Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks

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...

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Vydáno v:	Journal of the American Statistical Association Ročník 104; číslo 488; s. 1467 - 1481
Hlavní autoři:	Cai, T. Tony, Sun, Wenguang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Alexandria, VA Taylor & Francis 01.12.2009 American Statistical Association Assoc Taylor & Francis Ltd
Témata:	Applications Applied statistics Compound decision problem Conditional local false discovery rate Consistent estimators Data Data collection Decision making Decision theory Error Estimation Exact sciences and technology Exchangeability Exploration False discovery rate False information False positive errors General topics Group size Grouped hypotheses Heterogeneity Hypotheses Hypothesis testing Inference Information Large-scale multiple testing Mathematical procedures Mathematics Multiple criteria decision making Nonparametric inference Oracles Parametric inference Probability and statistics Sampling Sciences and techniques of general use Simulation Small schools Statistical methods Statistical theories Statistics Tests Theory and Methods Discriminant analysis Data analysis Conditional distribution Grouped data Asymptotic optimality Non parametric estimation Statistical estimation Statistical decision Multivariate analysis Statistical simulation Multiple decision Statistical method Hypothesis test Statistical test Compound decision problem Decision theory Grouped hypotheses Large-scale multiple testing False discovery rate Oracle Application Conditional local false discovery rate Exchangeability
ISSN:	0162-1459, 1537-274X
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Shrnutí:	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.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0162-1459 1537-274X
DOI:	10.1198/jasa.2009.tm08415