mODa 7 – Advances in Model-Oriented Design and …978-3-7908-2693-7/1.pdf · Alessandro Di Bucchianico ... Gauchi and Pazman and by Pazman and Pronzato cover special theoretical

mODa 7 ndash Advances in Model-Oriented Design and Analysis

Contributions to Statistics

V FedorovW G MuumlllerI N Vuchkov (Eds)Model-Oriented Data AnalysisXII248 pages 1992

J Antoch (Ed)Computational Aspects of Model ChoiceVII285 pages 1993

W G MuumlllerH P WynnA A Zhigljavsky(Eds)Model-Oriented Data AnalysisXIII287 pages 1993

P MandlM Huškovaacute (Eds)Asymptotic StatisticsX474 pages 1994

P DirschedlR Ostermann (Eds)Computational StatisticsVII553 pages 1994

C P KitsosW G Muumlller (Eds)MODA 4 ndash Advances in Model-OrientedData AnalysisXIV297 pages 1995

H SchmidliReduced Rank RegressionX179 pages 1995

W HaumlrdleM G Schimek (Eds)Statistical Theory and ComputationalAspects of SmoothingVIII265 pages 1996

S KlinkeData Structures for Computational StatisticsVIII284 pages 1997

A C AtkinsonL PronzatoH P Wynn(Eds)MODA 5 ndash Advances in Model-OrientedData Analysis and Experimental DesignXIV300 pages 1998

M MorysonTesting for Random Walk Coeffi cients inRegression and State Space ModelsXV317 pages 1998

S Biffi gnandi (Ed)Micro- and Macrodata of FirmsXII776 pages 1999

W HaumlrdleHua LiangJ GaoPartially Linear ModelsX203 pages 2000

W G MuumlllerCollecting Spatial Data2nd editionXII196 pages 2001

A C AtkinsonP HacklW G Muumlller (Eds)mODa 6 ndash Advances in Model-OrientedDesign and AnalysisXVI283 pages 2001

C LauroJ AntochV Esposito VinziG Saporta (Eds)Multivariate Total Quality ControlXIII236 pages 2002

P-A MonneyA Mathematical Theory of Argumentsfor Statistical EvidenceXIII154 pages 2003

Y HaitovskyH R LercheY Ritov (Eds)Foundations of Statistical InferenceXII230 pages 2003

C DagumG Ferrari (Eds)Household Behaviour Equivalence ScalesWelfare and PovertyXVI296 pages 2004

Alessandro Di Bucchianico

Henning Laumluter

Henry P Wynn (Editors)

mODa 7 ndash Advances in Model-Oriented Design and Analysis

Proceedings of the 7th International Workshop onModel-Oriented Design and Analysis held in HeezeThe Netherlands June 14 ndash18 2004

With 17 Figures and 26 Tables

Series EditorsWerner A MuumlllerMartina Bihn

EditorsDr Alessandro Di Bucchianico EURANDOM andEindhoven University of TechnologyDepartment of Mathematics andComputer SciencePO Box 5135600 MB EindhovenThe NetherlandsAdBucchianicoTUEnl

Prof Dr Henning LaumluterUniversity of PotsdamInstitute of Mathematics14415 Potsdamlaeuterrzuni-potsdamdeGermany

Prof Dr Henry P WynnLondon School of EconomicsHoughton StreetLondon WC2A 2AE UKhwynnlseacukUnited Kingdom

ISSN 1431-1968

Library of Congress Control Number 2004105253 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografi e detailed bibliographic data is available in the Internet at lthttpdnbddbdegt

This work is subject to copyright All rights are reserved whether the whole or part of the material is concerned specifi cally the rights of translation reprinting reuse of illustrations recitation broadcasting reproduction on microfi lm or in any other way and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9 1965 in its current version and permission for use must always be obtained from Physica-Verlag Viola tions are liable for prosecution under the German Copyright Law

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SPIN 10994474 883130-5 4 3 2 1 0 ndash Printed on acid-free and non-aging paper

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Originally published by Springer-Verlag Berlin Heidelberg New York in 2004

