  Consider a case-control study in which we have a random sample, constructed
in such a way that the proportion of cases in our sample is different from that
in the general population---for instance, the sample is constructed to achieve
a fixed ratio of cases to controls. Imagine that we wish to determine which of
the potentially many covariates under study truly influence the response by
applying the new model-X knockoffs approach. This paper demonstrates that it
suffices to design knockoff variables using data that may have a different
ratio of cases to controls. For example, the knockoff variables can be
constructed using the distribution of the original variables under any of the
following scenarios: (1) a population of controls only; (2) a population of
cases only; (3) a population of cases and controls mixed in an arbitrary
proportion (irrespective of the fraction of cases in the sample at hand). The
consequence is that knockoff variables may be constructed using unlabeled data,
which is often available more easily than labeled data, while maintaining
Type-I error guarantees.
