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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 104; no. 488; pp. 1467 - 1481
Main Authors: Cai, T. Tony, Sun, Wenguang
Format: Journal Article
Language:English
Published: Alexandria, VA Taylor & Francis 01.12.2009
American Statistical Association
Assoc
Taylor & Francis Ltd
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography: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