Collaborative Research: Constructing New Multiple Testing Methods

多重假设检验已经成为一个日益活跃的研究领域，因为它作为一种统计工具来分析来自现代科学调查的数据，例如DNA微阵列和功能磁共振成像(FMRI)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测试问题，但它们往往没有充分利用基本测试统计数据是相关的这一事实，尽管这种相关性是来自这些研究的数据的自然现象，如果没有适当地考虑，可能会导致误导结论。拟议的研究项目寻求通过适当处理所谓的“依赖性问题”来开发新的、创新的多种测试方法。它集中在三个广泛的研究领域：(I)开发控制某些标准错误率的广义版本的新的多重测试方法，允许少数错误拒绝(Ii)开发控制多个错误定向错误的新的多重测试方法，以及(Iii)开发控制家庭错误和错误发现率的新的数据自适应方法。预计该项目将对统计理论和实践产生广泛影响。这个项目的结果将对几乎任何通过检验几个假设而提出问题的统计调查具有重要意义。例如，在微阵列或功能磁共振研究中，差异表达基因或活动体素的检测通常被视为一个多重测试问题，在药物研究中，在剂量-反应研究中经常使用多种测试技术，或者在评估一种药物相对于标准药物或安慰剂的疗效时，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、将已开发的方法纳入统计课程而使教育受益。成果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。将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.