Smoothed nested testing on directed acyclic graphs

• 成果类型: Article
• 署名作者: Loper, J. H.; Lei, L.; Fithian, W.; Tansey, W.
• 署名单位: Columbia University; Stanford University; University of California System; University of California Berkeley; Memorial Sloan Kettering Cancer Center
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab041
• 发表日期: 2022
• 页码: 457471
• 关键词: false discovery rate; inequalities; hypotheses

摘要

We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove that a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent, but are derived from positively correlated normal observations, we prove control for all three error rates when the smoothing method is an arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.