A new approach to multiple testing of grouped hypotheses

• Build a hierarchical model for group structure naturally arising in scientific studies.
• A two-fold loop testing algorithm (TLTA) is proposed for grouped hypotheses.
• TLTA is a powerful FDR controlling method.
• Application to real data can foster domain knowledge.

A two-fold loop testing algorithm (TLTA) is proposed for testing grouped hypotheses controlling false discoveries. It is constructed by decomposing a posterior measure of false discoveries across all hypotheses into within- and between-group components, allowing a portion of the overall FDR level to be used to maintain control over within-group false discoveries. Numerical calculations performed under certain model assumption for the hidden states of the within-group hypotheses show its superior performance over its competitors that ignore the group structure, especially when only a few of the groups contain the signals, as expected in many modern applications. We offer data-driven version of the TLTA by estimating the parameters using EM algorithms and provide simulation evidence of its favorable performance relative to these competitors. Real data applications have also produced encouraging results for the TLTA.