Testing of Hierarchically Structured Families of Hypotheses with Multidimensional Directional Decisions

• Activity Number: 456
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Anjana Grandhi*+ and Wenge Guo and Shyamal Peddada
• Companies: New Jersey Institute of Technology and New Jersey Institute of Technology and NIH/NIEHS
• Keywords: BH procedure ; directional errors ; mixed directional FWER ; mixed directional FDR

Abstract

In the research related to uterine fibroids, a fundamental question is to identify differentially expressed genes and the pathways that are specific to tumor stage. A practical way to address this question is to analyze gene expressions from samples of different tumor sizes that correspond to different stages of tumor. First, identify all genes in tumor samples that are differentially expressed relative to a normal tissue. Next, identify genes that are specific to each tumor size. Finally, make directional decisions whether a given differentially expressed gene is up or down regulated relative to the normal tissue. Motivated by this application, we formulate the question as a three-stage multiple testing problem and propose a general procedure, that can be applied with any mdFWER controlling procedure for each gene discovered in the first stage, while controlling mdFDR as the overall error rate. The procedure is proved to control mdFDR when the underlying test statistics are independent across the genes. We illustrate the proposed methodology using the uterine fibroid gene expression data discussed in Davis et al. (2013).