by a using large number of unscreened controls (Edwards et al., 2005;Moskvina et al., 2005;Wellcome Trust Case Control Consortium, 2007;Zheng and Tian, 2005). While the single-stage study using only public controls generally had good power when the number of available public controls was large, we noted that inclusion of the study controls protected power when there were strong differences in ancestry between public controls and study cases or when there were relatively strong batch genotype effects present. Under most circumstances, the proposed replication-based two-stage study had greater power than the single-stage study with only study controls and, depending on the circumstance, greater or lesser power than the single-stage study based only on public controls.