Preface

This volume contains a substantial number of the papers presented at themODa 7 conference mODa stands for Model Oriented Data Analysis and preshyvious conferences have been held in Wartburg (1987) (then in the GDR) StKirik monastery Bulgaria (1990) Petrodvorets St Petersburg Russia (1992)The island of Spetsos Greece (1995) the Centre International de RencontresMathematiques Marseilles France (1998) and PuchbergSchneeberg Ausshytria (2001)

The purpose of these workshops has traditionally been to bring togetherscientists from the East and West interested in the optimal design of expershyiments and related topics and younger and senior researchers in the fieldThese traditions remain vital to the health of the series During this periodEurope has seen increasing unity and the organizers of and participants inmODa must take some satisfaction from the fact that the youthful ideals ofthe founders of the series are reflected in this transition

The present conference and mODa 6 are supported by a European Unionconference grant (contract HPCF-CT 2000 00045) whose funding emphasis ison younger participants The company GlaxoSmithKline has very generouslycontinued its support We are very grateful for these substantial contribushytions

mODa 7 has benefited from excellent administrative input from the staffof EURANDOM particularly Lucienne Coolen EURANDOM is a majorEuropean stochastics research institute housed within and partly supportedby the Eindhoven University of Technology The Netherlands The conferenceitself takes place at the conference centre Kapellerput in Heeze not far fromEindhoven Among the post-doctoral fellows and PhD students who helpedand participated in mODa 7 we should thank Peter van de Yen for tirelesswork processing papers for this volume

The mODa series both the conferences and the volumes have grown toa leadership position in experimental design and analysis It is not surprisingtherefore that most of the main developments in the area have been represhysented over the years

The most evident trend in the present volume is towards optimal deshysign for nonlinear models and models with nonstandard assumptions Thepapers by Atkinson by Biedermann Dette and Pepelyshev and by Ucinski

VI Preface

and Bogacka cover non-linear models arising from compartmental models inchemical kinetics given by first order differential equations Trandafir andLopez-Fidalgo cover the familiar Michaelis-Menten model The papers byGauchi and Pazman and by Pazman and Pronzato cover special theoreticalaspects of non-linear models The locally optimal design method of Melasalso falls into the non-linear category In all this work the main feature isthat the information matrix is parameter dependent This is also a feature ofthe generalized linear models covered by Pinto and Ponce de Leon who alsolook at Bayesian solutions

The area of biased coin designs up-and-down models urn models is stimshyulated by its application to dose-response experiments and clinical trials moregenerally The papers by Baldi Antognini by Biswas and Mandal by Gioshyvagnoli and by Tymofyeyev Rosenberger and Hu are in this area It is goodto see other papers on the application of optimal design ideas in medicineFedorov and Leonov investigate how to use optimal design methods for conshytrol in the presence of forced baseline measurements and Rabie and Flournoystudy the situation of double (contingent) responses such as toxicity and disshyease failure Yin Wang Wang and Zheng use a sophisticated controllearningstrategic for patient control during anesthesia

The main stream of optimal design is well represented Maximum EntropySampling relates optimal design to information theoretic formulations Thepapers by Anstreicher and Lee and by Wynn are closely related with thefirst covering bounds and computational aspects and the second sketchingthe links to D-optimality The paper by Pronzato Thierry and Wolsztynskiuse entropy as a basis for estimation rather than design Four papers coverdifferent aspects of optimal design for the standard linear model the coreof the field Harman looks at efficiency how close a given design is to theglobal optimum Miiller and Kitsos look at combined optimal design and sishymultaneous inference (confidence tolerance) Rodriguez Ortiz and Martinezstudy design for models with non-constant (heteroscedastic) error varianceTorsney and Mandal continue their work on algorithms

Two other areas are represented by single papers Basso Salmaso Evanshygelaras and Koukouvinos cover the difficult subject of experimental designcombined with non-parametric testing Vuchkov presents the important tolshyerance design method which is an aspect of robust engineering for the specialcase of mixture experiments

EindhovenJanuary 2004

Alessandro Di BucchianicoHenning LiiuterHenry P Wynn

Contents

A M asked Spectral Bound for Maximum-Entropy SamplingK M Anstreicher J Lee 11 Introdu ction 12 T he Masked Spect ral Bound 23 T he Minimization Method 34 Computational Result s 55 Alt ernat ive Use of Oppenheim s Inequality 96 Conclusion 10References 10

