  Modern biomedical research frequently involves testing multiple related
hypotheses, while maintaining control over a suitable error rate. In many
applications the false discovery rate (FDR), which is the expected proportion
of false positives among the rejected hypotheses, has become the standard error
criterion. Procedures that control the FDR, such as the well-known
Benjamini-Hochberg procedure, assume that all p-values are available to be
tested at a single time point. However, this ignores the sequential nature of
many biomedical experiments, where a sequence of hypotheses is tested without
having access to future p-values or even the number of hypotheses. Recently,
the first procedures that control the FDR in this online manner have been
proposed by Javanmard and Montanari (Ann. Stat. 2018), and built upon by Ramdas
et al. (NIPS 2017, ICML 2018). In this paper, we compare and contrast these
proposed procedures, with a particular focus on the setting where the p-values
are dependent. We also propose a simple modification of the procedures for when
there is an upper bound on the number of hypotheses to be tested. Using
comprehensive simulation scenarios and case studies, we provide recommendations
for which procedures to use in practice for online FDR control.
