Optimal Weights for Experimental Designs on Linearly Independent Support Points

Pukelsheim, Friedrich; Torsney, Ben

doi:10.1214/aos/1176348265

Cited by 88 publications

(46 citation statements)

References 13 publications

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“…For any choice of α, β = 0 and any model with Fisher information (2.1) there exists a c-optimal design for estimating β with exactly two support points. From Pukelsheim and Torsney (1991), we obtain an expression for the optimal weights, for example, a c-optimal design ξ * for β with support points x * 1 and x * 2 is given by…”

Section: C-optimal Designsmentioning

confidence: 99%

Optimal designs for two-parameter nonlinear models with application to survival models

Konstantinou

Biedermann²,

Kimber³

2014

STAT SINICA

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Censoring may occur in many industrial or biomedical 'time to event' experiments. Efficient designs for such experiments are needed but finding such designs can be problematic since the statistical models involved will usually be nonlinear, making the optimal choice of design parameter dependent. We provide analytical characterisations of locally D-and c-optimal designs for a large class of models. Our results are illustrated using the natural proportional hazards parameterisation of the exponential regression model, thus reducing the numerical effort for design search substantially. We also determine designs based on standardised optimality criteria when a range of parameter values is provided by the experimenter. Different censoring mechanisms are incorporated and the robustness of designs against parameter misspecification is assessed. We demonstrate that, unlike traditional designs, the designs found perform well across a broad range of scenarios.

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Section: C-optimal Designsmentioning

confidence: 99%

Optimal designs for two-parameter nonlinear models with application to survival models

Konstantinou

Biedermann²,

Kimber³

2014

STAT SINICA

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“…Again, we derive locally optimal designs with respect to arbitrary optimality criteria from the family of information functions. We also utilize some results of Pukelsheim and Torsney (1991) to derive formulas for the weights of the optimal designs with respect to a broad class of criteria, the so-called matrix means, among which we find the most commonly applied optimality criteria such as the D-, A-, E-and the T -criterion. To show the practical relevance of this approach, we apply our results in Section 4 towards the re-designing of the dose ranging trial conducted at the Merck Research Laboratories (Zeng and Zhu, 1997).…”

Section: Introductionmentioning

confidence: 99%

Optimal Designs for Dose–Response Models With Restricted Design Spaces

Biedermann

Dette

Zhu

2006

Journal of the American Statistical Association

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In dose response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve. The underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form. These include the fundamental binary response models -the logit and the probit as well as the skewed versions of these models. The results are illustrated through the re-design of a dose ranging trial conducted at the Merck Research Laboratories (Zeng and Zhu, 1997). This work is a generalization of the results of Dai and Zhu (2002) in terms of the design interval, the underlying dose response curve and the optimality criterion.

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“…for all 0 ≤ x 1 < x 2 < x 3 ≤ T, and we obtain from Theorem 7.7 (Chap X) in Karlin and Studden (1966) that the local D 1 -optimal design is supported at the Chebyshev points. Finally, the assertion regarding the weights of the local D 1 -optimal design follows from Pukelsheim and Torsney (1991). 2 Proof of Lemma 2.4.…”

Section: Discussionmentioning

confidence: 94%

Efficient experimental designs for sigmoidal growth models

Dette¹,

Pepelyshev²

2008

Journal of Statistical Planning and Inference

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For the Weibull-and Richards-regression model robust designs are determined by maximizing a minimum of D-or D 1 -efficiencies, taken over a certain range of the non-linear parameters. It is demonstrated that the derived designs yield a satisfactory solution of the optimal design problem for this type of model in the sense that these designs are efficient and robust with respect to misspecification of the unknown parameters. Moreover, the designs can also be used for testing the postulated form of the regression model against a simplified sub-model.

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Optimal Weights for Experimental Designs on Linearly Independent Support Points

Cited by 88 publications

References 13 publications

Optimal designs for two-parameter nonlinear models with application to survival models

Optimal designs for two-parameter nonlinear models with application to survival models

Optimal Designs for Dose–Response Models With Restricted Design Spaces

Efficient experimental designs for sigmoidal growth models

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