  False discovery rate (FDR) controlling procedures provide important
statistical guarantees for the replicability in signal identification based on
multiple hypotheses testing. In many fields of study, FDR controlling
procedures are used in high-dimensional (HD) analyses to discover features that
are truly associated with the outcome. In some recent applications, data on the
same set of candidate features are independently collected in multiple
different studies. For example, gene expression data are collected at different
facilities and with different cohorts, to identify the genetic biomarkers of
multiple types of cancers. These studies provide us opportunities to identify
signals by considering information from different sources (with potential
heterogeneity) jointly. This paper is about how to provide FDR control
guarantees for the tests of union null hypotheses of conditional independence.
We present a knockoff-based variable selection method (\textit{Simultaneous
knockoffs}) to identify mutual signals from multiple independent data sets,
providing exact FDR control guarantees under finite sample settings. This
method can work with very general model settings and test statistics. We
demonstrate the performance of this method with extensive numerical studies and
two real data examples.

Methodology