Optimal Design for Nonlinear Response Models

Optimal Design for Nonlinear Response Models

Author: Valerii V. Fedorov

Publisher: CRC Press

Published: 2013-07-15

Total Pages: 404

ISBN-13: 1439821518

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Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors’ many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design—such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints—are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The authors address all of these issues through many examples in the book.


Optimal Design of Experiments

Optimal Design of Experiments

Author: Friedrich Pukelsheim

Publisher: SIAM

Published: 2006-04-01

Total Pages: 527

ISBN-13: 0898716047

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Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.


Functional Approach to Optimal Experimental Design

Functional Approach to Optimal Experimental Design

Author: Viatcheslav B. Melas

Publisher: Springer Science & Business Media

Published: 2006-04-20

Total Pages: 337

ISBN-13: 0387316108

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The present book is devoted to studying optimal experimental designs for a wide class of linear and nonlinear regression models. This class includes polynomial, trigonometrical, rational, and exponential models as well as many particular models used in ecology and microbiology. As the criteria of optimality, the well known D-, E-, and c-criteria are implemented. The main idea of the book is to study the dependence of optimal - signs on values of unknown parameters and on the bounds of the design interval. Such a study can be performed on the base of the Implicit Fu- tion Theorem, the classical result of functional analysis. The idea was ?rst introduced in the author’s paper (Melas, 1978) for nonlinear in parameters exponential models. Recently, it was developed for other models in a n- ber of works (Melas (1995, 2000, 2001, 2004, 2005), Dette, Melas (2002, 2003), Dette, Melas, Pepelyshev (2002, 2003, 2004b), and Dette, Melas, Biederman (2002)). Thepurposeofthepresentbookistobringtogethertheresultsobtained and to develop further underlying concepts and tools. The approach, m- tioned above, will be called the functional approach. Its brief description can be found in the Introduction. The book contains eight chapters. The ?rst chapter introduces basic concepts and results of optimal design theory, initiated mainly by J.Kiefer.


Optimal Design of Experiments

Optimal Design of Experiments

Author: Peter Goos

Publisher: John Wiley & Sons

Published: 2011-06-28

Total Pages: 249

ISBN-13: 1119976162

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"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." —Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: How can I do screening inexpensively if I have dozens of factors to investigate? What can I do if I have day-to-day variability and I can only perform 3 runs a day? How can I do RSM cost effectively if I have categorical factors? How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? How can I include both ingredients in a mixture and processing factors in the same study? How can I design an experiment if there are many factor combinations that are impossible to run? How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? How can I take into account batch information in when designing experiments involving multiple batches? How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.


Design of Experiments in Nonlinear Models

Design of Experiments in Nonlinear Models

Author: Luc Pronzato

Publisher: Springer Science & Business Media

Published: 2013-04-10

Total Pages: 404

ISBN-13: 1461463637

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Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments. The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter. Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. A survey of algorithmic methods for the construction of optimal designs is provided.


mODa 8 - Advances in Model-Oriented Design and Analysis

mODa 8 - Advances in Model-Oriented Design and Analysis

Author: Jesus Lopez-Fidalgo

Publisher: Springer Science & Business Media

Published: 2007-05-14

Total Pages: 241

ISBN-13: 3790819522

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This volume contains the proceedings of the 8th Workshop on Model-Oriented Design and Analysis. It offers leading and pioneering work on optimal experimental designs, both from a mathematical/statistical point of view and with regard to real applications. Scientists from all over the world have contributed to this volume. Primary topics are designs for nonlinear models and applications to experimental medicine.


Pharmaceutical Statistics Using SAS

Pharmaceutical Statistics Using SAS

Author: Alex Dmitrienko

Publisher: SAS Institute

Published: 2007

Total Pages: 464

ISBN-13: 1599943573

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Introduces a range of data analysis problems encountered in drug development and illustrates them using case studies from actual pre-clinical experiments and clinical studies. Includes a discussion of methodological issues, practical advice from subject matter experts, and review of relevant regulatory guidelines.


Optimal Design for Nonlinear Response Models

Optimal Design for Nonlinear Response Models

Author: Valerii V. Fedorov

Publisher: CRC Press

Published: 2013-07-15

Total Pages: 402

ISBN-13: 1439821526

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Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of


MODA 7 - Advances in Model-Oriented Design and Analysis

MODA 7 - Advances in Model-Oriented Design and Analysis

Author: Alessandro Di Bucchianico

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 239

ISBN-13: 3790826936

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The volume contains the proceedings of the 7th Workshop on Model-Oriented Design and Analysis which has had the purpose of bringing together leading researchers in Eastern and Western Europe for an in-depth discussion of the optimal design of experiments. The papers are representative of the latest developments concerning non-linear models, computational algorithms and important applications, especially to medical statistics.