maximum velocity of the reaction and the concentration of the substrate, respectively, while K m is the value of S at which half of the maximum velocity V is reached, i.e., the Michaelis-Menten constant. Because of its importance the problem of designing experiments for statistical analysis based on the Michaelis-Menten model has found considerable interest in the literature and we refer to Rasch (1990); Song and Wong (1998); López-Fidalgo and Wong (2002); Dette and Biedermann (2003); Matthews and Allcock (2004) and Dette and Kunert (2014) among many others, who investigate optimal and efficient designs for the model (1.1) from different perspectives. The Michaelis-Menten model is very well justified in the absence of enzyme inhibition which are molecules that decrease the activity of enzymes.…”
Section: Introductionmentioning
confidence: 99%
“…Uciňski and Atkinson (2004) studied design for nonlinear timedependent models. Dette & Kunert (2014) studied optimal design for Michaelis-Menten model and Holland- Letz et al (2012) proposed an algorithm approach of deriving optimal design based on linear approximation.…”
Section: Introductionmentioning
confidence: 99%