Optimal Covariate Designs
Optimal Covariate Designs

Author: Premadhis Das

Publisher: Springer

Published: 2015-07-23

Total Pages: 231

ISBN-13: 8132224612

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This book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for the construction of optimum designs using Hadamard matrices, the Kronecker product, Rao-Khatri product, mixed orthogonal arrays to name a few.

Topics in Optimal Design
Topics in Optimal Design

Author: Erkki P. Liski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 173

ISBN-13: 1461300495

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This book covers a wide range of topics in both discrete and continuous optimal designs. The topics discussed include designs for regression models, covariates models, models with trend effects, and models with competition effects. The prerequisites are a basic course in the design and analysis of experiments and some familiarity with the concepts of optimality criteria.

Theory of Optimal Designs
Theory of Optimal Designs

Author: Kirti R. Shah

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 179

ISBN-13: 1461236622

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There has been an enormous growth in recent years in the literature on discrete optimal designs. The optimality problems have been formulated in various models arising in the experimental designs and substantial progress has been made towards solving some of these. The subject has now reached a stage of completeness which calls for a self-contained monograph on this topic. The aim of this monograph is to present the state of the art and to focus on more recent advances in this rapidly developing area. We start with a discussion of statistical optimality criteria in Chapter One. Chapters Two and Three deal with optimal block designs. Row-column designs are dealt with in Chapter Four. In Chapter Five we deal with optimal designs with mixed effects models. Repeated measurement designs are considered in Chapter Six. Chapter Seven deals with some special situations and Weighing designs are dis cussed in Chapter Eight. We have endeavoured to include all the major developments that have taken place in the last three decades. The book should be of use to research workers in several areas including combinatorics as well as to the experimenters in diverse fields of applications. Since the details of the construction of the designs are available in excellent books, we have only pointed out the designs which have optimality proper ties. We believe, this will be adequate for the experimenters.

Randomization in Clinical Trials
Randomization in Clinical Trials

Author: William F. Rosenberger

Publisher: John Wiley & Sons

Published: 2004-03-24

Total Pages: 286

ISBN-13: 0471654078

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A unique overview that melds the concepts of conditionalprobability and stochastic processes into real-lifeapplications The role of randomization techniques in clinical trials has becomeincreasingly important. This comprehensive guide combines both theapplied aspects of randomization in clinical trials with aprobabilistic treatment of properties of randomization. Taking anunabashedly non-Bayesian and nonparametric approach to inference,the book focuses on the linear rank test under a randomizationmodel, with added discussion on likelihood-based inference as itrelates to sufficiency and ancillarity. Developments in stochasticprocesses and applied probability are also given where appropriate.Intuition is stressed over mathematics, but not without a cleardevelopment of the latter in the context of the former. Providing a consolidated review of the field, the book includesrelevant and practical discussions of: * The benefits of randomization in terms of reduction of bias * Randomization as a basis for inference * Covariate-adaptive and response-adaptive randomization * Current philosophies, controversies, and new developments With ample problem sets, theoretical exercises, and short computersimulations using SAS, Randomization in Clinical Trials: Theory andPractice is equally useful as a standard textbook in biostatisticsgraduate programs as well as a reliable reference forbiostatisticians in practice.

Adaptive Designs for Sequential Treatment Allocation
Adaptive Designs for Sequential Treatment Allocation

Author: Alessandro Baldi Antognini

Publisher: CRC Press

Published: 2015-04-06

Total Pages: 210

ISBN-13: 1466505761

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Adaptive Designs for Sequential Treatment Allocation presents a rigorous theoretical treatment of the results and mathematical foundation of adaptive design theory. The book focuses on designing sequential randomized experiments to compare two or more treatments incorporating information accrued along the way. The authors first introduce the terminology and statistical models most commonly used in comparative experiments. They then illustrate biased coin and urn designs that only take into account past treatment allocations as well as designs that use past data, such as sequential maximum likelihood and various types of doubly adaptive designs. The book also covers multipurpose adaptive experiments involving utilitarian choices and ethical issues. It ends with adaptive methods that include covariates in the design. The appendices present basic tools of optimal design theory and address Bayesian adaptive designs. This book helps readers fully understand the theoretical properties behind various adaptive designs. Readers are then equipped to choose the best design for their experiment.

