Multiple Testing: Further Development Of Theory And Methodology

多重测试：理论和方法的进一步发展本项目研究者的主要目标是进一步发展统计理论和方法，以解决多重假设检验中的问题。在意识到控制家族错误率（FWER）的传统思想过于严格，无法在大量假设测试时使用后，研究人员最近专注于定义不太严格的错误率并开发控制它们的方法。错误发现率（FDR）是第一个受到相当关注的问题，尽管仍然有一些重要的相关问题尚未得到回答。拒绝至少一个大于1的数字的概率和超过某个阈值的错误发现比例是最近引入的两个概念，它们概括了FWER，并代表了FDR的有意义的替代方案。虽然最近提出了一些控制它们的方法，但研究人员最近的一些工作揭示了开发更新和更强大程序的潜力。发展这种新的程序和调查研究，比较他们与相关的方法，理论上和经验上，将是本研究的一个主要推力。当对双侧备选方案进行多个原假设检验时，通常需要对与被拒绝的备选假设相对应的备选假设进行方向性决策，并控制错误的方向性拒绝。虽然最近在罗斯福框架中提出了这样的程序，但根据研究人员与学生和同事的一些工作，开发更新的程序有很大的潜力。这种新方法的发展将是本研究的第二个主要目标，本研究的结果将对几乎任何统计调查都具有重要意义，因为这些调查在检验几个假设方面提出了问题。一个特别的应用领域是DNA微阵列，这是一种新的和有前途的生物技术，可以同时监测细胞中数千个基因的表达水平。差异表达基因的鉴定是这些实验中一个重要且常见的问题。差异表达的生物学问题被定义为多假设检验的统计学问题：同时检验每个基因的零假设，即表达水平与相关的响应或协变量无关。开发一个统计程序，发现差异表达的基因，通过控制统计措施的错误发现或错误的非发现在所需的水平是这样的问题的中心问题之一。另一个应用领域是药物调查，其中多种测试技术通常用于剂量反应研究或评估药物相对于标准药物或安慰剂的功效。这项研究有可能与生物制药行业和医学院的研究人员进行合作。它还将通过培训研究生、在统计课程中纳入所制定的方法以及编写教科书而使教育受益。

MULTIPLE TESTING: FURTHER DEVELOPMENT OF THEORY AND METHODOLOGY The primary goal of the investigator in this project is further development of statistical theory and methodology for problems in multiple hypothesis testing. Having realized that the traditional idea of controlling the familywise error rate (FWER) is too stringent to use when large number of hypotheses are tested, researchers have recently focused on defining less stringent error rates and developing methods that control them. The false discovery rate (FDR) is the first of these receiving considerable attention, even though there are still a number of important related issues that are yet to be answered. The probabilities of rejecting at least a number more than one and the false discovery proportion exceeding a certain threshold are the two most recently introduced concepts that generalize the FWER and represent meaningful alternatives to the FDR. While some methods controlling them have been suggested very recently, the potential to developing newer and more powerful procedures is revealed by some recent work by the investigator. The development of such new procedures and investigative studies comparing them to related methods, theoretically as well as empirically, will be one major thrust of the present research. When testing multiple null hypotheses against two-sided alternatives, making directional decisions for the alternative hypotheses corresponding to the rejected ones with a control of false directional rejections is often desired. While such a procedure has been recently put forward in the framework of the FDR, there is a good potential of developing newer procedures in light of some work of the investigator together with students and colleagues. The development of such new procedures will be the second major thrust of this research.The results from this research will be of importance to virtually any statistical investigation where questions are posed in terms of testing several hypotheses. One particular area of application is DNA microarrays which are a new and promising biotechnology that can monitor expression levels in cells for thousands of genes simultaneously. The identification of differentially expressed genes is an important and common question in these experiments. The biological question of differential expression is framed as a statistical problem of multiple hypotheses testing: the simultaneous test for each gene of the null hypothesis that the expression levels do not associate with the responses or covariates of interest. Developing a statistical procedure of discovering the genes that are differentially expressed by controlling statistical measures of false discoveries or false non-discoveries at a desired level is one of the central issues in such a problem. Another area of application is pharmaceutical investigations where multiple testing techniques are routinely used in dose-response study or in evaluating a drug's efficacy over a standard drug or placebo. This research has the potential to generate collaborations with researchers in the biopharmaceutical industry and medical schools. It would also benefit education through training of graduate students, incorporation of the developed methodologies in statistics courses, and writing textbooks.