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Multiple hypothesis testing is concerned with appropriately controlling the rate of false positives when testing a large number of hypotheses simultaneously, while maintaining the power of each test as much as possible. For testing multiple null hypotheses, the classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. However, quite often, especially when a large number of hypotheses are simultaneously tested, the notion of FWER turns out to be too stringent, allowing little chance to detect many false null hypotheses. Therefore, researchers have focused in the last decade on defining alternative less stringent error rates and developing methods that control them. The false discovery rate (FDR), the expected proportion of falsely rejected null hypotheses, due to Benjamini and Hochberg (1995), is the first of these alternative error rates that has received considerable attention. Recently, the ideas of controlling the probabilities of falsely rejecting at least k null hypotheses, which is the k-FWER, and the false discovery proportion (FDP) exceeding a certain threshold y have been introduced as alternatives to the FWER and methods controlling these new error rates have been suggested. Very recently, following the idea similar to that of the k-FWER, Sarkar (2006) generalized the FDR to the k-FDR, the expected ratio of k or more false rejections to the total number of rejections, which is a less conservative notion of error rate than the FDR and k-FWER. In this work, we develop multiple testing theory and methods for controlling the new type I error rates. Specifically, it consists of four parts: (1) We develop a new stepdown FDR controlling procedure under no assumption on dependency of the underlying p-values, which has much smaller critical constants than that of the existing Benjamini-Yekutieli stepup procedure; (2) We develop new k-FWER and FDP stepdown procedures under the assumption of independence, which are much more powerful than the existing k-FWER and FDP procedures and show that under certain condition, the k-FWER stepdown procedure is unimprovable; (3) We offer a unified approach for construction of k-FWER controlling procedures by generalizing the closure principle in the context of the FWER to the case of the k-FWER; (4) We develop new Benjamini-Hochberg type k-FDR stepup and stepdown procedures in different settings and apply them to one real microarray data analysis.
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.
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.
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.
According to the National Institute of Health, a genome-wide association study is defined as any study of genetic variation across the entire human genome that is designed to identify genetic associations with observable traits (such as blood pressure or weight), or the presence or absence of a disease or condition. Whole genome information, when combined with clinical and other phenotype data, offers the potential for increased understanding of basic biological processes affecting human health, improvement in the prediction of disease and patient care, and ultimately the realization of the promise of personalized medicine. In addition, rapid advances in understanding the patterns of human genetic variation and maturing high-throughput, cost-effective methods for genotyping are providing powerful research tools for identifying genetic variants that contribute to health and disease. This burgeoning science merges the principles of statistics and genetics studies to make sense of the vast amounts of information available with the mapping of genomes. In order to make the most of the information available, statistical tools must be tailored and translated for the analytical issues which are original to large-scale association studies. Analysis of Complex Disease Association Studies will provide researchers with advanced biological knowledge who are entering the field of genome-wide association studies with the groundwork to apply statistical analysis tools appropriately and effectively. With the use of consistent examples throughout the work, chapters will provide readers with best practice for getting started (design), analyzing, and interpreting data according to their research interests. Frequently used tests will be highlighted and a critical analysis of the advantages and disadvantage complimented by case studies for each will provide readers with the information they need to make the right choice for their research. Additional tools including links to analysis tools, tutorials, and references will be available electronically to ensure the latest information is available. Easy access to key information including advantages and disadvantage of tests for particular applications, identification of databases, languages and their capabilities, data management risks, frequently used tests Extensive list of references including links to tutorial websites Case studies and Tips and Tricks
This unique volume provides self-contained accounts of some recent trends in Biostatistics methodology and their applications. It includes state-of-the-art reviews and original contributions.The articles included in this volume are based on a careful selection of peer-reviewed papers, authored by eminent experts in the field, representing a well balanced mix of researchers from the academia, R&D sectors of government and the pharmaceutical industry.The book is also intended to give advanced graduate students and new researchers a scholarly overview of several research frontiers in biostatistics, which they can use to further advance the field through development of new techniques and results.
This book presents the statistical aspects of designing, analyzing and interpreting the results of genome-wide association scans (GWAS studies) for genetic causes of disease using unrelated subjects. Particular detail is given to the practical aspects of employing the bioinformatics and data handling methods necessary to prepare data for statistical analysis. The goal in writing this book is to give statisticians, epidemiologists, and students in these fields the tools to design a powerful genome-wide study based on current technology. The other part of this is showing readers how to conduct analysis of the created study. Design and Analysis of Genome-Wide Association Studies provides a compendium of well-established statistical methods based upon single SNP associations. It also provides an introduction to more advanced statistical methods and issues. Knowing that technology, for instance large scale SNP arrays, is quickly changing, this text has significant lessons for future use with sequencing data. Emphasis on statistical concepts that apply to the problem of finding disease associations irrespective of the technology ensures its future applications. The author includes current bioinformatics tools while outlining the tools that will be required for use with extensive databases from future large scale sequencing projects. The author includes current bioinformatics tools while outlining additional issues and needs arising from the extensive databases from future large scale sequencing projects.
Analysis of Clinical Trials Using SAS®: A Practical Guide, Second Edition bridges the gap between modern statistical methodology and real-world clinical trial applications. Tutorial material and step-by-step instructions illustrated with examples from actual trials serve to define relevant statistical approaches, describe their clinical trial applications, and implement the approaches rapidly and efficiently using the power of SAS. Topics reflect the International Conference on Harmonization (ICH) guidelines for the pharmaceutical industry and address important statistical problems encountered in clinical trials. Commonly used methods are covered, including dose-escalation and dose-finding methods that are applied in Phase I and Phase II clinical trials, as well as important trial designs and analysis strategies that are employed in Phase II and Phase III clinical trials, such as multiplicity adjustment, data monitoring, and methods for handling incomplete data. This book also features recommendations from clinical trial experts and a discussion of relevant regulatory guidelines. This new edition includes more examples and case studies, new approaches for addressing statistical problems, and the following new technological updates: SAS procedures used in group sequential trials (PROC SEQDESIGN and PROC SEQTEST) SAS procedures used in repeated measures analysis (PROC GLIMMIX and PROC GEE) macros for implementing a broad range of randomization-based methods in clinical trials, performing complex multiplicity adjustments, and investigating the design and analysis of early phase trials (Phase I dose-escalation trials and Phase II dose-finding trials) Clinical statisticians, research scientists, and graduate students in biostatistics will greatly benefit from the decades of clinical research experience and the ready-to-use SAS macros compiled in this book.