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Author: Yiyong Fu Publisher: ISBN: Category : Languages : en Pages : 122
Book Description
The importance of multiplicity adjustment has gained wide recognition in modern scientific research. Without it, there will be too many spurious results and reproducibility becomes an issue; with it, if overtly conservative, discoveries will be made more difficult. In the current literature on repeated testing of multiple hypotheses, Bonferroni-based methods are still the main vehicle carrying the bulk of multiplicity adjustment. There is room for power improvement by suitably utilizing both hypothesis-wise and analysis- wise dependencies. This research will contribute to the development of a natural group-sequential extension of the classical stepwise multiple testing procedures, such as Dunnett's stepdown and Hochberg's step-up procedures. It is shown that the proposed group-sequential procedures strongly control the familywise error rate while being more powerful than the recently developed class of group-sequential Bonferroni-Holm's procedures. Particularly in this research, a convexity property is discovered for the distribution of the maxima of pairwise null P-values with the underlying test statistics having distributions such as bivariate normal, t, Gamma, F, or Archimedean copulas. Such property renders itself for an immediate use in improving Holm's procedure by incorporating pairwise dependencies of P-values. The improved Holm's procedure, as all stepdown multiple testing procedures, can also be naturally extended to group-sequential setting.
Author: Yiyong Fu Publisher: ISBN: Category : Languages : en Pages : 122
Book Description
The importance of multiplicity adjustment has gained wide recognition in modern scientific research. Without it, there will be too many spurious results and reproducibility becomes an issue; with it, if overtly conservative, discoveries will be made more difficult. In the current literature on repeated testing of multiple hypotheses, Bonferroni-based methods are still the main vehicle carrying the bulk of multiplicity adjustment. There is room for power improvement by suitably utilizing both hypothesis-wise and analysis- wise dependencies. This research will contribute to the development of a natural group-sequential extension of the classical stepwise multiple testing procedures, such as Dunnett's stepdown and Hochberg's step-up procedures. It is shown that the proposed group-sequential procedures strongly control the familywise error rate while being more powerful than the recently developed class of group-sequential Bonferroni-Holm's procedures. Particularly in this research, a convexity property is discovered for the distribution of the maxima of pairwise null P-values with the underlying test statistics having distributions such as bivariate normal, t, Gamma, F, or Archimedean copulas. Such property renders itself for an immediate use in improving Holm's procedure by incorporating pairwise dependencies of P-values. The improved Holm's procedure, as all stepdown multiple testing procedures, can also be naturally extended to group-sequential setting.
Author: Alex Dmitrienko Publisher: CRC Press ISBN: 1584889853 Category : Mathematics Languages : en Pages : 323
Book Description
Useful Statistical Approaches for Addressing Multiplicity IssuesIncludes practical examples from recent trials Bringing together leading statisticians, scientists, and clinicians from the pharmaceutical industry, academia, and regulatory agencies, Multiple Testing Problems in Pharmaceutical Statistics explores the rapidly growing area of multiple c
Author: Tian Zhao Publisher: ISBN: Category : Biometry Languages : en Pages : 188
Book Description
With the rapid growth of the pharmaceutical industry, it became particularly important to develop efficient statistical techniques for conducting clinical trials. Practically clinical trials nowadays are conducted to answer many questions rather than exploring just one hypothesis. A treatment has to pass the efficacy and safety standards minimally. Handling multiplicity in clinical trials has become a hot topic. During the last two decades, a number of new statistical techniques appeared that improved the overall power of multiple testing procedures while still controlling the familywise Type I error rate. However, a large portion of modern clinical trials is conducted sequentially. The last five years or so, Bartroff and Lai, De and Baron, applied stepwise testing of multiple hypotheses. The procedures were open-ended. But the standard practice requires any clinical trials to be completed by the given date. Any stopping rules have to be truncated. This is the main difference in the problem considered in this dissertation from all the previously proposed methods. In this dissertation, we derived the simultaneous testing of multiple hypotheses that: - control the familywise Type I and Type II error rates; - terminate sampling with probability one at or before the given number of sampled groups; - optimize the expected sample size. For the purpose of testing multiple hypotheses, with a given truncation point, we developed a new group sequential procedure based on the truncated sequential probability ratio test. Our method resulted in an improved single-hypothesis testing that appeared to be more efficient than Pollock's method proposed earlier for the same problem. Extending this to multiple hypotheses by means of Holm-Bonferroni stepwise approach, we derive a truncated group sequential procedure for the simultaneous testing of multiple hypotheses that controls familywise Type I and Type II errors in the strong sense. The new methods can be applied to any truncated sequential sampling for multiple comparisons. Optimizing the expected sampling cost of a clinical trial in this context inevitably implies reduction in the cost of medical treatments, and therefore, it ultimately results in the reduced cost of health care.