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.

Optimum Experimental Designs, With SAS
Optimum Experimental Designs, With SAS

Author: Anthony Atkinson

Publisher: OUP Oxford

Published: 2007-05-24

Total Pages: 528

ISBN-13: 0191537942

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Experiments on patients, processes or plants all have random error, making statistical methods essential for their efficient design and analysis. This book presents the theory and methods of optimum experimental design, making them available through the use of SAS programs. Little previous statistical knowledge is assumed. The first part of the book stresses the importance of models in the analysis of data and introduces least squares fitting and simple optimum experimental designs. The second part presents a more detailed discussion of the general theory and of a wide variety of experiments. The book stresses the use of SAS to provide hands-on solutions for the construction of designs in both standard and non-standard situations. The mathematical theory of the designs is developed in parallel with their construction in SAS, so providing motivation for the development of the subject. Many chapters cover self-contained topics drawn from science, engineering and pharmaceutical investigations, such as response surface designs, blocking of experiments, designs for mixture experiments and for nonlinear and generalized linear models. Understanding is aided by the provision of "SAS tasks" after most chapters as well as by more traditional exercises and a fully supported website. The authors are leading experts in key fields and this book is ideal for statisticians and scientists in academia, research and the process and pharmaceutical industries.

Design and Analysis of Experiments, Volume 3
Design and Analysis of Experiments, Volume 3

Author: Klaus Hinkelmann

Publisher: John Wiley & Sons

Published: 2012-02-14

Total Pages: 598

ISBN-13: 0470530685

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Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues building upon the philosophical foundations of experimental design by providing important, modern applications of experimental design to the many fields that utilize them. The book also presents optimal and efficient designs for practice and covers key topics in current statistical research. Featuring contributions from leading researchers and academics, the book demonstrates how the presented concepts are used across various fields from genetics and medicinal and pharmaceutical research to manufacturing, engineering, and national security. Each chapter includes an introduction followed by the historical background as well as in-depth procedures that aid in the construction and analysis of the discussed designs. Topical coverage includes: Genetic cross experiments, microarray experiments, and variety trials Clinical trials, group-sequential designs, and adaptive designs Fractional factorial and search, choice, and optimal designs for generalized linear models Computer experiments with applications to homeland security Robust parameter designs and split-plot type response surface designs Analysis of directional data experiments Throughout the book, illustrative and numerical examples utilize SAS®, JMP®, and R software programs to demonstrate the discussed techniques. Related data sets and software applications are available on the book's related FTP site. Design and Analysis of Experiments, Volume 3 is an ideal textbook for graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, and business.

Applied Optimal Designs
Applied Optimal Designs

Author: Martijn P.F. Berger

Publisher: John Wiley & Sons

Published: 2005-03-11

Total Pages: 320

ISBN-13: 9780470856970

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There is an increasing need to rein in the cost of scientific study without sacrificing accuracy in statistical inference. Optimal design is the judicious allocation of resources to achieve the objectives of studies using minimal cost via careful statistical planning. Researchers and practitioners in various fields of applied science are now beginning to recognize the advantages and potential of optimal experimental design. Applied Optimal Designs is the first book to catalogue the application of optimal design to real problems, documenting its widespread use across disciplines as diverse as drug development, education and ground water modelling. Includes contributions covering: Bayesian design for measuring cerebral blood-flow Optimal designs for biological models Computer adaptive testing Ground water modelling Epidemiological studies and pharmacological models Applied Optimal Designs bridges the gap between theory and practice, drawing together a selection of incisive articles from reputed collaborators. Broad in scope and inter-disciplinary in appeal, this book highlights the variety of opportunities available through the use of optimal design. The wide range of applications presented here should appeal to statisticians working with optimal designs, and to practitioners new to the theory and concepts involved.

Optimum Designs for Multi-Factor Models
Optimum Designs for Multi-Factor Models

Author: Rainer Schwabe

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 132

ISBN-13: 1461240387

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In real applications most experimental situations are influenced by a large number of different factors. In these settings the design of an experiment leads to challenging optimization problems, even if the underlying relationship can be described by a linear model. Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.