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In many large scale multiple testing applications, the hypotheses often havea known graphical structure, such as gene ontology in gene expression data.Exploiting this graphical structure in multiple testing procedures can improvepower as well as aid in interpretation. However, incorporating the structureinto large scale testing procedures and proving that an error rate, such as thefalse discovery rate (FDR), is controlled can be challenging. In this paper, weintroduce a new general approach for large scale multiple testing, which canaid in developing new procedures under various settings with proven control ofdesired error rates. This approach is particularly useful for developing FDRcontrolling procedures, which is simplified as the problem of developingper-family error rate (PFER) controlling procedures. Specifically, for testinghypotheses with a directed acyclic graph (DAG) structure, by using the generalapproach, under the assumption of independence, we first develop a specificPFER controlling procedure and based on this procedure, then develop a new FDRcontrolling procedure, which can preserve the desired DAG structure among therejected hypotheses. Through a small simulation study and a real data analysis,we illustrate nice performance of the proposed FDR controlling procedure forDAG-structured hypotheses.

A New Approach for Large Scale Multiple Testing with Application to FDR Control for Graphically Structured Hypotheses