Applied Optimal Designs

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. Cover Page......Page 1 Title Page......Page 2 Copyright 2005 John Wiley & Sons Ltd......Page 3 2 Optimal On-line Calibration of Testlets......Page 4 4 Designing Optimal Two-stage Epidemiological Studies......Page 5 6 Design of Experiments for Microbiological Models......Page 6 8 Restricted Optimal Design in the Measurement of Cerebral Blood Flow Using the Kety- Schmidt Technique......Page 7 10 The Optimal Design of Blocked Experiments in Industry......Page 8 Index......Page 9 List of Contributors......Page 10 Editors’ Foreword......Page 13 (i) Education......Page 17 (iv) Microbiology and Pharmaceutical research......Page 18 (vi) Environmental Science......Page 19 References......Page 20 1.1 Introduction......Page 24 1.1.2 Dichotomous response......Page 25 1.1.3 Polytomous response......Page 27 1.1.4 Information functions......Page 28 1.2 Test Design......Page 30 1.2.1 Fixed-form test design......Page 31 1.2.2 Test design for CAT......Page 34 1.3.1 Paper-and-pencil calibration......Page 35 1.3.2 CAT calibration......Page 37 1.4 Future Directions......Page 38 References......Page 39 2.1 Introduction......Page 43 2.2.1 Item response functions......Page 45 2.2.2 D-optimal design criterion......Page 46 2.3.1 Mathematical programming model......Page 47 2.3.2 Unconstrained conjugate-gradient method......Page 49 2.3.4 Gradient of log det(B;Theta,x)......Page 50 2.3.5 MCMC sequential estimation of item parameters......Page 51 2.3.6 Note on performance measures......Page 52 2.4 Simulation Results......Page 53 2.5 Discussion......Page 57 Appendix A Derivation of the Gradient of log det M(B;Theta;x)......Page 60 Appendix B Projection on the Null Space of the Constraint Matrix......Page 61 References......Page 63 3.1 Introduction......Page 66 3.2 Conjoint Analysis......Page 69 3.3 Paired Comparison Models in Conjoint Analysis......Page 70 3.4 Design Issues......Page 74 3.5 Experiments......Page 75 3.5.1 Experiment 1......Page 76 3.5.2 Experiment 2......Page 79 3.6 Discussion......Page 82 References......Page 84 4.1 Introduction......Page 87 4.2.1 Example 1......Page 89 4.2.2 Example 2......Page 90 4.2.3 Example 3......Page 91 4.3 Meanscore......Page 92 4.3.1 Example of meanscore......Page 96 4.4.1 Optimal design derivation for fixed second-stage sample size......Page 97 4.4.2 Optimal design derivation for fixed budget......Page 98 4.4.3 Optimal design derivation for fixed precision......Page 99 4.4.4 Computational issues......Page 100 4.5.1 Data needed to compute optimal designs......Page 101 4.5.2 Examples of optimal design......Page 102 4.5.4 Sensitivity of design to sampling variation in pilot data......Page 105 4.6 Summary......Page 108 4.7.1 R language......Page 109 4.8 Appendix 2: The Optimal Sampling Package......Page 110 4.9 Appendix 3: Using the Optimal Package in R......Page 112 4.9.1 Syntax and features of optimal sampling command ‘budget’ in R......Page 113 4.9.2 Example......Page 114 4.11 Appendix 5: Using the Optimal Package in STATA......Page 117 4.11.1 Syntax and features of ‘optbud’ function in STATA......Page 118 4.11.3 Illustrative example......Page 119 References......Page 121 5.1 Introduction......Page 123 5.2 Motivating Example: Quantal Models for Dose Response......Page 124 5.2.1 Optimality criteria......Page 125 5.3.1 Example 3.1......Page 128 5.3.2 Example 3.2......Page 129 5.4 Variance Depending on Unknown Parameters and Multi-response Models......Page 130 5.4.1 Example 4.1......Page 134 5.4.2 Optimal designs as a reference point......Page 136 5.5 Optimal Designs with Cost Constraints......Page 137 5.5.1 Example 5.1......Page 140 5.5.2 Example 5.2 Pharmacokinetic model, serial sampling......Page 141 5.5.3 Remark 5.1......Page 144 5.6 Adaptive Designs......Page 147 5.6.1 Example 6.1......Page 149 5.7 Discussion......Page 151 References......Page 153 6.1 Introduction......Page 157 6.2 Experimental Design for Nonlinear Models......Page 158 6.2.2 Example 2.2 Three-parameter logistic distribution......Page 160 6.2.3 Example 2.3 The Monod differential equation......Page 161 6.2.4 Example 2.4......Page 163 6.3 Applications of Optimal Experimental Design in Microbiology......Page 168 6.3.1 The Monod model......Page 169 6.3.2 Application of optimal experimental design in microbiological models......Page 180 6.4 Bayesian Methods for Regression Models......Page 190 6.5 Conclusions......Page 193 Acknowledgements......Page 194 References......Page 195 7.1 Introduction......Page 201 7.2 The Choice between a Continuous or Dichotomous Outcome Variable......Page 202 7.2.1 Continuous outcome variable......Page 203 7.2.2 Dichotomous outcome variable......Page 204 7.3 The Choice between a Polychotomous or Dichotomous Outcome Variable......Page 209 7.4 Incorporation of Cost Considerations......Page 211 7.5 Final Comments......Page 213 Acknowledgement......Page 214 References......Page 215 8.1 Introduction......Page 216 8.2 The Kety–Schmidt Method......Page 217 8.3 The Statistical Model and Optimality Criteria......Page 218 8.4.1 D S -optimal designs......Page 221 8.4.2 Designs minimising var(D)......Page 222 8.5.1 Bayesian criteria......Page 224 8.5.2 Prior distribution......Page 225 8.6.1 Numerical methods......Page 227 8.6.2 D S -optimal designs......Page 228 8.6.3 Optimal designs for var(D)......Page 229 8.7.1 Reservations about the optimal designs......Page 230 8.7.2 Discrete designs......Page 231 8.8 Concluding Remarks......Page 235 References......Page 237 9.1 Introduction......Page 238 9.2.1 Governing equations......Page 239 9.2.2 Parameter estimation......Page 241 9.3.1 Experimental design for parameter estimation......Page 243 9.3.2 Monitoring network design for plume characterization......Page 245 9.4 Solution Algorithms......Page 249 9.5.1 Experimental design for parameter estimation......Page 250 9.5.2 Experimental design for contaminant plume detection......Page 257 9.6 Summary and Conclusions......Page 260 References......Page 262 10.1 Introduction......Page 265 10.2 The Pastry Dough Mixing Experiment......Page 266 10.3 The Problem......Page 267 10.4.1 Model and estimation......Page 269 10.4.2 The use of standard designs......Page 270 10.4.4 Some theoretical results......Page 272 10.4.5 Computational results......Page 274 10.5.1 Model and estimation......Page 275 10.5.2 Theoretical results......Page 276 10.6 The Pastry Dough Mixing Experiment Revisited......Page 280 10.7.1 Time trend effects......Page 283 10.7.2 Cost considerations......Page 284 10.7.3 The trade-off between trend resistance and cost-efficiency......Page 285 10.8.1 Model and estimation......Page 287 10.8.2 Computational results......Page 289 10.9 A Time Trend in the Pastry Dough Mixing Experiment......Page 291 Appendix: Design Construction Algorithms......Page 293 Index......Page 298

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.

"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." "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."--BOOK JACKET