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
Fundamentals and preliminary results
Contents of this chapter
The likelihood and Fisher’s information
Inference: Conditional on the design or unconditional?
Inferential optimality of an adaptive design
Most informative targets
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
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
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
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-adjusted response-adaptive designs
Combined optimal designs with covariates
Other adaptive designs with covariates
Appendix A: Optimal designs
Appendix B: Bayesian approaches in adaptive designs