Author: Aiying Chen Publisher: ISBN: Category : Languages : en Pages : 84
Book Description
This dissertation is focused on multiple hypotheses testing procedures under group sequential design, under which the data are accrued sequentially or periodically in time. We propose two stepwise procedures using the error spending function approach. The first procedure controls the Family-wise Error Rate (FWER), under the assumption that the test statistics follow normal distribution with known correlations. This procedure involves repeated application of a step-down procedure at each stage on the hypotheses that are not rejected in the previous stages. The second proposed procedure is a group sequential BH procedure (GSBH) controlling the False Discovery Rate (FDR), which is a natural extension of the original BH method from single to multiple stages under a group sequential design. Similar to the proposed step-down procedure controlling the FWER, a step-up procedure is applied on the active hypotheses at each stage in the GSBH procedure. This GSBH procedure is theoretically proved to control the FDR under some positive dependence condition. An adaptive version of GSBH procedure (ad.GSBH) is also introduced, which is proved to control the FDR under independence. Simulation studies are performed to investigate the performance of these three procedures. The simulation results show that these procedures are often powerful and provide more reduction of the expected sample sizes compared to their relevant competitors.
Author: Christopher Jennison Publisher: CRC Press ISBN: 9781584888581 Category : Mathematics Languages : en Pages : 416
Book Description
Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion. Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models. Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.
Author: Frank Bretz Publisher: CRC Press ISBN: 1420010905 Category : Mathematics Languages : en Pages : 202
Book Description
Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at http://CRAN.R-project.org After giving examples of multiplicity problems, the book covers general concepts and basic multiple comparisons procedures, including the Bonferroni method and Simes’ test. It then shows how to perform parametric multiple comparisons in standard linear models and general parametric models. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey’s all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. The last chapter reviews other multiple comparison procedures, such as resampling-based procedures, methods for group sequential or adaptive designs, and the combination of multiple comparison procedures with modeling techniques. Controlling multiplicity in experiments ensures better decision making and safeguards against false claims. A self-contained introduction to multiple comparison procedures, this book offers strategies for constructing the procedures and illustrates the framework for multiple hypotheses testing in general parametric models. It is suitable for readers with R experience but limited knowledge of multiple comparison procedures and vice versa. See Dr. Bretz discuss the book.
Author: Peter H. Westfall Publisher: John Wiley & Sons ISBN: 9780471557616 Category : Mathematics Languages : en Pages : 382
Book Description
Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Author: Douglas G. Altman Publisher: CRC Press ISBN: 1000228819 Category : Mathematics Languages : en Pages : 624
Book Description
Practical Statistics for Medical Research is a problem-based text for medical researchers, medical students, and others in the medical arena who need to use statistics but have no specialized mathematics background. The author draws on twenty years of experience as a consulting medical statistician to provide clear explanations to key statistical concepts, with a firm emphasis on practical aspects of designing and analyzing medical research. Using real data and including dozens of interesting data sets, this bestselling text gives special attention to the presentation and interpretation of results and the many real problems that arise in medical research.
Author: Yiyong Fu
Author: Yiyong Fu
Author: Alex Dmitrienko
Author: Tian Zhao
Author: Aiying Chen
Author: Hong Wan
Author: Christopher Jennison
Author: Frank Bretz
Author: Peter H. Westfall
Author: Yonghua Chen
Author: Douglas G. Altman