Constrained optimal designs

Lee, Carl M.-S.

doi:10.1016/0378-3758(88)90114-0

Cited by 37 publications

(10 citation statements)

References 54 publications

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“…From this theorem it follows that a necessary and sufficient condition for optimality of 5* is existence of U*E U such that while a((*) = 0. In addition, almost everywhere in supp (*, A number of similar examples for various optimality criteria can be found in Lee, 1988.…”

Section: Nonlinear Convex Constraints and Linearizationmentioning

confidence: 97%

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Invited Discussion Paper Constrained Optimization of Experimental Design

Cook

Федоров

1995

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This is an attempt to discuss various approaches developed in experimental design when constraints are imposed. These constraints may be on the total cost of the experiment, the location of the supporting point, the value of auxiliary objective functions, and so on. The basic idea of the paper is that all corresponding optimization problems can be imbedded in the convex theory of experimental design. Part 1 is concerned with the properties of optimal designs, while Part 2 is devoted mainly to numerical methods.We have tried to avoid details, emphasizing ideas rather than technicalities. This is not intended as a literature review. The authors subjectively surely left many excellent papers behind.A M S 1991 subject classifications: Primary 62KO5.

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Section: Nonlinear Convex Constraints and Linearizationmentioning

confidence: 97%

“…The analysis of (1 1) is mainly based on ideas of Theorem 2 and on the possibility of linearization of @(t) near an optimal design (compare with Gaivoronski, 1984 andLee, 1988). …”

Section: Nonlinear Convex Constraints and Linearizationmentioning

confidence: 99%

Invited Discussion Paper Constrained Optimization of Experimental Design

Cook

Федоров

1995

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“…Stigler [5], Lauter [6, 7] and Lee [8, 9] were early attempts to formalize the procedure. Most were concerned with polynomial regression problems.…”

Section: Multiple-objective Optimal Designsmentioning

confidence: 99%

Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Hyun

Wong

2015

The International Journal of Biostatistics

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We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.

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“…In this case, one may require that the design deliver at least 90% efficiency for estimating b and subject to this constraint devote the rest of the resources to estimating a. This is an example of a constrained optimal design discussed seminally in Stigler (1971), Studden (1982) and Lee (1988), where they considered homoscedastic polynomial models. Such optimal designs are easy to motivate and interpret but usually they are difficult to find.…”

Section: Optimal Designmentioning

confidence: 99%

Optimal designs for estimating critical effective dose under model uncertainty in a dose response study

Dette

Pepelyshev

Shpilev

et al. 2009

Statistics and Its Interface

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Provided in Cooperation withToxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is the first to address design issues for this popular class of models among toxicologists. Specifically we construct a variety of optimal designs under model uncertainty and study their properties for estimating the critical effective dose (CED), which is model dependent. Two types of optimal designs are proposed: one type maximizes the minimum of efficiencies for estimating the CED regardless which member in the class of models is the appropriate model, and (ii) dual-objectives optimal design that simultaneously selects the most appropriate model and provide the best estimates for CED at the same time. We compare relative efficiencies of these optimal designs and other commonly used designs for estimating CED. To facilitate use of these designs, we have constructed a website that practitioners can generate tailor-made designs for their settings.Keyword and phrases: compound optimal design, critical effect size, local optimal design, maximin optimal design, model discrimination, robust design.

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Constrained optimal designs

Cited by 37 publications

References 54 publications

Invited Discussion Paper Constrained Optimization of Experimental Design

Invited Discussion Paper Constrained Optimization of Experimental Design

Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Optimal designs for estimating critical effective dose under model uncertainty in a dose response study

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