New Problems in Multiple Hypotheses Testing

近年来，多重假设检验领域的研究突然兴起，产生了更新的想法，并提出了一些重要的统计问题。本提案打算解决其中一些问题。这项研究的主要目的将是进一步发展错误发现率(FDR)理论，这是一个新的和强大的多重测试错误率的概念，它在各种统计应用中受到越来越多的关注。虽然研究人员和其他研究人员最近已经确定，在涉及独立和某些类型的正相关检验统计量的情况下，存在可以控制FDR的多个检验程序，但还没有理论发展到对这些程序进行统计上有意义的比较。这项建议考虑在涉及假阴性率(FNR)的一些新标准方面发展这一理论。这项研究的第二个主要目的将是研究分步多重测试过程中与定向错误控制相关的一些重要的开放问题。到目前为止，多重测试中的定向差错控制理论大多集中在独立测试统计的框架内，限制了其在测试统计很少独立的实际应用中的范围。研究人员最近用独立的检验统计重新审视了这一理论，并将其改进为逐级程序。该项目旨在进一步发展这一理论，以适应不一定独立的其他逐步程序和检验统计。最近发表的研究和研究者的一些初步调查为拟议的研究提供了强大的动机和基础。这项研究的结果将对统计学应用的几个领域具有重要意义，包括微阵列实验，其中错误发现率的概念已被接受为检测差异表达基因的误差的统计衡量标准，以及制药研究，其中多种测试技术被常规用于评估一种药物相对于标准药物或安慰剂的疗效。这项研究有可能与生物制药统计方面的研究人员进行合作。它还将通过培训研究生和本科生以及将已开发的方法纳入统计课程而使教育受益。

A sudden upsurge of research in the area of multiple hypotheses testing has been taking place in the recent years resulting in newer ideas and raising a number of important statistical questions. The present proposal intends to address a number of those questions. A major thrust of the research will be to provide further development of the theory of false discovery rate (FDR), a new and powerful concept of error rate in multiple testing, which has been receiving increasing attention in a wide variety of statistical applications. While it has been established by the investigator and other researchers recently that there exist multiple testing procedures which can control the FDR in situations involving independent as well as some types of positively dependent test statistics, no theory has yet been developed toward a statistically meaningful comparisons of these procedures. This proposal considers developing this theory in terms of some new criteria involving false negatives rate (FNR). A second major thrust of the proposed research will be the investigation of some important open problems related to directional error control in stepwise multiple testing procedures. The theory of directional error control in multiple testing has so far been concentrated mostly within the framework of independent test statistics, limiting its scope in real applications where the test statistics are rarely independent. The investigator has recently revisited this theory with independent test statistics and improved it for a step-down procedure. This project aims at developing this theory further accommodating other stepwise procedures and test statistics that are not necessarily independent. Recent published research and some preliminary investigations by the investigator provide strong motivation and lay the foundation for the proposed research. The results from this research will be of importance to several areas of statistical applications, including microarray experiments where the concept of false discovery rate has been receiving acceptance as a statistical measure of error in detecting differentially expressed genes, and pharmaceutical studies where multiple testing techniques are routinely used in evaluating a drug's efficacy over standard drug or placebo. This research has the potential to generate collaborations with researchers in biopharmaceutical statistics. It would also benefit education through training of graduate as well as undergraduate students and incorporation of the developed methodologies in statistics courses.