Optimal design for nonlinear response models / Valerii V. Fedorov and Sergei L. Leonov.

"A CRC title."

Includes bibliographical references and index.

1. Regression Models and Their Analysis
1.1 Linear Model, Single Response
1.2 More about Information Matrix
1.3 Generalized Versions of Linear Regression Model
1.4 Nonlinear Models
1.5 Maximum Likelihood and Fisher Information Matrix
1.6 Generalized Regression and Elemental Fisher Information Matrices
1.7 Nonlinear Regression with Normally Distributed Observations
2. Convex Design Theory
2.1 From Optimal Estimators to Optimal Designs
2.2 Optimality Criteria
2.3 Properties of Optimality Criteria
2.4 Continuous Optimal Designs
2.5 Sensitivity Function and Equivalence Theorems
2.6 Equivalence Theorem, Examples
2.7 Optimal Designs with Prior Information
2.8 Regularization
2.9 Optimality Criterion Depends on Estimated Parameters or Unknown Constants
2.10 Response Function Contains Uncontrolled and Unknown Independent Variables
2.11 Response Models with Random Parameters
3. Algorithms and Numerical Techniques
3.1 First-Order Algorithm: D-Criterion
3.2 First-Order Algorithm: General Case
3.3 Finite Sample Size
3.4 Other Algorithms
4. Optimal Design under Constraints
4.1 Single Constraint
4.2 Multiple Constraints
4.3 Constraints for Auxiliary Criteria
4.4 Directly Constrained Design Measures
5. Nonlinear Response Models
5.1 Bridging Linear and Nonlinear Cases
5.2 Mitigating Dependence on Unknown Parameters
5.3 Box and Hunter Adaptive Design
5.4 Generalized Nonlinear Regression: Use of Elemental Information Matrices
5.5 Model Discrimination
6. Locally Optimal Designs in Dose Finding
6.1 Comments on Numerical Procedures
6.2 Binary Models
6.3 Normal Regression Models
6.4 Dose Finding for Efficacy-Toxicity Response
6.5 Bivariate Probit Model for Correlated Binary Responses
7. Locally Optimal Designs in PK/PD Studies
7.1 Introduction
7.2 PK Models with Serial Sampling: Estimation of Model Parameters
7.3 Estimation of PK Metrics
7.4 Pharmacokinetic Models Described by Stochastic Differential Equations
7.5 Software for Constructing Optimal Population PK/PD Designs
8. Adaptive Model-Based Designs
8.1 Adaptive Design for Emax model
8.2 Adaptive Designs for Bivariate Cox Model
8.3 Adaptive Designs for Bivariate Probit Model
9. Other Applications of Optimal Designs
9.1 Methods of Selecting Informative Variables
9.2 Best Intention Designs in DoseFinding Studies
10. Useful Matrix Formulae
10.1 Matrix Derivatives
10.2 Partitioned Matrices
10.3 Equalities
10.4 Inequalities
Bibliography
Index
Symbol Description

The book is intended for graduate students and researchers who are interested in the theory and applications of model-based experimental design. The main body of the book requires a modest formal background in calculus, matrix algebra and statistics. Thus the book is accessible not only to statisticians, but also to a relatively broad readership, in particular those with backgrounds in natural sciences and engineering.