Email updates

Keep up to date with the latest news and content from BMC Bioinformatics and BioMed Central.

Open Access Methodology article

A two-step hierarchical hypothesis set testing framework, with applications to gene expression data on ordered categories

Yihan Li and Debashis Ghosh*

Author Affiliations

Department of Statistics, Pennsylvania State University, University Park, State College, Pennsylvania 16802, USA

For all author emails, please log on.

BMC Bioinformatics 2014, 15:108  doi:10.1186/1471-2105-15-108

Published: 14 April 2014

Abstract

Background

In complex large-scale experiments, in addition to simultaneously considering a large number of features, multiple hypotheses are often being tested for each feature. This leads to a problem of multi-dimensional multiple testing. For example, in gene expression studies over ordered categories (such as time-course or dose-response experiments), interest is often in testing differential expression across several categories for each gene. In this paper, we consider a framework for testing multiple sets of hypothesis, which can be applied to a wide range of problems.

Results

We adopt the concept of the overall false discovery rate (OFDR) for controlling false discoveries on the hypothesis set level. Based on an existing procedure for identifying differentially expressed gene sets, we discuss a general two-step hierarchical hypothesis set testing procedure, which controls the overall false discovery rate under independence across hypothesis sets. In addition, we discuss the concept of the mixed-directional false discovery rate (mdFDR), and extend the general procedure to enable directional decisions for two-sided alternatives. We applied the framework to the case of microarray time-course/dose-response experiments, and proposed three procedures for testing differential expression and making multiple directional decisions for each gene. Simulation studies confirm the control of the OFDR and mdFDR by the proposed procedures under independence and positive correlations across genes. Simulation results also show that two of our new procedures achieve higher power than previous methods. Finally, the proposed methodology is applied to a microarray dose-response study, to identify 17 β-estradiol sensitive genes in breast cancer cells that are induced at low concentrations.

Conclusions

The framework we discuss provides a platform for multiple testing procedures covering situations involving two (or potentially more) sources of multiplicity. The framework is easy to use and adaptable to various practical settings that frequently occur in large-scale experiments. Procedures generated from the framework are shown to maintain control of the OFDR and mdFDR, quantities that are especially relevant in the case of multiple hypothesis set testing. The procedures work well in both simulations and real datasets, and are shown to have better power than existing methods.

Keywords:
Multiple testing; Overall false discovery rate; Mixed-directional false discovery rate; Benjamini-Hochberg procedure; Microarray; Time course; Dose response