Collaborative Research: New Directions for Research on Some Large-Scale Multiple Testing Problems

在过去的15年里，假设检验在统计应用到现代科学研究中从单一假设到多假设的范式转变，如脑成像、微阵列分析、天文学、大气科学、药物发现等，在大规模多重检验领域产生了巨大的研究热潮。然而，在开发必要的统计工具之前，许多此类调查中出现的一些根本重要的理论和方法问题仍有待充分解决。例如，在涉及多个测试的临床药物基因组学中，当这些假设被分组顺序测试时(这通常是为了满足经济和伦理问题而需要的)，或者当这些假设属于树形结构的层级家族时(由于不同的假设集合的基于重要性的排序而经常发生)，在非渐近的环境中还没有开发出控制错误发现的方法。此外，在许多多项测试的实际应用中，执行测试的顺序是预先指定的或可以根据现有数据进行评估，但利用这种预排序的现有FDR方法的潜在改进仍有待探索。该项目旨在开发新的和创新的多重测试方法，以解决这些突出的和相关的问题，重点放在以下三个广泛的研究领域：(I)群体顺序多重测试，(Ii)固定序列多重测试，和(Iii)测试多个假设家族。该项目涵盖了统计学家在许多实际环境中面临的一系列重要的多重测试问题。这些问题是新的，并提出了几个技术挑战，因为现有的多重测试控制虚假发现的理论和方法需要从单一阶段或单一家庭的框架扩展到多阶段或多家庭的框架。这项拟议的研究有可能为在更新的方向上进行多重测试的研究打开大门。它不仅旨在推进多重测试理论的发展，而且特别注重已有理论的应用。该项目预计将对统计理论和实践产生广泛影响。它的目的是通过推进现代科学实验中重要领域的研究，使统计领域现代化，从而造福社会。例如，该项目可能为解决现代药物发现和生物医学实验中面临的统计问题的新技术铺平道路。它还将通过培训研究生和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。

The paradigm shift of hypothesis testing from single to multiple hypotheses, often large number of them, in statistical applications to modern scientific investigations, such as brain imaging, microarray analysis, astronomy, atmospheric science, drug discovery and many others, has generated tremendous upsurge of research in the field of large-scale multiple testing in the last one and half decades. Nevertheless, some fundamentally important theoretical as well as methodological issues arising in many of these investigations still remain to be fully addressed before developing the necessary statistical tools. For instance, in clinical pharmacogenomics involving multiple testing, methods controlling false discoveries are yet to be developed in non-asymptotic setting when these hypotheses are tested group sequentially which is often required in order to meet economical and ethical concerns, or when these hypotheses belong to tree-structured hierarchical families which often happens due to importance based ordering of different sets of hypotheses. Also, in many practical applications of multiple testing where the order in which the tests are to be performed is pre-specified or can be assessed based on available data, but the potential improvements of the existing FDR methodologies exploiting this pre-ordering are yet to be explored. The project seeks to develop new and innovative multiple testing methods tackling these outstanding and related issues by focusing on the following three broad areas of research: (i) group sequential multiple testing, (ii) fixed sequence multiple testing, and (iii) testing multiple families of hypotheses. The project covers a wide spectrum of important multiple testing problems statisticians face in many practical settings. These problems are new and pose several technical challenges, as the existing theory and methodologies on multiple testing controlling false discoveries need to be extended from the framework of single stage or single family to that of multiple stages or multiple families. The proposed research has the potential to open up the door for research on multiple testing in newer directions. It not only aims at advancing the theory of multiple testing but also pays special attention to applications of the developed theories. This project is expected to have a broad impact on the theory and practice of statistics. It aims at modernizing the field of statistics by advancing research in areas of importance in modern scientific experiments, and thus can benefit the society. For instance, the project can potentially pave the way for novel techniques to address statistical issues faced in modern drug discoveries and biomedical experiments. It would also benefit education through training of graduate students and 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.