Optimal Design for Nonlinear Response Models
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Features
- Presents major concepts of the mathematical theory of optimal experimental design
- Discusses numerical procedures for both parameter estimation and construction of optimal designs
- Explains how various optimal experimental design techniques can be modified for use in dose-finding, pharmacokinetic (PK), pharmacodynamic (PD), and other biopharmaceutical applications
- Emphasizes penalized and cost-based designs
- Describes a MATLAB®-based library for the construction of optimal sampling schemes for PK/PD models
- Requires a modest background in calculus, matrix algebra, and statistics, making the book accessible not only to statisticians, but also to readers in the natural sciences and engineering
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.
Table of Contents
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
Author Bio(s)
Valerii Fedorov, PhD, is Vice President of Predictive Analytics, Innovation at Quintiles.
Sergei Leonov, PhD, is a Senior Principal Scientist at AstraZeneca.
