High-Dimensional Multiple Testing in a Two-Stage Adaptive Design Setting

• Activity Number: 50
• Type: Invited
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Sanat K. Sarkar*+
• Companies: Temple University
• Keywords: Multiple testing ; Two-stage design ; False Discovery Rate

Abstract

We consider the problem of testing multiple null hypotheses in a two-stage design setting in which early decisions are made on the hypotheses in terms of rejection, acceptance, or continuation to the second stage based on some rejection and acceptance thresholds for the p-values, and the follow-up hypotheses are tested having combined their p-values from the two stages. For this problem, we will present two Benjamini-Hochberg (BH) type methods to control the false discovery rate (FDR), extending the original BH and its adaptive version from single-stage to a two-stage setting. These methods will be shown to control the FDR theoretically under independence. Numerical evidence will be provided for their performance in terms of maintaining a control over the FDR under certain dependence situations. Application of these methods to a real data set will also be presented.