Sequential FDR and pFDR Control Under Arbitrary Dependence, with Application to Pharmacovigilance Database Monitoring

We propose sequential multiple testing procedures which control the false discovery rate (FDR) or the positive-false discovery rate (pFDR) under arbitrary dependence between the data streams. This is accomplished by “optimizing” an upper bound on these error metrics for a class of step-down sequential testing procedures. Both open-ended and truncated versions of these sequential procedures are given, both being able to control both the type I multiple testing metric (FDR or pFDR) at specified levels, and the former being able to control both the type I and type II (e.g., FDR and the false nondiscovery rate, FNR). In simulation studies, these procedures provide 45–65% savings in average sample size over their fixed-sample competitors. We illustrate our procedures on drug data from the United Kingdom’s Yellow Card Pharmacovigilance Database.