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.
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 Introduction 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 Introduction 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 Introduction 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 Introduction 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 Introduction 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 Bibliography Subject Index