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This book addresses the issue of designing experiments for comparing two or more treatments, when the experiment is sequential and the experimenter wishes to make use of the information accrued along the way. This type of experimental design is called adaptive. The aim of the book is reviewing and reorganizing the existing results of adaptive design theory, with particular attention to its mathematical foundation. It is intended primarily as a research book. Our approach is essentially theoretical, highlighting the mathematical difficulties and the statistical properties of adaptive designs as regards statistical inference following the experiment. We feel that this approach is needed, since the choice of an experimental design cannot be made without a full understanding of its properties, and we hope that this book will complement part of the present day literature in which a large number of authors base their conclusions on simulations. Simulations are generally very useful, but not always sufficiently convincing, and in some cases they may be plainly misleading.
Ours is a book mainly devoted to general results, so it does not address problems related only to particular applications. Specifically, it is not a book on clinical trials, although a large number of the designs we present are clearly inspired by clinical and pharmaceutical research, and the vast bibliography dedicated to this field. These designs are discussed, in particular, in Atkinson and Biswas’ survey Randomized Response-Adaptive Designs in Clinical Trials, 2014; our motivations are different and we have chosen to dwell on general aspects more than on individual trials, so there is little overlap, and we think of our book as a complement to theirs. This book follows the lead of two fundamental works by W. F. Rosenberger and his coauthors (Hu and Rosenberger, The Theory of Response-Adaptive Randomization in Clinical Trials, 2006, and Rosenberger and Lachin, Randomization in Clinical Trials: Theory and Practice, 2002), to whom we are deeply indebted. We have updated several results and included new topics.
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