On Procedures Controlling the FDR for Testing Hierarchically Ordered Hypotheses

Abstract

Complex large-scale studies, such as those related to microarray data and fMRI studies, often involve testing multiple hierarchically ordered hypotheses. However, most existing false discovery rate (FDR) controlling procedures do not exploit the inherent hierarchical structure among the tested hypotheses. In this paper, we first present a generalized stepwise procedure which generalizes the usual stepwise procedure to the case where each hypothesis is tested with a different set of critical constants. This procedure is helpful in creating a general framework under which our hierarchical testing procedures are developed. Then, we present several hierarchical testing procedures which control the FDR under various forms of dependence such as positive dependence and block dependence. Our simulation studies show that these proposed methods can be more powerful in some situations than alternative methods such as Yekutieli's hierarchical testing procedure (Yekutieli, \emph{JASA} \textbf{103} (2008) 309-316). Finally, we apply our proposed procedures to a real data set involving abundances of microbes in different ecological environments.

34 pages, 4 figures

References in corpus (2)

• Adaptive Controls of FWER and FDR Under Block Dependence
• The Control of the False Discovery Rate in Fixed Sequence Multiple Testing

Cited by in corpus (6)

• STAR: A general interactive framework for FDR control under structural constraints
• DAGGER: A sequential algorithm for FDR control on DAGs
• A New Approach for Large Scale Multiple Testing with Application to FDR Control for Graphically Structured Hypotheses
• AdaPT-GMM: Powerful and robust covariate-assisted multiple testing
• Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes
• Controlling the False Split Rate in Tree-Based Aggregation