An Introduction to Optimal Designs for Social and Biomedical Research

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.

Optimal design theory combats the problems researchers find when trying to meet the necessary objectives of experimental research. It can help reduce the costs involved, and means fewer observations are needed to find real effects, leading to ethical benefits such as smaller sample sizes. This book will provide guidelines to implement such increased efficiency in the readers research. Although there has been a growth in the literature on optimal design in social and biomedical research, there are few books on optimal designs, and currently none aimed at this market. Previous texts have focused on analytical solutions, and required a strong mathematical background, largely excluding this books target audience. This book will take a less formal approach, making the subject more accessible, with only a basic knowledge of statistical methods and minimal calculus required. Each chapter will follow a similar, user-friendly pattern, introducing the statistical model, discussing design issues, and then developing the optimal design. Beginning with an introduction to the stages of research, each subsequent chapter is dedicated to a specific design. The reader is guided from basic designs for simple linear models, through to designs for advanced repeated measures and nonlinear models. Mathematical formulae will be presented when it enhances understanding of the material, and references for technical details, will be provided. Practical examples and problems from relevant social and biomedical research will further enhance the readers understanding, and web-based resources for constructing designs and determining sample size are provided in a final, summarizing chapter.  

Preface xi Acknowledgements 1 Introduction to designs 1.1 Introduction 1.2 Stages of the research process 1.3 Research design 1.4 Types of research designs 1.5 Requirements for a good design 1.6 Ethical aspects of design choice 1.7 Exact versus approximate designs 1.8 Examples 1.9 Summary 2 Designs for simple linear regression 2.1 Design problem for a linear model 2.2 Designs for radiation-dosage example 2.3 Relative efficiency and sample size 2.4 Simultaneous inference 2.5 Optimality criteria 2.6 Relative efficiency 2.7 Matrix formulation of designs for linear regression 2.8 Summary 3 Designs for multiple linear regression analysis 3.1 Design problem for multiple linear regression 3.2 Designs for vocabulary-growth study 3.3 Relative efficiency and sample size 3.4 Simultaneous inference 3.5 Optimality criteria for a subset of parameters 3.6 Relative efficiency 3.7 Designs for polynomial regression model 3.8 The Poggendorff and Ponzo illusion study 3.9 Uncertainty about best fitting regression models 3.10 Matrix notation of designs for multiple regression models 3.11 Summary 4 Designs for analysis of variance models 4.1 A typical design problem for an analysis of variance model 4.2 Estimation of parameters and efficiency 4.3 Simultaneous inference and optimality criteria 4.4 Designs for groups under stress study 4.4.1 A priori planned unequal sample sizes 4.4.2 Not planned unequal sample sizes 4.5 Specific hypotheses and contrasts 4.5.1 Loss of efficiency and power 4.6 Designs for the composite faces study 4.7 Balanced designs versus unbalanced designs 4.8 Matrix notation for Groups under Stress study 4.9 Summary 5 Designs for logistic regression models 5.1 Design problem for logistic regression 5.2 The design 5.3 The logistic regression model 5.4 Approaches to deal with local optimality 5.5 Designs for calibration of item parameters in item response theory models 5.6 Matrix formulation of designs for logistic regression 5.7 Summary 6 Designs for multilevel models 6.1 Design problem for multilevel models 6.2 The multilevel regression model 6.3 Cluster versus subject randomization 6.4 Cost function 6.5 Example: Nursing home study 6.6 Optimal design and power 6.7 Design effect in multilevel surveys 6.8 Matrix formulation of the multilevel model   6.9 Summary 7 Longitudinal designs for repeated measurement models 7.1 Design problem for repeated measurements 7.2 The design 7.3 Analysis techniques for repeated measures 7.4 The linear mixed effects model for repeated measurement data 7.5 Variancecovariance structures 7.6 Estimation of parameters and efficiency 7.7 Bone mineral density example 7.8 Cost function 7.9 D-optimal designs for linear mixed effects models with autocorrelated errors 7.10 Miscellanea 7. 11 Homoscedasticity 7. 12 Uninformative dropout 7. 13 Matrix formulation of the linear mixed effects model 7. 14 Summary 8 Two-treatment crossover designs 8.1 Design problem for crossover studies 8.2 The design 8.3 Confounding treatment effects with nuisance effects 8.4 The linear model for crossover designs 8.5 Estimation of parameters and efficiency 8.6 Cost and efficiency of the crossover design 8.6.1 Cost function 8.7 Optimal crossover designs for two treatments 8.7.1 Some further observations 8.8 Matrix formulation of the mixed model for crossover designs 8.9 Summary 9 Alternative optimal designs for linear models 9.1 Introduction 9.2 Information matrix 9.3 DA- or Ds-optimal designs 9.4 Extrapolation optimal design 9.5 L-optimal designs 9.6 Bayesian optimal designs 9.7 Minimax optimal design 9.8 Multiple-objective optimal designs 9.9 Summary Optimal designs for nonlinear models 10.1 Introduction 10.2 Linear models versus nonlinear models 10.3 Design issues for nonlinear models 10.4 Alternative optimal designs with examples 10.5 Bayesian optimal designs 10.6 Minimax optimal design 10.7 Multiple-objective optimal designs 10.8 Optimal design for model discrimination 10.9 Summary Resources for the construction of optimal designs 11.1 Introduction 11.2 Sequential construction of optimal designs 11.3 Exchange of design points 11.4 Other algorithms 11.5 Optimal design software 11.6 A web site for finding optimal designs 11.7 Summary References Further reading Index