  This paper develops a method based on model-X knockoffs to find conditional
associations that are consistent across diverse environments, controlling the
false discovery rate. The motivation for this problem is that large data sets
may contain numerous associations that are statistically significant and yet
misleading, as they are induced by confounders or sampling imperfections.
However, associations consistently replicated under different conditions may be
more interesting. In fact, consistency sometimes provably leads to valid causal
inferences even if conditional associations do not. While the proposed method
is flexible and can be deployed in a wide range of applications, this paper
highlights its relevance to genome-wide association studies, in which
consistency across populations with diverse ancestries mitigates confounding
due to unmeasured variants. The effectiveness of this approach is demonstrated
by simulations and applications to the UK Biobank data.
