Adaptive designs: Sequential tests of multiple hypotheses

研究者将开发用于分析多个连续数据流的自适应设计，希望测试一组统计假设。这些设计需要的知识很少（在某些情况下没有）这些数据流之间的依赖性--因为这种依赖性通常很强，但在实践中很难或不可能建模--并且将提供顺序的多个假设检验过程，其通过控制总体错误率来单独地得出关于每个单独的流和假设的结论，以及作为整体的假设集，同时通过一旦不需要附加信息就“丢弃”数据流来达到确信的结论而自适应地有效。这将针对两个最广泛使用的多重测试错误度量，错误发现率和族错误率进行。对于这两个指标，研究者将：（1）为现有程序开发序贯多重检验程序和统一理论;（2）通过分析和广泛的数值模拟评估其性能和最优性;（3）找到其操作特征的表达式或近似值，包括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中的真实的数据，并修改程序以帮助这些领域的实际实施;以及（5）发展免费软件以方便应用。该计划将提供新的统计方法，以处理按顺序到达的多个数据流的分析随着时间的推移，以连贯的方式。 处理这类数据的需求出现在大量的现实情况中，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、人类和动物群体的疾病监测、遗传学和基因组学。 尽管如此，除了在某些特殊情况下，几乎没有现有的统计程序可以使用。因此，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，这项工作将是统计这一基本但基本上尚未探索的领域的一个突破，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.