Applied optimal designs

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Applied optimal designs

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... distribution Optimal Bayesian Designs 8.6.1 Numerical methods 8.6.2 DS -optimal designs ^Þ 8.6.3 Optimal designs for varðD Practical Designs 8.7.1 Reservations about the optimal designs 197 198... Kety–Schmidt Method The Statistical Model and Optimality Criteria Locally Optimal Designs 8.4.1 DS -optimal designs ^Þ 8.4.2 Designs minimising varðD Bayesian Designs and Prior Distributions 8.5.1 Bayesian... precision 4.4.4 Computational issues Deriving Optimal Designs in Practice 4.5.1 Data needed to compute optimal designs 4.5.2 Examples of optimal design 4.5.3 The optimal sampling package 4.5.4 Sensitivity

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  • Cover Page

  • Title Page

  • Copyright 2005 John Wiley & Sons Ltd

  • Contents

    • List of Contributors

    • Editors’ Foreword

    • 1 Optimal Design in Educational Testing

    • 2 Optimal On-line Calibration of Testlets

    • 3 On the Empirical Relevance of Optimal Designs for the Measurement of Preferences

    • 4 Designing Optimal Two-stage Epidemiological Studies

    • 5 Response-Driven Designs in Drug Development

    • 6 Design of Experiments for Microbiological Models

    • 7 Selected Issues in the Design of Studies of Interrater Agreement

    • 8 Restricted Optimal Design in the Measurement of Cerebral Blood Flow Using the Kety- Schmidt Technique

    • 9 Optimal Experimental Design for Parameter Estimation and Contaminant Plume Characterization in Groundwater Modelling

    • 10 The Optimal Design of Blocked Experiments in Industry

    • Index

  • List of Contributors

  • Editors’ Foreword

    • (i) Education

    • (ii) Business Marketing

    • (iii) Epidemiology

    • (iv) Microbiology and Pharmaceutical research

    • (v) Medical Research

    • (vi) Environmental Science

    • (vii) Manufacturing Industry

    • Acknowledgements

    • References

  • 1 Optimal Design in Educational Testing

    • 1.1 Introduction

      • 1.1.1 Paper-and-pencil or computerized adaptive testing

      • 1.1.2 Dichotomous response

      • 1.1.3 Polytomous response

      • 1.1.4 Information functions

      • 1.1.5 Design problems

    • 1.2 Test Design

      • 1.2.1 Fixed-form test design

      • 1.2.2 Test design for CAT

    • 1.3 Sampling Design

      • 1.3.1 Paper-and-pencil calibration

      • 1.3.2 CAT calibration

    • 1.4 Future Directions

    • Acknowledgements

    • References

  • 2 Optimal On-line Calibration of Testlets

    • 2.1 Introduction

    • 2.2 Background

      • 2.2.1 Item response functions

      • 2.2.2 D-optimal design criterion

    • 2.3 Solution for Optimal Designs

      • 2.3.1 Mathematical programming model

      • 2.3.2 Unconstrained conjugate-gradient method

      • 2.3.3 Constrained conjugate-gradient method

      • 2.3.4 Gradient of log det(B;Theta,x)

      • 2.3.5 MCMC sequential estimation of item parameters

      • 2.3.6 Note on performance measures

    • 2.4 Simulation Results

    • 2.5 Discussion

    • Appendix A Derivation of the Gradient of log det M(B;Theta;x)

    • Appendix B Projection on the Null Space of the Constraint Matrix

    • Acknowledgements

    • References

  • 3 On the Empirical Relevance of Optimal Designs for the Measurement of Preferences

