Online Multi-Layer FDR Control

When hypotheses are tested in a stream and real-time decision-making is needed, online sequential hypothesis testing procedures are needed. Furthermore, these hypotheses are commonly partitioned into groups by their nature. For example, RNA nanocapsules can be partitioned based on the therapeutic nucleic acids (siRNAs) being used, as well as the delivery nanocapsules. When selecting effective RNA nanocapsules, simultaneous false discovery rate control at multiple partition levels is needed. In this paper, we develop hypothesis testing procedures which control the false discovery rate (FDR) simultaneously for multiple partitions of hypotheses in an online fashion. We provide rigorous proofs for their FDR or modified FDR (mFDR) control properties and use extensive simulations to demonstrate their performances.