In a multiple-stage association study [30], the number of SNPs to be taken into the follow-up steps is usually fixed in advance by cost considerations so that the SNPs are selected based on the ranking of their test statistics rather than their P-values. In CGEMS, the number of SNPs to be taken in follow-up 1 was approximately 5% of those used in the initial genome wide scan [21]. Consequently, adjusting for PCs in the association test would be expected to change the ranking of the SNPs. In Figures 5, 6 and 7 we show the rank shuffling among the set of 475,116 testing SNPs in the prostate cancer study with internal controls (PLCOca-PLCOco) and with external controls (PLCOca-NHSco). In either case, PCs were selected by the proposed permutation procedure. A similar pattern can be observed in the breast cancer studies with internal and external controls (results shown in Figures S3, S4, S5). Comparing Figure 5A with 5B shows the high correlation of the two sets of ranks in the original study with internal controls and the lower correlation in the
