Multiple Testing Procedures for Control of Tail Probability of Proportion of False Positives

• Activity Number: 76
• Type: Invited
• Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Mark van der Laan*+ and Sandrine Dudoit and Katherine S. Pollard and Merrill Birkner
• Companies: University of California, Berkeley and University of California, Berkeley and University of California, Santa Cruz and University of California, Berkeley
• Keywords: Multiple testing ; Genomics ; GO ; Microarrays

Abstract

A fundamental tool in the analysis of genomic data is a valid multiple testing procedure controlling a specified Type-I error rate. We have provided, for general hypotheses and test statistics, single-step and step-down resampling-based multiple testing procedures asymptotically controlling family wise error at a specified level alpha. The proposed procedures differ from the currently used by the choice of null distribution, and, as a consequence, they could be shown to provide asymptotic control of family wise error in general (no need for a so-called subset pivotality condition). In this talk, we show that any multiple testing procedure (asymptotically) controlling family wise error at level alpha can be augmented into 1) a multiple testing procedure (asymptotically) controlling the generalized family wise error (GFWE) (i.e., the probability of having more than k false positives) at level alpha and 2) a multiple testing procedure (asymptotically) controlling the proportion of false positives (PFP) at user-supplied proportion q at level alpha.