ISBN: 3790802131
TITLE: mODa 7 - Advances in Model-oriented Design and Analysis
AUTHOR: Bucchianico, Luter, Wynn
TOC:

A Masked Spectral Bound for Maximum-Entropy Sampling
K.M. Anstreicher, J. Lee 1
1 Introduction 1
2 The Masked Spectral Bound 2
3 The Minimization Method 3
4 Computational Results 5
5 Alternative Use of Oppenheim's Inequality 9
6 Conclusion 10
References 10
Some Bayesian Optimum Designs for Response Transformation in Nonlinear Models with Nonconstant Variance
A.C. Atkinson 13
1 Introduction 13
2 Transformations and First-Order Decay 14
3 Optimum Design for a Multivariate Response 15
4 Parameter Sensitivities and Transforming Both Sides 16
5 Two Consecutive First-Order Reactions 17
6 Eficiencies and Bayesian Optimum Designs 17
7 Discussion 20
References 21
Extensions of the Ehrenfest Urn Designs for Comparing Two Treatments
A. Baldi Antognini 23
1 Introduction 23
2 The Ehrenfest Urn Design 25
3 Symmetric Ehrenfest Design for Achieving Balance 26
4 Asymmetric Ehrenfest Design for a Generic Target 26
5 Ehrenfest-Brillouin Design 27
6 Some Convergence Properties 29
References 30
Nonparametric Testing for Main Effects on Inequivalent Designs
D. Basso, L. Salmaso, H. Evangelaras, C. Koukouvinos 33
1 Introduction 33
2 The IMP Test 35
3 A Comparative Simulation Study 37
4 Conclusions 39
References 40
Maximin Optimal Designs for a Compartmental Model
S. Biedermann, H. Dette, A. Pepelyshev 41
1 Introduction 41
2 Locally D-optimal Designs 43
3 Standardized Maximin D-optimal Designs 45
References 48
Optimal Adaptive Designs in Phase III Clinical Trials for Continuous Responses with Covariates
A. Biswas, S. Mandal 51
1 Introduction 51
2 Optimal Designs for Continuous Distributions 52
2.1 Response Distributions with one Unknown Parameter 52
2.2 Distributions Having more than one Parameter 53
3 Presence of Covariates 54
4 Conclusions 56
References 58
Optimal Designs for Regression Models with Forced Measurements at Baseline
V.V. Fedorov, S. Leonov 61
1 Introduction 61
2 Model 62
3 Optimal Designs for Model (1) 63
3.1 Equivalence of D-optimal Designs when only gamma are Unknown 63
3.2 Unknown y and Population Variance Lambda 66
4 Case when Baseline and Placebo Responses Coincide 67
4.1 Only Response Parameters gamma Unknown 68
4.2 Unknown Parameters gamma and Lambda 68
References 68
Small Size Designs in Nonlinear Models Computed by Stochastic Optimization
J.-P. Gauchi, A. Pzman 71
1 Introduction 71
2 Optimality Criteria Expressed as an Integral 72
3 Density of the Estimator 73
4 The Penalty for the Boundary of Theta 74
5 Accelerated Method of Stochastic Optimization 75
6 Examples and Numerical Results 77
References 78
Asymptotic Properties of Biased Coin Designs for Treatment Allocation
A. Giovagnoli 81
1 Introduction 81
2 Markovian Experiments 82
3 Different Types of Biased Coin Designs 84
3.1 BCD's for Comparing Two Treatments 84
3.2 Biased Coin Design for Targeting a Quantile 85
4 Asymptotic Properties of the Adjustable Biased Coin Designs 86
5 Asymptotic Properties of Up-and-Down Designs 87
References 88
Lower Bounds an Efficiency Ratios Based on Phi_p-Optimal Designs
R. Harman 89
1 Introduction 89
2 Bounds an the Ek-optimal Values Based on the Eigenvalues of Phi_p-optimal Information Matrices 91
3 Bounds on the E-efficiency and the Minimal Efficiency Ratio of Phi_p-optimal Designs 91
4 Example: the Minimal Efficiency Ratio of the D-optimal Design for the Model of Spring Balance Weighing 93
5 Appendix - Proofs 94
References 96
On a lunctional Approach to Locally Optimal Designs
V.B. Melas 97
1 Introduction 97
2 Outline of the Problem 98
3 Basic Analytical Results 99
4 The Three-Parameter Logistic Distribution 101
References 104
Optimal Design Criteria Based on Tolerance Regions
C.H. Mller, C.P. Kitsos 107
1 Introduction 107
2 beta-expectation Bayesian Tolerance Regions 109
3 Optimal Designs 112
References 114
Simultaneous Choice of Design and Estimator in Nonlinear Regression with Parameterized Variance
A. Pzman, L. Pronzato 117
1 Introduction 117
2 Randomized Designs and Uniform Strong Law of Large Numbers 118
3 Penalized Weighted LS and Two-Stage LS Estimation 119
3.1 Penalized Weighted LS Estimation 120
3.2 Two-stage LS Estimation 121
4 Choosing the Design and the Estimator 122
References 124
Minimum Entropy Estimation in Semi-Parametric Models: a Candidate for Adaptive Estimation?
