{"product_id":"an-introduction-to-optimal-designs-for-social-and-biomedical-research-isbn-9780470694503","title":"An Introduction to Optimal Designs for Social and Biomedical Research","description":"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.  \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eThis Book:\u003c\/p\u003e \u003cul type=\"disc\"\u003e \u003cli\u003eIntroduces optimal experimental design in an accessible format.\u003c\/li\u003e \u003cli\u003eProvides guidelines for practitioners to increase the efficiency of their designs, and demonstrates how optimal designs can reduce a study’s costs.\u003c\/li\u003e \u003cli\u003eDiscusses the merits of optimal designs and compares them with commonly used designs.\u003c\/li\u003e \u003cli\u003eTakes the reader from simple linear regression models to advanced designs for multiple linear regression and nonlinear models in a systematic manner.\u003c\/li\u003e \u003cli\u003eIllustrates design techniques with practical examples from social and biomedical research to enhance the reader’s understanding.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eResearchers 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. \u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgements xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to designs 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Stages of the research process 4\u003c\/p\u003e \u003cp\u003e1.2.1 Choice of a ‘good’ design 5\u003c\/p\u003e \u003cp\u003e1.3 Research design 6\u003c\/p\u003e \u003cp\u003e1.3.1 Choice of independent variables and levels 6\u003c\/p\u003e \u003cp\u003e1.3.2 Units of analysis 6\u003c\/p\u003e \u003cp\u003e1.3.3 Variables 7\u003c\/p\u003e \u003cp\u003e1.3.4 Replication 8\u003c\/p\u003e \u003cp\u003e1.4 Types of research designs 8\u003c\/p\u003e \u003cp\u003e1.5 Requirements for a ‘good’ design 9\u003c\/p\u003e \u003cp\u003e1.5.1 Statistical conclusion validity 10\u003c\/p\u003e \u003cp\u003e1.5.2 Internal validity 12\u003c\/p\u003e \u003cp\u003e1.5.3 Control of (unwanted) variation 13\u003c\/p\u003e \u003cp\u003e1.6 Ethical aspects of design choice 16\u003c\/p\u003e \u003cp\u003e1.7 Exact versus approximate designs 17\u003c\/p\u003e \u003cp\u003e1.8 Examples 19\u003c\/p\u003e \u003cp\u003e1.8.1 Radiation dosage example 19\u003c\/p\u003e \u003cp\u003e1.8.2 Designs for the Poggendorff and Ponzo illusion experiments 20\u003c\/p\u003e \u003cp\u003e1.8.3 Uncertainty about best fitting regression models 22\u003c\/p\u003e \u003cp\u003e1.8.4 Designs for a priori contrasts among composite faces 23\u003c\/p\u003e \u003cp\u003e1.8.5 Designs for calibration of item parameters in item response theory models 24\u003c\/p\u003e \u003cp\u003e1.9 Summary 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Designs for simple linear regression 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Design problem for a linear model 27\u003c\/p\u003e \u003cp\u003e2.1.1 The design 28\u003c\/p\u003e \u003cp\u003e2.1.2 The linear regression model 31\u003c\/p\u003e \u003cp\u003e2.1.3 Estimation of parameters and efficiency 32\u003c\/p\u003e \u003cp\u003e2.2 Designs for radiation-dosage example 35\u003c\/p\u003e \u003cp\u003e2.3 Relative efficiency and sample size 36\u003c\/p\u003e \u003cp\u003e2.4 Simultaneous inference 37\u003c\/p\u003e \u003cp\u003e2.5 Optimality criteria 39\u003c\/p\u003e \u003cp\u003e2.5.1 D-optimality criterion 40\u003c\/p\u003e \u003cp\u003e2.5.2 A-optimality criterion 41\u003c\/p\u003e \u003cp\u003e2.5.3 G-optimality criterion 41\u003c\/p\u003e \u003cp\u003e2.5.4 E-optimality criterion 43\u003c\/p\u003e \u003cp\u003e2.5.5 Number of distinct design points 43\u003c\/p\u003e \u003cp\u003e2.6 Relative efficiency 44\u003c\/p\u003e \u003cp\u003e2.7 Matrix formulation of designs for linear regression 44\u003c\/p\u003e \u003cp\u003e2.8 Summary 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Designs for multiple linear regression analysis 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Design problem for multiple linear regression 51\u003c\/p\u003e \u003cp\u003e3.1.1 The design 52\u003c\/p\u003e \u003cp\u003e3.1.2 The multiple linear regression model 54\u003c\/p\u003e \u003cp\u003e3.1.3 Estimation of parameters and efficiency 54\u003c\/p\u003e \u003cp\u003e3.2 Designs for vocabulary-growth study 56\u003c\/p\u003e \u003cp\u003e3.3 Relative efficiency and sample size 60\u003c\/p\u003e \u003cp\u003e3.4 Simultaneous inference 61\u003c\/p\u003e \u003cp\u003e3.5 Optimality criteria for a subset of parameters 62\u003c\/p\u003e \u003cp\u003e3.6 Relative efficiency 64\u003c\/p\u003e \u003cp\u003e3.7 Designs for polynomial regression model 65\u003c\/p\u003e \u003cp\u003e3.7.1 Exact D-optimal designs for a quadratic regression model 69\u003c\/p\u003e \u003cp\u003e3.7.2 Scale dependency of A- and E-optimality criteria 71\u003c\/p\u003e \u003cp\u003e3.8 The Poggendorff and Ponzo illusion study 71\u003c\/p\u003e \u003cp\u003e3.9 Uncertainty about best fitting regression models 76\u003c\/p\u003e \u003cp\u003e3.10 Matrix notation of designs for multiple regression models 79\u003c\/p\u003e \u003cp\u003e3.10.1 Design for regression models with two independent variables 80\u003c\/p\u003e \u003cp\u003e3.10.2 Design for regression models with two non-additive independent variables 82\u003c\/p\u003e \u003cp\u003e3.11 Summary 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Designs for analysis of variance models 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 A typical design problem for an analysis of variance model 87\u003c\/p\u003e \u003cp\u003e4.1.1 The design 89\u003c\/p\u003e \u003cp\u003e4.1.2 The analysis of variance model 90\u003c\/p\u003e \u003cp\u003e4.1.3 Formulation of an ANOVA model as a regression model 91\u003c\/p\u003e \u003cp\u003e4.2 Estimation of parameters and efficiency 95\u003c\/p\u003e \u003cp\u003e4.2.1 Measures of uncertainty 96\u003c\/p\u003e \u003cp\u003e4.3 Simultaneous inference and optimality criteria 97\u003c\/p\u003e \u003cp\u003e4.4 Designs for groups under stress study 98\u003c\/p\u003e \u003cp\u003e4.4.1 A priori planned unequal sample sizes 99\u003c\/p\u003e \u003cp\u003e4.4.2 Not planned unequal sample sizes 100\u003c\/p\u003e \u003cp\u003e4.5 Specific hypotheses and contrasts 101\u003c\/p\u003e \u003cp\u003e4.5.1 Loss of efficiency and power 103\u003c\/p\u003e \u003cp\u003e4.6 Designs for the composite faces study 106\u003c\/p\u003e \u003cp\u003e4.7 Balanced designs versus unbalanced designs 109\u003c\/p\u003e \u003cp\u003e4.8 Matrix notation for Groups under Stress study 109\u003c\/p\u003e \u003cp\u003e4.9 Summary 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Designs for logistic regression models 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Design problem for logistic regression 113\u003c\/p\u003e \u003cp\u003e5.2 The design 114\u003c\/p\u003e \u003cp\u003e5.3 The logistic regression model 115\u003c\/p\u003e \u003cp\u003e5.3.1 Design for a single dichotomous independent variable 116\u003c\/p\u003e \u003cp\u003e5.3.2 Design for multiple qualitative independent variables 122\u003c\/p\u003e \u003cp\u003e5.3.3 Design for a single quantitative independent variable 125\u003c\/p\u003e \u003cp\u003e5.3.4 Design for two independent quantitative variables 130\u003c\/p\u003e \u003cp\u003e5.4 Approaches to deal with local optimality 133\u003c\/p\u003e \u003cp\u003e5.5 Designs for calibration of item parameters in item response theory models 134\u003c\/p\u003e \u003cp\u003e5.6 Matrix formulation of designs for logistic regression 137\u003c\/p\u003e \u003cp\u003e5.6.1 Hours of practice experiment 138\u003c\/p\u003e \u003cp\u003e5.6.2 Problem solving study 140\u003c\/p\u003e \u003cp\u003e5.7 Summary 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Designs for multilevel models 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Design problem for multilevel models 143\u003c\/p\u003e \u003cp\u003e6.1.1 The design 144\u003c\/p\u003e \u003cp\u003e6.1.2 Validity considerations 146\u003c\/p\u003e \u003cp\u003e6.2 The multilevel regression model 147\u003c\/p\u003e \u003cp\u003e6.2.1 Cluster randomization of treatment 147\u003c\/p\u003e \u003cp\u003e6.2.2 Subject randomization of treatment 149\u003c\/p\u003e \u003cp\u003e6.3 Cluster versus subject randomization 151\u003c\/p\u003e \u003cp\u003e6.4 Cost function 153\u003c\/p\u003e \u003cp\u003e6.5 Example: Nursing home