Collaborative Research: Constructing New Multiple Testing Methods

多重假设检验已成为一个日益活跃的研究领域，因为它作为一种统计工具，分析数据从现代科学调查，如DNA微阵列和功能性磁共振成像（fMRI）的研究。虽然已经提出了几种统计方法来解决这些研究中出现的不同的多重检验问题，但这些方法的开发往往没有充分利用基本检验统计量是相关的这一事实，尽管这种相关性对于这些研究中的数据来说是一种自然现象，如果不加以适当考虑，可能会导致误导性结论。拟议的研究项目旨在通过适当解决所谓的“依赖性问题”，开发新的和创新的多种测试方法。它侧重于三个广泛的研究领域：（i）开发新的多重测试方法，控制一些标准错误率的广义版本，允许一些错误拒绝（ii）开发新的多重测试方法，控制多个错误的方向错误，以及（iii）开发新的数据自适应方法，控制家庭错误和错误发现率。预计该项目将对统计理论和实践产生广泛影响。这个项目的结果将是重要的，几乎任何统计调查的问题，在测试几个假设。例如，在微阵列或功能磁共振成像研究中，差异表达基因或活性体素的检测通常被视为一个多重测试问题，在药物研究中，多种测试技术通常用于剂量反应研究或评估药物对标准药物或安慰剂的疗效，我们的项目可能会提供新的和改进的方法。该项目还将通过培训研究生、将所制定的方法纳入统计课程而使教育受益。将通过在国家和国际会议上的介绍和讨论以及对其他机构的访问来传播结果。在该项目下开发的软件将免费提供给科学界。

Multiple hypothesis testing has become an increasingly active area of research because of its usefulness as a statistical tool to analyze data from modern scientific investigations, such as DNA microarray and functional magnetic resonance imaging (fMRI) studies. While several statistical methods have been put forward to address different multiple testing problems arising in these studies, often they were developed without fully utilizing the fact that the underlying test statistics are dependent, although such dependence is a natural phenomenon for data from these studies and might lead to misleading conclusions if not properly taken into consideration. The proposed research project seeks to develop new and innovative multiple testing methods by properly addressing the so called `dependence issues?. It focuses on three broad areas of research: (i) developing new multiple testing methods controlling generalized versions of some standard error rates that allow a few false rejections (ii) developing new multiple testing methods controlling multiple false directional errors, and (iii) developing new data-adaptive methods controlling the familywise error and false discovery rates. This project will be expected to have a broad impact on the theory and practice of statistics. The results from this project will be of importance to virtually any statistical investigation where questions are posed in terms of testing several hypotheses. For instance, in microarray or fMRI studies where detection of differentially expressed genes or active voxels is often framed as a multiple testing problem, in pharmaceutical investigations where multiple testing techniques are routinely used in dose-response study or in evaluating a drug's efficacy over standard drug or placebo, our project can potentially offer new and improved methodologies. The project would also benefit education through training of graduate students, incorporation of the developed methodologies in statistics courses. The results will be disseminated through presentations and discussions at national and international conferences, and visits to other institutions. The software to be developed under this project will be made available, free of charge, to the scientific community.