A Decision Theoretic Approach to Multiple Testing of Grouped Hypotheses

• Activity Number: 503
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yanping Liu*+ and Sanat K. Sarkar and Zhigen Zhao
• Companies: Temple University and Temple University and Temple University
• Keywords: False Discovery Rate ; Grouped Hypotheses ; Hidden Markov Model ; Large-Scale Multiple Testing

Abstract

In many modern large-scale multiple testing problems, the hypotheses appear in non-overlapping groups with the associated p-values exhibiting dependence within but not between groups. Such group formation is often a natural phenomenon due to the underlying experimental process or can be created based on other considerations. In this paper, we take a compound decision theoretic approach toward developing a multiple testing procedure for grouped hypotheses subject to controlling the false discovery rate (FDR). Our procedure works in two stages. At the first stage, hypotheses in each group are screened for possible rejection subject to a certain constraint on group-specific FDR. At the second stage, these hypotheses are ultimately rejected if the corresponding groups are determined to be rejected when controlling the overall or total FDR at the specified level. We provide numerical evidence of superior performance of the oracle version of our procedure over its natural competitors, including the one without using the group structure, in certain scenarios under two different model settings for the within-group pairs of p-value and the truth or falsity of the associated null hypothesis.