An Introduction to Optimal Designs for Social and Biomedical Research

1. Auflage 2009
ISBN: 978-0-470-69450-3
Verlag: Wiley

Buch, Englisch, 346 Seiten, Format (B × H): 157 mm x 231 mm, Gewicht: 612 g

Reihe: Statistics in Practice

The increasing cost of research means that scientists are in more urgent need of optimal design theory to increase the efficiency of parameter estimators and the statistical power of their tests.
The objectives of a good design are to provide interpretable and accurate inference at minimal costs. Optimal design theory can help to identify a design with maximum power and maximum information for a statistical model and, at the same time, enable researchers to check on the model assumptions.

This Book:

- Introduces optimal experimental design in an accessible format.
- Provides guidelines for practitioners to increase the efficiency of their designs, and demonstrates how optimal designs can reduce a study’s costs.
- Discusses the merits of optimal designs and compares them with commonly used designs.
- Takes the reader from simple linear regression models to advanced designs for multiple linear regression and nonlinear models in a systematic manner.
- Illustrates design techniques with practical examples from social and biomedical research to enhance the reader’s understanding.

Researchers and students studying social, behavioural and biomedical sciences will find this book useful for understanding design issues and in putting optimal design ideas to practice.

Autoren/Hrsg.

Berger, Martijn P F

Wong, Weng-Kee

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizinische Mathematik & Informatik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizintechnik, Biomedizintechnik, Medizinische Werkstoffe
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Medizintechnik, Biomedizintechnik
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik

Inhaltsverzeichnis

Preface xi

Acknowledgements xiii

1 Introduction to designs 1

1.1 Introduction 1

1.2 Stages of the research process 4

1.2.1 Choice of a ‘good’ design 5

1.3 Research design 6

1.3.1 Choice of independent variables and levels 6

1.3.2 Units of analysis 6

1.3.3 Variables 7

1.3.4 Replication 8

1.4 Types of research designs 8

1.5 Requirements for a ‘good’ design 9

1.5.1 Statistical conclusion validity 10

1.5.2 Internal validity 12

1.5.3 Control of (unwanted) variation 13

1.6 Ethical aspects of design choice 16

1.7 Exact versus approximate designs 17

1.8 Examples 19

1.8.1 Radiation dosage example 19

1.8.2 Designs for the Poggendorff and Ponzo illusion experiments 20

1.8.3 Uncertainty about best fitting regression models 22

1.8.4 Designs for a priori contrasts among composite faces 23

1.8.5 Designs for calibration of item parameters in item response theory models 24

1.9 Summary 26

2 Designs for simple linear regression 27

2.1 Design problem for a linear model 27

2.1.1 The design 28

2.1.2 The linear regression model 31

2.1.3 Estimation of parameters and efficiency 32

2.2 Designs for radiation-dosage example 35

2.3 Relative efficiency and sample size 36

2.4 Simultaneous inference 37

2.5 Optimality criteria 39

2.5.1 D-optimality criterion 40

2.5.2 A-optimality criterion 41

2.5.3 G-optimality criterion 41

2.5.4 E-optimality criterion 43

2.5.5 Number of distinct design points 43

2.6 Relative efficiency 44

2.7 Matrix formulation of designs for linear regression 44

2.8 Summary 49

3 Designs for multiple linear regression analysis 51

3.1 Design problem for multiple linear regression 51

3.1.1 The design 52

3.1.2 The multiple linear regression model 54

3.1.3 Estimation of parameters and efficiency 54

3.2 Designs for vocabulary-growth study 56

3.3 Relative efficiency and sample size 60

3.4 Simultaneous inference 61

3.5 Optimality criteria for a subset of parameters 62

3.6 Relative efficiency 64

3.7 Designs for polynomial regression model 65

3.7.1 Exact D-optimal designs for a quadratic regression model 69

3.7.2 Scale dependency of A- and E-optimality criteria 71

3.8 The Poggendorff and Ponzo illusion study 71

3.9 Uncertainty about best fitting regression models 76

3.10 Matrix notation of designs for multiple regression models 79

3.10.1 Design for regression models with two independent variables 80

3.10.2 Design for regression models with two non-additive independent variables 82

3.11 Summary 85

4 Designs for analysis of variance models 87

4.1 A typical design problem for an analysis of variance model 87

4.1.1 The design 89

4.1.2 The analysis of variance model 90

4.1.3 Formulation of an ANOVA model as a regression model 91

4.2 Estimation of parameters and efficiency 95

4.2.1 Measures of uncertainty 96

4.3 Simultaneous inference and optimality criteria 97

4.4 Designs for groups under stress study 98

4.4.1 A priori planned unequal sample sizes 99

4.4.2 Not planned unequal sample sizes 100

4.5 Specific hypotheses and contrasts 101

4.5.1 Loss of efficiency and power 103

4.6 Designs for the composite faces study 106

4.7 Balanced designs versus unbalanced designs 109

4.8 Matrix notation for Groups under Stress study 109

4.9 Summary 111

5 Designs for logistic regression models 113

5.1 Design problem for logistic regression 113

5.2 The design 114

5.3 The logistic regression model 115

5.3.1 Design for a single dichotomous independent variable 116

5.3.2 Design for multiple qualitative independent variables 122

5.3.3 Design for a single qu

Über Autor(innen)

Martijn Berger, Department of Methodology and Statistics, University of Maastricht, The Netherlands
Professor Berger has been teaching and conducting research in this area for over 20 years. He has an extensive collection of publications to his name, including articles in a wide range of journals, a contributed chapter in Wiley's recent Encyclopedia of Statistics in Behavioural Science, and the 2005 book Applied Optimal Designs, co-authored with Weng Kee Wong.

Weng Kee Wong, Department of Biostatistics, University of California - Los Angeles, USA
One of the leading experts in the US working in this field, Professor Wong is currently conducting grant-funded research into making optimal design methods more accessible for practitioners. As well as co-authoring Applied Optimal Designs, he has published over a hundred refereed articles, in numerous journals. He has held the position of Associate Editor for many such journals, including a current, second 3-year term for Biometrics.