Adaptive Designs for Sequential Treatment Allocation: 1st Edition (Hardback) book cover

Adaptive Designs for Sequential Treatment Allocation

1st Edition

By Alessandro Baldi Antognini, Alessandra Giovagnoli

Chapman and Hall/CRC

216 pages | 7 B/W Illus.

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Hardback: 9781466505759
pub: 2015-04-06
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Adaptive Designs for Sequential Treatment Allocation presents a rigorous theoretical treatment of the results and mathematical foundation of adaptive design theory. The book focuses on designing sequential randomized experiments to compare two or more treatments incorporating information accrued along the way.

The authors first introduce the terminology and statistical models most commonly used in comparative experiments. They then illustrate biased coin and urn designs that only take into account past treatment allocations as well as designs that use past data, such as sequential maximum likelihood and various types of doubly adaptive designs. The book also covers multipurpose adaptive experiments involving utilitarian choices and ethical issues. It ends with adaptive methods that include covariates in the design. The appendices present basic tools of optimal design theory and address Bayesian adaptive designs.

This book helps readers fully understand the theoretical properties behind various adaptive designs. Readers are then equipped to choose the best design for their experiment.


"I fully endorse views of the authors that researchers working in the area of adaptive designs may find this book a useful reference. Further, since this book includes a fair number of examples, teachers of graduate-level courses on designs may also find this book useful."

—Sada Nand Dwivedi, International Society for Clinical Biostatistics

"… the book illustrates theoretical properties of adaptive designs so that researchers can choose the best design for the experiment, covering impressively diverse approaches. … I find the book quite appealing in that the authors believed on the theoretical properties of the designs and mathematical foundations more than how and what of adaptive designs … highly useful as a reference book in a graduate-level course on designs with nearly exhaustive approaches to adaptive design construction."

Biometrics, December 2015

Table of Contents

Fundamentals and preliminary results

Contents of this chapter

Some notation

Statistical models

The likelihood and Fisher’s information

Inference: Conditional on the design or unconditional?

Inferential optimality of an adaptive design

Most informative targets

Asymptotic inference

Some examples of convergence of designs

The class of Markovian designs

Some examples of Markovian designs

Sequential designs and stopping rules

Some practical issues in the implementation of adaptive designs

Simulating adaptive designs

Randomization procedures that are functions of the past allocations


Randomization and balance as conflicting demands

Indicators of balance and randomness

Classic biased coin designs

Urn designs

Some extensions of the biased coin and urn designs of this chapter

Randomization procedures that depend on the responses


A more general model for the response

The sequential maximum likelihood design

The doubly adaptive biased coin design

The efficient randomized adaptive design

The up-and-down design

Multipurpose adaptive designs: step-by-step procedures


Designs of play-the-winner and drop-the-loser type

Bandyopadhyay and Biswas’ link-based design

The compound probability approach

Randomly reinforced urn designs

Asymptotic inference

Extensions of the step-by-step strategies to the case of several treatments

Multipurpose adaptive designs: Constrained and combined optimality


Optimality of target allocations for two treatments

Non-admissible targets

Multi-objective optimal targets: The constrained optimization approach

Multi-objective optimal targets: The combined optimization approach

The case of several treatments

Randomization procedures that depend on the covariates


Inferentially optimal target allocations in the presence of covariates

Covariate-adaptive randomization

Covariate-adjusted response-adaptive designs

Combined optimal designs with covariates

Other adaptive designs with covariates

Some conclusions

Appendix A: Optimal designs

Appendix B: Bayesian approaches in adaptive designs


Subject Index

About the Authors

Alessandro Baldi Antognini is a full professor of statistics at the University of Bologna. His main research interests include optimal design theory, sequential methods, and applied probability with applications to industrial experiments and biostatistics.

Alessandra Giovagnoli, now retired, was a full professor in the Department of Statistical Sciences at the University of Bologna. Her main research area is the design of experiments, particularly sequential experiments. She is also interested in stochastic order relations and biomedical and technological applications of statistics. She served on the editorial board of Biometrika and was associate editor of SMA, the journal of the Italian Statistical Society. She is on the board of Model-Oriented Data Analysis and Optimum Design (MODA), an international statistical association that promotes research in the area of experimental designs.

About the Series

Chapman & Hall/CRC Biostatistics Series

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Subject Categories

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