Title: Simultaneous confidence bounds for the false discovery proportion: A permutation approach
Authors: Jesse Hemerik - Leiden University Medical Centre (Netherlands)
Aldo Solari - University of Milano-Bicocca (Italy) [presenting]
Jelle Goeman - Leiden University Medical Center (Netherlands)
Abstract: Testing of multiple hypotheses has received much attention in recent years due to the availability of ever-larger data sets. It is often desirable to reject as many hypotheses as possible while keeping the false discovery proportion (FDP) in check. The FDP attracted considerable interest recently because under strong dependence among p-values, it represents a more relevant measure than the False Discovery Rate (FDR), which is the expected value of the FDP. In fact, the stronger the positive dependence among p-values, the higher the variability of FDP around its expected value, and the FDR can be far from the actual FDP. However, high dimensionality and dependency impose a formidable methodological challenge in constructing tight upper bounds for the FDP. By using a permutation approach. A powerful method to derive simultaneous confidence bounds for the FDP has been previously provided. We show that such a method can be generalised and improved. First, we allow for more flexibility in constructing the simultaneous confidence bounds. Second, we show how the power of the previous method can be uniformly increased by using closed testing.