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

在脑成像、微阵列分析、天文学、大气科学、药物发现等现代科学研究的统计应用中，假设检验从单一到多个（通常是大量的）假设检验的范式转变，在过去的15年里，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，在许多这些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，控制错误发现的方法尚未在非渐近环境中开发，当这些假设按组顺序进行测试时，这通常是为了满足经济和伦理问题，或者当这些假设属于树状结构的等级家庭时，这通常是由于不同假设集的重要性排序而发生的。此外，在多次测试的许多实际应用中，进行测试的顺序是预先规定的，或者可以根据现有数据进行评估，但尚未探索利用这种预先排序对现有FDR方法的潜在改进。该项目旨在通过关注以下三个广泛的研究领域，开发新的和创新的多重测试方法来解决这些突出的和相关的问题：(i)群体顺序多重测试，（ii）固定顺序多重测试，（iii）测试多个假设家族。该项目涵盖了统计学家在许多实际设置中面临的重要多重测试问题的广泛范围。这些问题都是新出现的问题，对现有的多次测试控制错误发现的理论和方法提出了一些技术挑战，需要从单阶段或单家族的框架扩展到多阶段或多家族的框架。所提出的研究有可能为新方向的多重测试研究打开大门。它不仅旨在推进多重测试理论，而且特别关注已发展理论的应用。该项目有望对统计学的理论和实践产生广泛的影响。它旨在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，从而使社会受益。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。通过培训研究生和将发展的方法纳入统计课程，也将有利于教育。研究结果将通过在国家和国际会议上的演讲和讨论以及访问其他机构来传播。在这个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.