The Control of the False Discovery Rate in Fixed Sequence Multiple Testing

• Activity Number: 585
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wenge Guo*+ and Gavin Lynch and Sanat K. Sarkar
• Companies: New Jersey Institute of Technology and New Jersey Institute of Technology and Temple University
• Keywords: arbitrary dependence ; false discovery rate ; fixed sequence procedure ; multiple testing ; negative association ; PRDS property

Abstract

Controlling the false discovery rate (FDR) is a powerful approach to multiple testing. However, in the existing FDR controlling procedures, the order in which the hypotheses are tested is typically determined based on their p-values, not based on their relative importance, even though such importance based ordering is often available in advance or can be assessed from the data. More powerful FDR controlling procedures than some existing standard ones can potentially be obtained in such fixed sequence multiple testing problems, which is the motivation behind this paper. We first consider a conventional fixed sequence method that stops testing once an acceptance occurs, and develop such a method controlling the FDR under both arbitrary and negative dependencies. The method under arbitrary dependence is shown to be unimprovable without losing control of the FDR. To account for any potential mistakes in the ordering of the tests, we extend the conventional fixed sequence method to one that allows more but a given number of acceptances. Simulation studies and real data analysis show that the proposed procedures can be powerful alternatives to existing FDR controlling procedures.