Adaptive designs: Sequential tests of multiple hypotheses

研究人员将开发用于分析多个顺序数据流的自适应设计，以检验一组统计假设。设计将需要对这些数据流之间的相关性的最低限度的了解(在某些情况下不需要)--因为这种相关性通常很强，但在实践中很难或不可能建模--并将提供顺序的多重假设检验程序，通过控制总体错误率单独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，同时通过一旦不需要额外的信息来得出确信的结论而自适应地有效地“丢弃”数据流。这将对两个最广泛使用的多测试错误度量进行，即错误发现率和家庭错误率。对于这两个指标，研究人员将：(1)为现有程序开发连续的多重测试程序和统一的理论；(2)通过分析和广泛的数值模拟来评估它们的性能和最佳性；(3)找到它们的操作特性的表达式或近似值，包括实现的错误率以及预期的总样本量和最大样本量；(4)将这些程序应用于遗传学、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；以及(5)开发免费软件包，以方便应用程序。该项目将提供新的统计方法，以一致的方式处理随着时间顺序到达的多个数据流的分析。处理此类数据的需求出现在过多的现实世界情况中，包括恐怖威胁检测、质量控制、金融、新疗法的生物医学临床试验、人类和动物种群中的疾病监测、遗传学和基因组学。尽管如此，除了在一些特殊情况下，几乎没有现有的统计程序可以使用。因此，在该项目中开发的程序将被这些领域的科学家和工作人员广泛应用。从方法上讲，这项工作将是一个基本但在很大程度上尚未探索的统计领域的突破，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.