study 155\u003c\/p\u003e \u003cp\u003e6.5.1 Cluster randomization 157\u003c\/p\u003e \u003cp\u003e6.5.2 Subject randomization 159\u003c\/p\u003e \u003cp\u003e6.6 Optimal design and power 160\u003c\/p\u003e \u003cp\u003e6.6.1 Power for cluster randomized design 162\u003c\/p\u003e \u003cp\u003e6.6.2 Power for multi-center design 164\u003c\/p\u003e \u003cp\u003e6.6.3 Increase of efficiency and power by including covariates 165\u003c\/p\u003e \u003cp\u003e6.6.4 Unequal sample sizes 165\u003c\/p\u003e \u003cp\u003e6.7 Design effect in multilevel surveys 166\u003c\/p\u003e \u003cp\u003e6.7.1 Values of intra-class correlation ρ 168\u003c\/p\u003e \u003cp\u003e6.7.2 Cluster randomized sampling versus simple random sampling 168\u003c\/p\u003e \u003cp\u003e6.8 Matrix formulation of the multilevel model 169\u003c\/p\u003e \u003cp\u003e6.8.1 Cluster randomization of treatment 170\u003c\/p\u003e \u003cp\u003e6.8.2 Subject randomization of treatment 172\u003c\/p\u003e \u003cp\u003e6.9 Summary 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Longitudinal designs for repeated measurement models 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Design problem for repeated measurements 175\u003c\/p\u003e \u003cp\u003e7.2 The design 179\u003c\/p\u003e \u003cp\u003e7.3 Analysis techniques for repeated measures 180\u003c\/p\u003e \u003cp\u003e7.4 The linear mixed effects model for repeated measurement data 181\u003c\/p\u003e \u003cp\u003e7.4.1 Random intercept model 182\u003c\/p\u003e \u003cp\u003e7.4.2 Random intercept and slope model 183\u003c\/p\u003e \u003cp\u003e7.5 Variance–covariance structures 184\u003c\/p\u003e \u003cp\u003e7.5.1 Compound symmetry structure 184\u003c\/p\u003e \u003cp\u003e7.5.2 Auto-correlation structure 185\u003c\/p\u003e \u003cp\u003e7.6 Estimation of parameters and efficiency 187\u003c\/p\u003e \u003cp\u003e7.6.1 Small sample behaviour of estimators 188\u003c\/p\u003e \u003cp\u003e7.7 Bone mineral density example 189\u003c\/p\u003e \u003cp\u003e7.7.1 Improvement of the longitudinal design 194\u003c\/p\u003e \u003cp\u003e7.8 Cost function 196\u003c\/p\u003e \u003cp\u003e7.9 D-optimal designs for linear mixed effects models with autocorrelated errors 200\u003c\/p\u003e \u003cp\u003e7.10 Miscellanea 207\u003c\/p\u003e \u003cp\u003e7.10.1 Homoscedasticity 207\u003c\/p\u003e \u003cp\u003e7.10.2 Uninformative dropout 208\u003c\/p\u003e \u003cp\u003e7.11 Matrix formulation of the linear mixed effects model 208\u003c\/p\u003e \u003cp\u003e7.12 Summary 211\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Two-treatment crossover designs 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Design problem for crossover studies 213\u003c\/p\u003e \u003cp\u003e8.2 The design 216\u003c\/p\u003e \u003cp\u003e8.3 Confounding treatment effects with nuisance effects 218\u003c\/p\u003e \u003cp\u003e8.4 The linear model for crossover designs 221\u003c\/p\u003e \u003cp\u003e8.5 Estimation of parameters and efficiency 223\u003c\/p\u003e \u003cp\u003e8.6 Cost and efficiency of the crossover design 223\u003c\/p\u003e \u003cp\u003e8.6.1 Cost function 226\u003c\/p\u003e \u003cp\u003e8.7 Optimal crossover designs for two treatments 229\u003c\/p\u003e \u003cp\u003e8.7.1 Some further observations 231\u003c\/p\u003e \u003cp\u003e8.8 Matrix formulation of the mixed model for crossover designs 232\u003c\/p\u003e \u003cp\u003e8.9 Summary 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Alternative optimal designs for linear models 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 237\u003c\/p\u003e \u003cp\u003e9.2 Information matrix 238\u003c\/p\u003e \u003cp\u003e9.3 DA- or Ds-optimal designs 239\u003c\/p\u003e \u003cp\u003e9.4 Extrapolation optimal design 241\u003c\/p\u003e \u003cp\u003e9.5 L-optimal designs 242\u003c\/p\u003e \u003cp\u003e9.6 Bayesian optimal designs 244\u003c\/p\u003e \u003cp\u003e9.7 Minimax optimal design 247\u003c\/p\u003e \u003cp\u003e9.8 Multiple-objective optimal designs 250\u003c\/p\u003e \u003cp\u003e9.8.1 Constrained optimal design 251\u003c\/p\u003e \u003cp\u003e9.8.2 Compound optimal design 253\u003c\/p\u003e \u003cp\u003e9.9 Summary 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Optimal