Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks

• 成果类型: Article
• 署名作者: Cai, T. Tony; Sun, Wenguang
• 署名单位: University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08415
• 发表日期: 2009
• 页码: 1467-1481
• 关键词: false discovery rate; compound decision rules; EMPIRICAL BAYES; NULL

摘要

In large-scale multiple testing problems, data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics. Conventional approaches, including the pooled and separate analyses, fail to efficiently utilize the external grouping information. We develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate. It is shown that both the pooled and separate analyses can be uniformly improved by the oracle procedure. We then propose a data-driven procedure that is shown to be asymptotically optimal. Simulation studies show that our procedures enjoy superior performance and yield the most accurate results in comparison with both the pooled and separate procedures. A real-data example with grouped hypotheses is studied in detail using different methods. Both theoretical and numerical results demonstrate that exploiting external information of the sample can greatly improve the efficiency of a multiple testing procedure. The results also provide insights on how the grouping information is incorporated for optimal simultaneous inference.