Some Bayesian Optimum Designs for ResponseTransformation in Nonlinear Models with NonconstantVarianceAC Atkinson 131 Introduction 132 Transforma tio ns and First-O rder Decay 143 Optimum Design for a Multivariate Response 154 Par ameter Sensit ivit ies and Transform ing Both Sides 165 Two Consecut ive First-Order Reactions 176 Efficiencies and Bayesian Optimum Designs 177 Discussion 20References 21

Extensions of the Ehrenfest Urn Designs for Comparing TwoTreatmentsA Baldi Antognini 231 Int roduction 232 T he Ehrenfest Urn Design 253 Symmet ric Ehrenfest Design for Achieving Balance 264 Asymmetric Ehrenfest Design for a Generic Target 265 Ehrenfest-Brillouin Design 276 Some Convergence Properties 29References 30

VIn Contents

Nonparametric Testing for Main Effects on InequivalentDesignsD Basso L Salm aso H Evangeiaras C Koukouvino s 331 Introduction 332 The IMP Test 353 A Compar ative Simulation Study 374 Conclusions 39References 40

Maximin Optimal Designs for a Compartmental ModelS Biederm ann H Dette A Pepeiyshev 411 Introduction 412 Locally D-optimal Designs 433 St andardized Maximin D-optimal Designs 45References 48

Optimal Adaptive Designs in Phase III Clinical Trials forContinuous Responses with CovariatesA Biswas S Mandai 511 Introduct ion 512 Optimal Designs for Continuous Distributions 52

21 Response Distributions with one Unknown Param eter 5222 Distributions Having more than one Parameter 53

3 Presence of Covariates 544 Conclusions 56References 58

Optimal Designs for Regression Models with ForcedMeasurements at BaselineV V Fedorov S Leonov 611 Int roduct ion 612 Model 623 Optimal Designs for Model (1) 63

31 Equivalence of D-optimal Designs when only are Unknown 6332 Unknown and Population Varian ce A 66

4 Case when Baseline and Placebo Responses Coincide 6741 Only Resp onse Parameters Unknown 6842 Unknown Param eters an d A 68

References 68

Small Size Designs in Nonlinear Models Computed byStochastic OptimizationJ-P Gauchi A Pdzma si 711 Introduction 712 Optimality Criteri a Expressed as an Integral 723 Densit y of t he Estimator 73

Contents IX

4 The Penalty for the Boundary of 8 745 Accelerated Method of Stochast ic Optimization 756 Examples and Numerical Results 77References 78

Asymptotic Properties of Biased Coin Designs for TreatmentAllocationA Giovagnoli 811 Introduction 812 Markovian Experiments 823 Different Types of Biased Coin Designs 84

31 BCDs for Comparing Two Treatments 8432 Biased Coin Design for Targeting a Quantile 85

4 Asymptotic Properties of the Adjust able Biased Coin Designs 865 Asymptotic Properties of Up-and-Down Designs 87References 88

Lower Bounds on Efficiency Ratios Based on q)p-OptimalDesignsR Harrnan 891 Introduction 892 Bounds on the Ek-optimal Values Based on the Eigenvalues of

q)p-optimal Information Matrices 913 Bounds on the E-efficiency and t he Minimal Efficiency Ratio of

q)p-optimal Designs 914 Ex ample the Minimal Efficiency Ratio of the D-optimal Design

for the Model of Spring Balance Weighing 935 Appendix - Proofs 94References 96

On a Functional Approach to Locally Optimal DesignsVB Melas 971 Introduction 972 Outline of the Problem 983 Basic Analytical Results 994 T he T hree-Paramete r Logistic Distribution 101References 104

Optimal Design Criteria Based on Tolerance RegionsCH Miiller CP Kitsos 1071 Introduct ion 1072 3-expectat ion Bayesian Tolerance Regions 1093 Optimal Designs 112References 114

X Contents

Simultaneous Choice of Design and Estimator in NonlinearRegression with Parameterized VarianceA Ptizmasi L Pronzato 1171 Introduction 1172 Randomized Designs and Uniform Strong Law of Large Numbers 1183 Penalized Weighted LS and Two-Stage LS Estimation 119