designs for nonlinear models 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 257\u003c\/p\u003e \u003cp\u003e10.2 Linear models versus nonlinear models 258\u003c\/p\u003e \u003cp\u003e10.2.1 The Arrhenius equation 258\u003c\/p\u003e \u003cp\u003e10.2.2 The compartmental model 259\u003c\/p\u003e \u003cp\u003e10.2.3 The Michaelis–Menten model 260\u003c\/p\u003e \u003cp\u003e10.2.4 The Emax model 261\u003c\/p\u003e \u003cp\u003e10.3 Design issues for nonlinear models 261\u003c\/p\u003e \u003cp\u003e10.3.1 Local optimality 262\u003c\/p\u003e \u003cp\u003e10.4 Alternative optimal designs with examples 265\u003c\/p\u003e \u003cp\u003e10.4.1 DA or Ds-optimal design 265\u003c\/p\u003e \u003cp\u003e10.4.2 Extrapolation optimal design 266\u003c\/p\u003e \u003cp\u003e10.4.3 Optimal design for estimating percentiles 266\u003c\/p\u003e \u003cp\u003e10.5 Bayesian optimal designs 267\u003c\/p\u003e \u003cp\u003e10.6 Minimax optimal design 269\u003c\/p\u003e \u003cp\u003e10.7 Multiple-objective optimal designs 271\u003c\/p\u003e \u003cp\u003e10.8 Optimal design for model discrimination 273\u003c\/p\u003e \u003cp\u003e10.9 Summary 275\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Resources for the construction of optimal designs 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 277\u003c\/p\u003e \u003cp\u003e11.2 Sequential construction of optimal designs 278\u003c\/p\u003e \u003cp\u003e11.3 Exchange of design points 283\u003c\/p\u003e \u003cp\u003e11.3.1 Exchange algorithms 283\u003c\/p\u003e \u003cp\u003e11.4 Other algorithms 284\u003c\/p\u003e \u003cp\u003e11.5 Optimal design software 285\u003c\/p\u003e \u003cp\u003e11.6 A web site for finding optimal designs 286\u003c\/p\u003e \u003cp\u003e11.6.1 Optimal designs for the Michaelis–Menten and Emax models 288\u003c\/p\u003e \u003cp\u003e11.6.2 Optimal designs for discriminating among toxicological models 290\u003c\/p\u003e \u003cp\u003e11.7 Summary 294\u003c\/p\u003e \u003cp\u003eReferences 295\u003c\/p\u003e \u003cp\u003eAuthor Index 313\u003c\/p\u003e \u003cp\u003eSubject Index 319\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMartijn Berger, Department of Methodology and Statistics, University of Maastricht, The Netherlands\u003c\/b\u003e\u003cbr\u003eProfessor 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 \u003ci\u003eEncyclopedia of Statistics in Behavioural Science\u003c\/i\u003e, and the 2005 book \u003ci\u003eApplied Optimal Designs\u003c\/i\u003e, co-authored with Weng Kee Wong.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eWeng Kee Wong, Department of Biostatistics, University of California - Los Angeles, USA\u003c\/b\u003e\u003cbr\u003eOne 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 \u003ci\u003eApplied Optimal Designs\u003c\/i\u003e, 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 \u003ci\u003eBiometrics\u003c\/i\u003e.\u003c\/p\u003e  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.  \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eThis Book:\u003c\/p\u003e \u003cul type=\"disc\"\u003e \u003cli\u003eIntroduces optimal experimental design in an accessible format.\u003c\/li\u003e \u003cli\u003eProvides guidelines for practitioners to increase the efficiency of their designs, and demonstrates how optimal designs can reduce a study’s costs.\u003c\/li\u003e \u003cli\u003eDiscusses the merits of optimal designs and compares them with commonly used designs.\u003c\/li\u003e \u003cli\u003eTakes the reader from simple linear regression models to advanced designs for multiple linear regression and nonlinear models in a systematic manner.\u003c\/li\u003e \u003cli\u003eIllustrates design techniques with practical examples from social and biomedical research to enhance the reader’s understanding.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eResearchers 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988728856805,"sku":"NP9780470694503","price":96.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470694503.jpg?v=1761781358","url":"https:\/\/k12savings.com\/products\/an-introduction-to-optimal-designs-for-social-and-biomedical-research-isbn-9780470694503","provider":"K12savings","version":"1.0","type":"link"}