New Problems in Multiple Hypotheses Testing

近年来，多假设检验领域的研究突然兴起，产生了新的想法，并提出了一些重要的统计问题。本提案旨在解决其中一些问题。研究的一个主要方向是进一步发展错误发现率（FDR）理论，这是一个新的和强大的概念，错误率在多重测试中，已受到越来越多的关注，在各种各样的统计应用。虽然它已经建立了由调查员和其他研究人员最近，存在多个测试程序，可以控制FDR的情况下，涉及独立的，以及某些类型的正相关的测试统计，还没有理论已经发展到一个统计上有意义的比较这些程序。该建议考虑在涉及假阴性率（FNR）的一些新标准方面发展该理论。第二个主要的推力，拟议的研究将是调查的一些重要的开放性问题有关的方向误差控制在逐步多个测试程序。多重检验中的方向误差控制理论迄今为止主要集中在独立检验统计量的框架内，限制了其在检验统计量很少独立的真实的应用中的范围。研究人员最近重新审视了这一理论与独立的测试统计，并改进了它的逐步下降的程序。这个项目的目的是发展这个理论，进一步容纳其他逐步的程序和检验统计，不一定是独立的。最近发表的研究和研究者的一些初步调查提供了强大的动力，并为拟议的研究奠定了基础。从这项研究的结果将是重要的几个领域的统计应用，包括微阵列实验的概念，错误的发现率已被接受作为一个统计测量错误检测差异表达的基因，和药物研究，其中多种测试技术是常规使用在评估药物的疗效超过标准药物或安慰剂。这项研究有可能产生与生物制药统计研究人员的合作。它还将通过培训研究生和本科生以及在统计课程中纳入所制定的方法来促进教育。

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.