Optimal Design for Nonlinear Response Models (Hardback) book cover

Optimal Design for Nonlinear Response Models

By Valerii V. Fedorov, Sergei L. Leonov

© 2013 – CRC Press

402 pages | 85 B/W Illus.

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pub: 2013-07-15
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About the Book

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


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


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


Matrix Derivatives

Partitioned Matrices

Kronecker Products





About the Authors

Valerii Fedorov, PhD, is Vice President of Predictive Analytics, Innovation at Quintiles.

Sergei Leonov, PhD, is a Senior Principal Scientist at AstraZeneca.

About the Series

Chapman & Hall/CRC Biostatistics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Pharmacology