Optimal Sequentially Planned Decision Procedures
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| Author | : Norbert Schmitz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461227364 |
Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.
| Author | : Shelemyahu Zacks |
| Publisher | : John Wiley & Sons |
| Total Pages | : 411 |
| Release | : 2009-05-11 |
| Genre | : Medical |
| ISBN | : 0470466944 |
An expert introduction to stage-wise adaptive designs in all areas of statistics Stage-Wise Adaptive Designs presents the theory and methodology of stage-wise adaptive design across various areas of study within the field of statistics, from sampling surveys and time series analysis to generalized linear models and decision theory. Providing the necessary background material along with illustrative S-PLUS functions, this book serves as a valuable introduction to the problems of adaptive designs. The author begins with a cohesive introduction to the subject and goes on to concentrate on generalized linear models, followed by stage-wise sampling procedures in sampling surveys. Adaptive forecasting in the area of time series analysis is presented in detail, and two chapters are devoted to applications in clinical trials. Bandits problems are also given a thorough treatment along with sequential detection of change-points, sequential applications in industrial statistics, and software reliability. S-Plus functions are available to accompany particular computations, and all examples can be worked out using R, which is available on the book's related FTP site. In addition, a detailed appendix outlines the use of these software functions, while an extensive bibliography directs readers to further research on the subject matter. Assuming only a basic background in statistical topics, Stage-Wise Adaptive Designs is an excellent supplement to statistics courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and practitioners in the fields of statistics and biostatistics.
| Author | : Rainer Schwabe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 132 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461240387 |
In real applications most experimental situations are influenced by a large number of different factors. In these settings the design of an experiment leads to challenging optimization problems, even if the underlying relationship can be described by a linear model. Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.
| Author | : Mark Chang |
| Publisher | : CRC Press |
| Total Pages | : 442 |
| Release | : 2012-10-09 |
| Genre | : Mathematics |
| ISBN | : 1584889632 |
Adaptive design has become an important tool in modern pharmaceutical research and development. Compared to a classic trial design with static features, an adaptive design allows for the modification of the characteristics of ongoing trials based on cumulative information. Adaptive designs increase the probability of success, reduce costs and the t
| Author | : Gernot Wassmer |
| Publisher | : Springer |
| Total Pages | : 310 |
| Release | : 2016-07-04 |
| Genre | : Medical |
| ISBN | : 3319325620 |
This book provides an up-to-date review of the general principles of and techniques for confirmatory adaptive designs. Confirmatory adaptive designs are a generalization of group sequential designs. With these designs, interim analyses are performed in order to stop the trial prematurely under control of the Type I error rate. In adaptive designs, it is also permissible to perform a data-driven change of relevant aspects of the study design at interim stages. This includes, for example, a sample-size reassessment, a treatment-arm selection or a selection of a pre-specified sub-population. Essentially, this adaptive methodology was introduced in the 1990s. Since then, it has become popular and the object of intense discussion and still represents a rapidly growing field of statistical research. This book describes adaptive design methodology at an elementary level, while also considering designing and planning issues as well as methods for analyzing an adaptively planned trial. This includes estimation methods and methods for the determination of an overall p-value. Part I of the book provides the group sequential methods that are necessary for understanding and applying the adaptive design methodology supplied in Parts II and III of the book. The book contains many examples that illustrate use of the methods for practical application. The book is primarily written for applied statisticians from academia and industry who are interested in confirmatory adaptive designs. It is assumed that readers are familiar with the basic principles of descriptive statistics, parameter estimation and statistical testing. This book will also be suitable for an advanced statistical course for applied statisticians or clinicians with a sound statistical background.
| Author | : Annpey Pong |
| Publisher | : CRC Press |
| Total Pages | : 475 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1439810176 |
In response to the US FDA's Critical Path Initiative, innovative adaptive designs are being used more and more in clinical trials due to their flexibility and efficiency, especially during early phase development. Handbook of Adaptive Designs in Pharmaceutical and Clinical Development provides a comprehensive and unified presentation of the princip
| Author | : Klaus Hinkelmann |
| Publisher | : John Wiley & Sons |
| Total Pages | : 598 |
| Release | : 2012-02-14 |
| Genre | : Mathematics |
| ISBN | : 0470530685 |
Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues building upon the philosophical foundations of experimental design by providing important, modern applications of experimental design to the many fields that utilize them. The book also presents optimal and efficient designs for practice and covers key topics in current statistical research. Featuring contributions from leading researchers and academics, the book demonstrates how the presented concepts are used across various fields from genetics and medicinal and pharmaceutical research to manufacturing, engineering, and national security. Each chapter includes an introduction followed by the historical background as well as in-depth procedures that aid in the construction and analysis of the discussed designs. Topical coverage includes: Genetic cross experiments, microarray experiments, and variety trials Clinical trials, group-sequential designs, and adaptive designs Fractional factorial and search, choice, and optimal designs for generalized linear models Computer experiments with applications to homeland security Robust parameter designs and split-plot type response surface designs Analysis of directional data experiments Throughout the book, illustrative and numerical examples utilize SAS®, JMP®, and R software programs to demonstrate the discussed techniques. Related data sets and software applications are available on the book's related FTP site. Design and Analysis of Experiments, Volume 3 is an ideal textbook for graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, and business.
| Author | : Sandeep Menon |
| Publisher | : SAS Institute |
| Total Pages | : 364 |
| Release | : 2015-12-09 |
| Genre | : Computers |
| ISBN | : 1629600849 |
This book covers domains of modern clinical trial design: classical, group sequential, adaptive, and Bayesian methods applicable to and used in various phases of pharmaceutical development. Written for biostatisticians, pharmacometricians, clinical developers, and statistical programmers involved in the design, analysis, and interpretation of clinical trials, as well as students in graduate and postgraduate programs in statistics or biostatistics, it covers topics including: dose-response and dose-escalation designs; sequential methods to stop trials early for overwhelming efficacy, safety, or futility; Bayesian designs incorporating historical data; adaptive sample size re-estimation and randomization to allocate subjects to effective treatments; population enrichment designs. Methods are illustrated using clinical trials from diverse therapeutic areas, including dermatology, endocrinology, infectious disease, neurology, oncology and rheumatology. --
| Author | : Nancy Flournoy |
| Publisher | : IMS |
| Total Pages | : 218 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780940600461 |
| Author | : Ibrahim Rahimov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 207 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242169 |
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
