of FDR control at level q , as follows from Appendix B. Specifically, in our simulation f$_{00}$ = 0 . 9990, f$_{01}$ = 0 . 00036 on average, after preprocessing. For FDR control at level q = 0 . 05, on average q ′ = 0 . 048 for w$_{1}$ = 0 , 1 and q ′ = 0 . 049 for w$_{1}$ = 0 . 5. Table 3 shows the average FDP and average number of rejections for Procedure 4.1 with and without the oracle. Although the average FDP is higher with the oracle, it is still below the nominal 0.05 level for two main reasons. First, our simulation preserves the LD pattern of the SNPs, and thus the p -values within each study are not independent. Second, the upper bound of f$_{00}$ ( q $^{′}$) 2 + ( f$_{01}$ + 1) q ′ is not a tight upper bound for the actual FDR level. A tighter oracle upper bound requires knowing the expectation of |R 1 ∩ I$_{10}$ | / |R 1 | , and this bound is tight if the non-null effect sizes in I$_{10}$ ∪ I$_{01}$ are extremely large. Table 3: The average FDP and average number of rejections for Procedure 4.1 with and without the oracle, for FDR control at level 0.05. FDP # Replicated findings Oracle ( q$_{1}$, q ) = (0 . 025 , 0 . 05) Oracle ( q$_{1}$, q ) = (0 . 025 , 0 . 05) w$_{1}$ = 0 . 5 0.023 0.011 90 78 w$_{1}$ = 1 0.023 0.012 85 76 w$_{1}$ = 0 0.029 0.007 50 41 For the two studies from the CEU and CHD populations, a meta-analysis was per- formed by first combining the SNP p -values using Fisher’s combining method, and then applying the BH procedure at level 0.05 on the combined p -values. The average number of SNPs associated with the disease in at least one study was 393, while less than 80 SNPs were discovered to have replicated associations (Table 2). The two main reasons for discovering more SNPs in a typical meta analysis are as follows. First, the simulation setting contained five times more associated SNPs than SNPs with replicated associations. Second, for a SNP with a replicated association, the power to detect that the association is replicated is lower than the power to detect 18