  High dimensional case control studies are ubiquitous in the biological
sciences, particularly genomics. To maximise power while constraining cost and
to minimise type-1 error rates, researchers typically seek to replicate
findings in a second experiment on independent cohorts before proceeding with
further analyses.
  This paper presents a method in which control (or case) samples from the
discovery cohort are re-used in the replication study. The theoretical
implications of this method are discussed and simulations used to compare
performance against the standard method in a range of circumstances. In several
common study designs, a shared-control method allows a substantial improvement
in power while retaining type-1 error rate control.
  An important area of potential application arises when control samples are
difficult to recruit or ascertain; for example in inter-disease comparisons, or
studies on degenerative diseases. Using similar methods, a procedure is
proposed for `partial replication' using a new independent cohort consisting of
only controls. This methods can be used to provide some validation of findings
when a full replication procedure is not possible.
  The new method has differing sensitivity to confounding in study cohorts
compared to the standard procedure, which must be considered in its
application. Type-1 error rates in these scenarios are analytically and
empirically derived, and an online tool for comparing power and error rates is
provided.
  Although careful consideration must be made of all necessary assumptions,
this method can enable more efficient use of data in genome-wide association
studies (GWAS) and other applications.
