Adaptive designs: Sequential tests of multiple hypotheses

研究者将为多个连续数据流的分析开发自适应设计，希望测试一组统计假设。这些设计将需要对这些数据流之间的依赖关系了解最少（在某些情况下不需要），因为这种依赖关系通常很强，但在实践中很难或不可能建模，并且将提供连续的多个假设检验程序，这些假设检验程序可以通过控制总体错误率得出关于每个单独的流和假设的结论，以及作为一个整体的假设集。当不需要额外的信息来得出确信的结论时，通过“丢弃”数据流来实现自适应效率。这将用于两个最广泛使用的多重测试错误指标，即错误发现率和家庭错误率。对于这两个指标，研究者将：(1)开发连续的多个测试程序和现有程序的统一理论；(2)通过分析和广泛的数值模拟来评估它们的性能和最优性；（三）找出其运行特性的表达式或近似表达式，包括已实现的错误率和预期的总样本量和最大样本量；(4)将程序应用于遗传学、基因组学和多臂生物医学试验的真实数据，并修改程序以帮助这些领域的实际实施；(5)开发方便应用的免费软件包。该项目将提供新的统计方法，以连贯的方式处理随时间顺序到达的多个数据流分析。处理这类数据的需求出现在现实世界的大量情况中，包括恐怖主义威胁检测、质量控制、金融、新疗法的生物医学临床试验、人类和动物种群的疾病监测、遗传学和基因组学。尽管如此，除了在一些特殊情况下，很少有现有的统计程序可以使用。因此，本项目制定的程序将广泛适用于这些领域的科学家和工作人员。从方法上讲，这项工作将是统计学中一个基本但基本上尚未探索的领域的突破，对社会有许多好处和更广泛的影响。

The investigator will develop adaptive designs for the analysis of multiple sequential data streams, about which it is desired to test a set of statistical hypotheses. The designs will require minimal knowledge (none in some cases) of the dependence between these data streams -- since such dependence is often strong but difficult or impossible to model in practice -- and will provide sequential multiple hypothesis testing procedures which reach conclusions about each individual stream and hypothesis individually, as well as the set of hypotheses as a whole by controlling overall error rates, while being adaptively efficient by "dropping" a data stream once no additional information is needed to reach a confident conclusion. This will be done for the two most widely-used multiple testing error metrics, false-discovery rate and familywise error rate. For these two metrics, the investigator will: (1) develop sequential multiple testing procedures and a unified theory for existing procedures; (2) assess their performance and optimality through analysis and extensive numerical simulations; (3) find expressions or approximations for their operating characteristics including achieved error rates and expected total and maximum sample size; (4) apply the procedures to real data in genetics, genomics, and multi-arm biomedical trials and modify the procedures to aid practical implementation in these areas; and (5) develop free software packages to facilitate applications.The project will provide new statistical methods to handle the analysis of multiple data streams arriving sequentially over time in a coherent fashion. The need to handle this type of data arises in a plethora of real-world situations including terrorist threat detection, quality control, finance, biomedical clinical trials for new treatments, disease monitoring in human and animal populations, genetics, and genomics. Despite this, there are few existing statistical procedures that one can use except in some special cases. The procedures developed in this project will therefore be widely applicable by scientists and workers in these areas. Methodologically, the work will be a breakthrough in a fundamental yet largely unexplored area of statistics, with many benefits and broader impacts to society.