An Introduction to Optimal Designs for Social and Biomedical Research

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.

Preface. 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. 4.5 Specific hypotheses and contrasts. 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 Variance-covariance 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 Matrix formulation of the linear mixed effects model. 7. 12 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. 8.7 Optimal crossover designs for two treatments. 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. 10 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. 11 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. Author Index. Subject Index.