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Author: Ang Li Publisher: ISBN: 9780355234114 Category : Languages : en Pages : 137
Book Description
Multiple testing problems arise when we simultaneously test thousands or even millions of hypotheses. In many applications, the hypotheses have certain structures, based on prior studies or domain knowledge, which is a valuable source of information. We study how incorporating such information could improve the performance of multiple testing.
Author: Ang Li Publisher: ISBN: 9780355234114 Category : Languages : en Pages : 137
Book Description
Multiple testing problems arise when we simultaneously test thousands or even millions of hypotheses. In many applications, the hypotheses have certain structures, based on prior studies or domain knowledge, which is a valuable source of information. We study how incorporating such information could improve the performance of multiple testing.
Author: Publisher: Academic Press ISBN: 0323952690 Category : Mathematics Languages : en Pages : 322
Book Description
Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Advancements in Bayesian Methods and Implementation
Author: Xiaoyu Dai Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 104
Book Description
In the last decade, motivated by a variety of applications in medicine, bioinformatics, genomics, brain imaging, etc., a growing amount of statistical research has been devoted to large-scale multiple testing, where thousands or even greater numbers of tests are conducted simultaneously. However, due to the complexity of real data sets, the assumptions of many existing multiple testing procedures, e.g. that tests are independent and have continuous null distributions of p-values, may not hold. This poses limitations in their performances such as low detection power and inflated false discovery rate (FDR). In this dissertation, we study how to better proceed the multiple testing problems under complex data structures. In Chapter 2, we study the multiple testing with discrete test statistics. In Chapter 3, we study the discrete multiple testing with prior ordering information incorporated. In Chapter 4, we study the multiple testing under complex dependency structure. We propose novel procedures under each scenario, based on the marginal critical functions (MCFs) of randomized tests, the conditional random field (CRF) or the deep neural network (DNN). The theoretical properties of our procedures are carefully studied, and their performances are evaluated through various simulations and real applications with the analysis of genetic data from next-generation sequencing (NGS) experiments.
Author: Lilun Du Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In chapter 2, we present a single-index modulated multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value for each hypothesis. To find the optimal rejection region for the bivariate p-value, we propose a criteria based on the ratio of probability density functions of the bivariate p-value under the true null and non-null. This criteria in the bivariate normal setting further motivates us to project the bivariate p-value to a single index p-value, for a wide range of directions. The true null distribution of the single index p-value is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Multiple testing based on chi-squared test statistics is commonly used in many scientific fields such as genomics research and brain imaging studies. However, the challenges associated with designing a formal testing procedure when there exists a general dependence structure across the chi-squared test statistics have not been well addressed. In chapter 3, we propose a Factor Connected procedure to fill in this gap. We first adopt a latent factor structure to construct a testing framework for approximating the false discovery proportion (FDP) for a large number of highly correlated chi-squared test statistics with finite degrees of freedom k. The testing framework is then connected to simultaneously testing k linear constraints in a large dimensional linear factor model involved with some observable and unobservable common factors, resulting in a consistent estimator of FDP based on the associated unadjusted p-values.
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: Gavin Lynch Publisher: ISBN: Category : Languages : en Pages :
Book Description
The hypotheses in many multiple testing problems often have some inherent structure based on prior information such as Gene Ontology in gene expression data. However, few false discovery rate (FDR) controlling procedures take advantage of this inherent structure. In this dissertation, we develop FDR controlling methods which exploit the structural information of the hypotheses. \ First, we study the fixed sequence structure where the testing order of the hypotheses has been pre-specified. We are motivated to study this structure since it is the most basic of structures, yet, it has been largely ignored in the literature on large scale multiple testing. We first develop procedures using the conventional fixed sequence method, where the procedures stop testing after the first hypothesis is accepted. Then, we extend the method and develop procedures which stop after a pre- specified number of acceptances. A simulation study and real data analysis show that these procedures can be a powerful alternative to the standard Benj amini- Hochberg and Benjamini-Yekutieli procedures. Next, we consider the testing of hierarchically ordered hypotheses where hypotheses are arranged in a tree-like structure. First, we introduce a new multiple testing method called the generalized stepwise procedure and use it to create a general approach for testing hierarchically order hypotheses. Then, we develop several hierarchical testing procedures which control the FDR under various forms of dependence. Our simulation studies and real data analysis show that these proposed methods can be more powerful than alternative hierarchical testing methods, such as the method by Yekutieli (2008b). Finally, we focus on testing hypotheses along a directed acyclic graph (DAG). First, we introduce a novel approach to develop procedures for controlling error rates appropriate for large scale multiple testing. Then, we use this approach to develop an FDR controlling procedure which tests hypotheses along the DAG. To our knowledge, no other FDR controlling procedure exists to test hypotheses with this structure. The procedure is illustrated through a real microarray data analysis where Gene Ontology terms forming a DAG are tested for significance. In summary, this dissertation offers new FDR controlling methods which utilize the inherent structural information among the tested hypotheses.
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: Xinping Cui Publisher: CRC Press ISBN: 0429633882 Category : Mathematics Languages : en Pages : 418
Book Description
Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows. Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values. Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement. Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9. Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Author: Jason T. Newsom Publisher: Taylor & Francis ISBN: 1000905977 Category : Psychology Languages : en Pages : 522
Book Description
Longitudinal Structural Equation Modeling is a comprehensive resource that reviews structural equation modeling (SEM) strategies for longitudinal data to help readers determine which modeling options are available for which hypotheses. This accessibly written book explores a range of models, from basic to sophisticated, including the statistical and conceptual underpinnings that are the building blocks of the analyses. By exploring connections between models, it demonstrates how SEM is related to other longitudinal data techniques and shows when to choose one analysis over another. Newsom emphasizes concepts and practical guidance for applied research rather than focusing on mathematical proofs, and new terms are highlighted and defined in the glossary. Figures are included for every model along with detailed discussions of model specification and implementation issues and each chapter also includes examples of each model type, descriptions of model extensions, comment sections that provide practical guidance, and recommended readings. Expanded with new and updated material, this edition includes many recent developments, a new chapter on growth mixture modeling, and new examples. Ideal for graduate courses on longitudinal (data) analysis, advanced SEM, longitudinal SEM, and/or advanced data (quantitative) analysis taught in the behavioral, social, and health sciences, this new edition will continue to appeal to researchers in these fields.
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: Ang Li
Author: Ang Li
Author: 
Author: Xiaoyu Dai
Author: Lilun Du
Author: Peter H. Westfall
Author: Gavin Lynch
Author: Alex Dmitrienko
Author: Xinping Cui
Author: Jason T. Newsom
Author: Frank Bretz