Accumulation tests for FDR control in ordered hypothesis testing

Understand

Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals.

• In this paper, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list in order to increase the number of discoveries.
• Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR).
• Generalizing several existing methods, we develop a family of "accumulation tests" to choose a cutoff k that adapts to the amount of signal at the top of the ranked list.