31 Penalized Weighted LS Estimation 12032 Two-stage LS Estimation 121

4 Choosing the Design and the Estimator 122References 124

Minimum Entropy Estimation in Semi-Parametric Models aCandidate for Adaptive EstimationL Pronzato E Thierry E Wolsztynski 1251 Introduction 1252 Minimizing Entropy 1263 Adaptive Estimation in the Location Model 1284 Adaptive Estimation in Nonlinear Regression 130References 132

Optimal Designs for Contingent Response ModelsHB Rabie N Flournoy 1331 Introduction 1332 The Contingent Response Model 1343 The Design Problem 1354 Locally D-optimal Designs 136

41 Unequal Slopes 131 =I 132 8 = (al 131 a2 (32) e = (a2 132 p r) 13642 Equal Slopes 131 = 132 = 13 8 = (a113a2) () = (a2 13p) 138

5 Locally c-optimal Designs 13851 Unequal Slopes 131 =I 1328 = (a1131a2132)() =

(a2132pr) 13952 Equal Slopes 131 = 132 = 13 8 = (a2 13(1) () = (a2 13p) 139

6 Conclusion 140References 141

Bayesian D-Optimal Designs for Generalized Linear Modelswith a Varying Dispersion ParameterE Rodrigues Pinto A Ponce de Leon 1431 Introduction 1432 The Quasi-Likelihood 1443 The Extended Quasi-Likelihood 1454 The Model 1465 The Equivalence Theorem 1476 Cake Mix Example 1487 Final Considerations 150

References

Contents XI

151

pound-optimum Designs in Multi-factor Models withHeteroscedastic ErrorsC Rodriguez I Ortiz I Martinez 1531 Introduction 1532 Product Models 1543 Additive Models 155

31 Additive Models with Constant Term 15532 Orthogonal Additive Model 158

4 Some Remarks 159References 160

Multiplicative Algorithms for Constructing OptimizingDistributions Further DevelopmentsB Torsney S Mandai 1631 Introduction 1632 Optimality Conditions 1643 Algorithms 164

31 Properties of the Iteration (3) 1654 Optimal Distribution on Spaces 1665 Objective Choices 1686 Conclusions 170References 171

Locally Optimal Designs for an Extension of theMichaelis-Menten ModelC Trandafir J Lopez-Fidalqo 1731 Introduction 1732 Theoretical Background 174

21 The Nonlinear Regression Model 17422 The Design Criteria 175

3 Extension of the Michaelis-Menten Model 1754 Compound Optimal Designs for 3 Parameters 177

41 c-optimal Designs 17742 c-efficiencies of the D-optimal Design 17843 Compound Optimal Designs 178

References 180

Asymptotic Properties of Urn Designs for Three-arm ClinicalTrialsY Tymofyeyev WF Rosenberger F Hu 1831 Introduction 1832 Spectral Analysis of Generating Matrix 1853 Asymptotic Distribution of Y n bull 1864 Asymptotic Distribution of N n 188

XII Contents

5 Discussion 189References 190

T-Optimum Designs for Multiresponse DynamicHeteroscedastic ModelsD Uciriski B Bogacka 1911 Introduction 1912 T-optimality Criterion for Heteroscedastic Models 1933 Numerical Construction of Optimum Designs 1954 Conclusion 197References 198

Error Transmission in Mixture ExperimentsLN Vuchkov 2011 Introduction 2012 Mean and Vari ance Models for Mixture Experim ents 2023 Mean and Variance Models for Experiments with Mixture and

Process Vari ables 2044 Example 207References 209

Maximum Entropy Sampling and General EquivalenceTheoryHP Wynn 2111 Introduction 211

11 Max imum Entropy Sampling 21212 Limit of Bayes Case 213

2 Continuous Theory 21421 Constrained Measures for the MES Case 215

3 General MES and D-optimality 216References 218

Towards Identification of Patient Responses to AnesthesiaInfusion in Real TimeG Yin H Wang L Y Wang H Zheng 2191 Introduction 2192 System 220

21 Basic Two-Step Setup for Real-Time Learning Algorithms 2223 Recursive Algorithms 2224 Convergence and Rates of Convergence 224References 226

List of Contributors 229

List of Referees 233

Contents XIII

List of Figures 235

List of Tables 237

Index 239