Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA.
Department of Machine Learning, Carnegie Mellon University, Pittsburgh, PA, USA.
Stat Methods Med Res. 2021 Apr;30(4):976-993. doi: 10.1177/0962280220983381. Epub 2021 Jan 7.
Biological research often involves testing a growing number of null hypotheses as new data are accumulated over time. We study the problem of online control of the familywise error rate, that is testing an a priori unbounded sequence of hypotheses (-values) one by one over time without knowing the future, such that with high probability there are no false discoveries in the entire sequence. This paper unifies algorithmic concepts developed for offline (single batch) familywise error rate control and online false discovery rate control to develop novel online familywise error rate control methods. Though many offline familywise error rate methods (e.g., Bonferroni, fallback procedures and Sidak's method) can trivially be extended to the online setting, our main contribution is the design of new, powerful, adaptive online algorithms that control the familywise error rate when the -values are independent or locally dependent in time. Our numerical experiments demonstrate substantial gains in power, that are also formally proved in an idealized Gaussian sequence model. A promising application to the International Mouse Phenotyping Consortium is described.
生物研究通常涉及随着时间的推移积累新数据而测试越来越多的零假设。我们研究了同时控制多个零假设的问题，即随着时间的推移逐个测试一个事先无界的假设序列（-值），而不知道未来的情况，以便在整个序列中极大概率没有错误发现。本文将为离线（单次批量）组误率控制和在线错误发现率控制开发的算法概念统一起来，以开发新的在线组误率控制方法。虽然许多离线组误率方法（例如 Bonferroni、回退程序和 Sidak 的方法）可以简单地扩展到在线设置，但我们的主要贡献是设计新的、强大的、自适应的在线算法，当-值在时间上独立或局部依赖时，这些算法可以控制组误率。我们的数值实验证明了在理想的高斯序列模型中也得到了正式证明的强大的功效增益。还描述了一种很有前途的应用，即国际小鼠表型联盟。