L. Pronzato, . Thierry, . Wolsztynski 125
1 Introduction 125
2 Minimizing Entropy 126
3 Adaptive Estimation in the Location Model 128
4 Adaptive Estimation in Nonlinear Regression 130
References 132
Optimal Designs for Contingent Response Models
H.S. Rabie, N. Flournoy 133
1 Introduction 133
2 The Contingent Response Model 134
3 The Design Problem 135
4 Locally D-optimal Designs 136
4.1 Unequal Slopes beta_1 notequal beta_2; Theta = (alpha_1, beta_1, alpha_2, beta_2); theta = (alpha_2, beta_2, mu, r) 136
4.2 Equal Slopes beta_1 = beta_2 = beta; Theta = (alpha_1, beta, alpha_2); theta = (alpha_2, beta, mu ) 138
5 Locally c-optimal Designs 138
5.1 Unequal Slopes beta_1 notequal beta_2; Theta = (alpha_1, beta_1, alpha_2, beta_2); theta = (alpha_2, beta_2, mu, r) 139
5.2 Equal Slopes beta_1 = beta_2 = beta; Theta = (alpha_2, beta, alpha_1); theta = (alpha_2, beta, mu) 139
6 Conclusion 140
References 141
Bayesian D-Optimal Designs for Generalized Linear Models with a Varying Dispersion Parameter
E. Rodrigues Pinto, A. Ponce de Leon 143
1 Introduction 143
2 The Quasi-Likelihood 144
3 The Extended Quasi-Likelihood 145
4 The Model 146
5 The Equivalence Theorem 147
6 Cake Mix Example 148
7 Final Considerations 150
References 151
L-optimum Designs in Multi-factor Models with Heteroscedastic Errors
C. Rodrguez, I. Ortiz, I. Martnez 153
1 Introduction 153
2 Product Models 154
3 Additive Models 155
3.1 Additive Models with Constant Term 155
3.2 Orthogonal Additive Model 158
4 Some Remarks 159
References 160
Multiplicative Algorithms for Constructing Optimizing Distributions : Further Developments
B. Torsney, S. Mandal 163
1 Introduction 163
2 Optimality Conditions 164
3 Algorithms 164
3.1 Properties of the Iteration (3) 165
4 Optimal Distribution on Spaces 166
5 Objective Choices 168
6 Conclusions 170
References 171
Locally Optimal Designs for an Extension of the Michaelis-Menten Model
C. Trandafir, J. Lpez-Fidalgo 173
1 Introduction 173
2 Theoretical Background 174
2.1 The Nonlinear Regression Model 174
2.2 The Design Criteria 175
3 Extension of the Michaelis-Menten Model 175
4 Compound Optimal Designs for 3 Parameters 177
4.1 c-optimal Designs 177
4.2 c-efficiencies of the D-optimal Design 178
4.3 Compound Optimal Designs 178
References 180
Asymptotic Properties of Urn Designs for Three-arm Clinical Trials
Y Tymofyeyev, W.F. Rosenberger, F. Hu 183
1 Introduction 183
2 Spectral Analysis of Generating Matrix 185
3 Asymptotic Distribution of Y_n 186
4 Asymptotic Distribution of N_n 188
5 Discussion 189
References 190
T-Optimum Designs for Multiresponse Dynamic Heteroscedastic Models
D. Uciniski, B. Bogacka 191
1 Introduction 191
2 T-optimality Criterion for Heteroscedastic Models 193
3 Numerical Construction of Optimum Designs 195
4 Conclusion 197
References 198
Error Transmission in Mixture Experiments
L.N. Vuchkov 201
1 Introduction 201
2 Mean and Variance Models for Mixture Experiments 202
3 Mean and Variance Models for Experiments with Mixture and Process Variables 204
4 Example 207
References 209
Maximum Entropy Sampling and General Equivalence Theory
H.P. Wynn 211
1 Introduction 211
1.1 Maximum Entropy Sampling 212
1.2 Limit of Bayes Case 213
2 Continuous Theory 214
2.1 Constrained Measures for the MES Case 215
3 General MES and D-optimality 216
References 218
Towards Identification of Patient Responses to Anesthesia Infusion in Real Time
G. Yin, H. Wang, L.Y. Wang, H. Zheng 219
1 Introduction 219
2 System 220
2.1 Basic Two-Step Setup for Real-Time Learning Algorithms 222
3 Recursive Algorithms 222
4 Convergence and Rates of Convergence 224
References 226
List of Contributors 229
List of Referees 233
List of Figures 235
List of Tables 237
Index 239
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