associations is at most the set of SNPs that are discovered by the BH procedure (as discussed in Section 3). Table 2 presents the average number of replicated findings, as well as the average false discovery proportion (FDP) for the methods compared. The standard error (SE) is presented in parentheses. From rows 1 and 2 we see that if there is no division into primary and follow-up studies, then the symmetric Procedure 4.1 discovers more SNPs with replicated associations than the BH procedure on maximum p -values, while maintaining a low FDP. From rows 3-5, and 6-8, we see that the choice of which study was the primary study had a large effect on the average number of discoveries, and the choice of q$_{1}$ mattered little. From the last column in Table 2 we see that the average FDP was far below 0.05, suggesting that the procedures are conservative. This conservatism can be alleviated if the following oracle information were known: the fraction of SNPs with no association with the phenotype in both studies, f$_{00}$ , and with association with the phenotype only in the follow-up study, f$_{01}$ . Then it was possible to perform Procedure 4.1 at level ( w$_{1}$, q $^{′}$, 2 q $^{′}$), where q ′ is the solution to f$_{00}$ ( q $^{′}$) $^{2}$+( f$_{01}$ +1) q ′ = q for w$_{1}$ ∈ { 0 , 1 } , and the solution to f$_{00}$ (0 . 5 q $^{′}$) 2 + ( f$_{01}$ + 1)0 . 5 q ′ = 0 . 5 q for w$_{1}$ = 0 . 5, with the same guarantee 17 Table 2: For 4500 cases and 4500 referents in both studies, the average number of associated and disease SNPs discovered (SE), and the average FDP (SE), for different procedures. The selection rule for Procedure 4.1 was the BH procedure at level w$_{1}$q$_{1}$ when the CEU study was the primary study, and at level (1 − w$_{1}$ ) q$_{1}$ when the CHD study was the primary study. Procedure # Replicated findings FDP associated SNPs (SE) disease SNPs (SE) (SE) BH on maximum p -values 29.182 (3.205) 7.364 (0.432) 0.000 (0.000) 4.1 with w$_{1}$ = 0 . 5 , q$_{1}$ = 0 . 025 , q = 0 . 05 77.727 (6.378) 11.455 (0.366) 0.011 (0.005) 4.1 with w$_{1}$ = 1 , q$_{1}$ = 0 . 01 , q = 0 . 05 74.091 (6.748) 10.364 (0.310) 0.012 (0.006) 4.1 with w$_{1}$ = 1 , q$_{1}$ = 0 . 025 , q = 0 . 05 76.091 (6.221) 10.727 (0.359) 0.012 (0.005) 4.1 with w$_{1}$ = 1 , q$_{1}$ = 0 . 04 , q = 0 . 05 69.545 (5.745) 10.818 (0.352) 0.009 (0.005) 4.1 with w$_{1}$ = 0 , q$_{1}$ = 0 . 01 , q = 0 . 05 35.545 (4.575) 7.364 (0.607) 0.008 (0.008) 4.1 with w$_{1}$ = 0 , q$_{1}$ = 0 . 025 , q = 0 . 05 41.455 (5.294) 8.273 (0.469) 0.007 (0.007) 4.1 with w$_{1}$ = 0 , q$_{1}$ = 0 . 04 , q = 0 . 05 42.273 (4.158) 8.545 (0.312) 0.000 (0.000)