    • 3.1 Introduction

    • 3.2 Conjoint Analysis

    • 3.3 Paired Comparison Models in Conjoint Analysis

    • 3.4 Design Issues

    • 3.5 Experiments

      • 3.5.1 Experiment 1

      • 3.5.2 Experiment 2

    • 3.6 Discussion

    • Acknowledgements

    • References

  • 4 Designing Optimal Two-stage Epidemiological Studies

    • 4.1 Introduction

    • 4.2 Illustrative Examples

      • 4.2.1 Example 1

      • 4.2.2 Example 2

      • 4.2.3 Example 3

    • 4.3 Meanscore

      • 4.3.1 Example of meanscore

    • 4.4 Optimal Design and Meanscore

      • 4.4.1 Optimal design derivation for fixed second-stage sample size

      • 4.4.2 Optimal design derivation for fixed budget

      • 4.4.3 Optimal design derivation for fixed precision

      • 4.4.4 Computational issues

    • 4.5 Deriving Optimal Designs in Practice

      • 4.5.1 Data needed to compute optimal designs

      • 4.5.2 Examples of optimal design

      • 4.5.3 The optimal sampling package

      • 4.5.4 Sensitivity of design to sampling variation in pilot data

    • 4.6 Summary

    • 4.7 Appendix 1: Brief Description of Software Used

      • 4.7.1 R language

      • 4.7.2 S-PLUS

      • 4.7.3 STATA

    • 4.8 Appendix 2: The Optimal Sampling Package

      • 4.8.1 Illustrative data sets

    • 4.9 Appendix 3: Using the Optimal Package in R

      • 4.9.1 Syntax and features of optimal sampling command ‘budget’ in R

      • 4.9.2 Example

    • 4.10 Appendix 4: Using the Optimal Package in S-Plus

    • 4.11 Appendix 5: Using the Optimal Package in STATA

      • 4.11.1 Syntax and features of ‘optbud’ function in STATA

      • 4.11.2 Analysis with categorical variables

      • 4.11.3 Illustrative example

    • References

  • 5 Response-Driven Designs in Drug Development

    • 5.1 Introduction

    • 5.2 Motivating Example: Quantal Models for Dose Response

      • 5.2.1 Optimality criteria

    • 5.3 Continuous Models

      • 5.3.1 Example 3.1

      • 5.3.2 Example 3.2

    • 5.4 Variance Depending on Unknown Parameters and Multi-response Models

      • 5.4.1 Example 4.1

      • 5.4.2 Optimal designs as a reference point

      • 5.4.3 Remark 4.1

    • 5.5 Optimal Designs with Cost Constraints

      • 5.5.1 Example 5.1

      • 5.5.2 Example 5.2 Pharmacokinetic model, serial sampling

      • 5.5.3 Remark 5.1

    • 5.6 Adaptive Designs

      • 5.6.1 Example 6.1

    • 5.7 Discussion

    • Acknowledgements

    • References

  • 6 Design of Experiments for Microbiological Models

    • 6.1 Introduction

    • 6.2 Experimental Design for Nonlinear Models

      • 6.2.1 Example 2.1 The exponential regression model

      • 6.2.2 Example 2.2 Three-parameter logistic distribution

      • 6.2.3 Example 2.3 The Monod differential equation

      • 6.2.4 Example 2.4

    • 6.3 Applications of Optimal Experimental Design in Microbiology

      • 6.3.1 The Monod model

      • 6.3.2 Application of optimal experimental design in microbiological models

    • 6.4 Bayesian Methods for Regression Models

    • 6.5 Conclusions

    • Acknowledgements

    • References

  • 7 Selected Issues in the Design of Studies of Interrater Agreement

    • 7.1 Introduction

    • 7.2 The Choice between a Continuous or Dichotomous Outcome Variable

      • 7.2.1 Continuous outcome variable

      • 7.2.2 Dichotomous outcome variable

    • 7.3 The Choice between a Polychotomous or Dichotomous Outcome Variable

    • 7.4 Incorporation of Cost Considerations

    • 7.5 Final Comments

    • Appendix

    • Acknowledgement

    • References

  • 8 Restricted Optimal Design in the Measurement of Cerebral Blood Flow Using the Kety-Schmidt Technique

    • 8.1 Introduction

    • 8.2 The Kety–Schmidt Method

    • 8.3 The Statistical Model and Optimality Criteria

    • 8.4 Locally Optimal Designs

      • 8.4.1 D S -optimal designs

      • 8.4.2 Designs minimising var(D)

    • 8.5 Bayesian Designs and Prior Distributions

      • 8.5.1 Bayesian criteria

      • 8.5.2 Prior distribution

    • 8.6 Optimal Bayesian Designs

      • 8.6.1 Numerical methods

      • 8.6.2 D S -optimal designs

      • 8.6.3 Optimal designs for var(D)

    • 8.7 Practical Designs

      • 8.7.1 Reservations about the optimal designs

      • 8.7.2 Discrete designs

    • 8.8 Concluding Remarks

    • References

  • 9 Optimal Experimental Design for Parameter Estimation and Contaminant Plume Characterization in Groundwater Modelling

    • 9.1 Introduction

    • 9.2 Groundwater Flow and Mass Transport in Porous Media: Modelling Issues

      • 9.2.1 Governing equations

      • 9.2.2 Parameter estimation

    • 9.3 Problem Formulation

      • 9.3.1 Experimental design for parameter estimation

      • 9.3.2 Monitoring network design for plume characterization

    • 9.4 Solution Algorithms

    • 9.5 Case Studies

      • 9.5.1 Experimental design for parameter estimation

      • 9.5.2 Experimental design for contaminant plume detection

    • 9.6 Summary and Conclusions

    • Acknowledgements

    • References

  • 10 The Optimal Design of Blocked Experiments in Industry

    • 10.1 Introduction

    • 10.2 The Pastry Dough Mixing Experiment

    • 10.3 The Problem

    • 10.4 Fixed Block Effects Model

      • 10.4.1 Model and estimation

      • 10.4.2 The use of standard designs

      • 10.4.3 Optimal design

      • 10.4.4 Some theoretical results

      • 10.4.5 Computational results

    • 10.5 Random Block Effects Model

      • 10.5.1 Model and estimation

      • 10.5.2 Theoretical results

      • 10.5.3 Computational results

    • 10.6 The Pastry Dough Mixing Experiment Revisited

    • 10.7 Time Trends and Cost Considerations

      • 10.7.1 Time trend effects

      • 10.7.2 Cost considerations

      • 10.7.3 The trade-off between trend resistance and cost-efficiency

    • 10.8 Optimal Run Orders for Blocked Experiments

      • 10.8.1 Model and estimation

      • 10.8.2 Computational results

    • 10.9 A Time Trend in the Pastry Dough Mixing Experiment

    • 10.10 Summary

    • Acknowledgement

    • Appendix: Design Construction Algorithms

  • Index

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