Optimal design for nonlinear response models
- Valerii V. Fedorov, Sergei L. Leonov.
- Boca Raton, FL : CRC Press, 
- Physical description
- xxviii, 373 pages : ill. ; 25 cm.
- Chapman & Hall/CRC biostatistics series (Unnumbered)
Math & Statistics Library
QA279 .F435 2014
- Unknown QA279 .F435 2014
- Includes bibliographical references and index.
- Regression Models and Their Analysis Linear Model, Single Response More about Information Matrix Generalized Versions of Linear Regression Model Nonlinear Models Maximum Likelihood and Fisher Information Matrix Generalized Regression and Elemental Fisher Information Matrices Nonlinear Regression with Normally Distributed Observations Convex Design Theory From Optimal Estimators to Optimal Designs Optimality Criteria Properties of Optimality Criteria Continuous Optimal Designs Sensitivity Function and Equivalence Theorems Equivalence Theorem, Examples Optimal Designs with Prior Information Regularization Optimality Criterion Depends on Estimated Parameters or Unknown Constants Response Function Contains Uncontrolled and Unknown Independent Variables Response Models with Random Parameters Algorithms and Numerical Techniques First-Order Algorithm: D-Criterion First-Order Algorithm: General Case Finite Sample Size Other Algorithms Optimal Design under Constraints Single Constraint Multiple Constraints Constraints for Auxiliary Criteria Directly Constrained Design Measures Nonlinear Response Models Bridging Linear and Nonlinear Cases Mitigating Dependence on Unknown Parameters Box and Hunter Adaptive Design Generalized Nonlinear Regression: Use of Elemental Information Matrices Model Discrimination Locally Optimal Designs in Dose Finding Binary Models Normal Regression Models Dose Finding for Efficacy-Toxicity Response Bivariate Probit Model for Correlated Binary Responses Examples of Optimal Designs in PK/PD Studies Introduction PK Models with Serial Sampling: Estimation of Model Parameters Estimation of PK Metrics Pharmacokinetic Models Described by Stochastic Differential Equations Software for Constructing Optimal Population PK/PD Designs Adaptive Model-Based Designs Adaptive Design for Emax model Adaptive Designs for Bivariate Cox Model Adaptive Designs for Bivariate Probit Model Other Applications of Optimal Designs Methods of Selecting Informative Variables Best Intention Designs in DoseFinding Studies Useful Matrix Formulae Symbols and Notation Definitions Matrix Derivatives Partitioned Matrices Kronecker Products Equalities Inequalities Bibliography Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design-such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints-are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The authors address all of these issues through many examples in the book.
(source: Nielsen Book Data)
- Publication date
- Chapman & Hall/CRC biostatistics series
- "A Chapman & Hall Book."
- 9781439821510 (hardcover : alk. paper)
- 1439821518 (hardcover : alk. paper)