Table 2.
Mean false discovery proportion (FDP), mean number of falsely rejected null hypotheses out of 99,600, i.e. false positives (FP) and mean number of correctly rejected non-null hypotheses out of 400 s, i.e. true positives (TP) over 100 simulation runs and a covariate-modulated false discovery rate (cmfdr) cut-off of 0.05
| # | ρ | Independent | Overlapping | Overlapping, corrected | |
|---|---|---|---|---|---|
| 0 | 0 | ||||
| FDP | 5.96E-03 (4.99E-03, 6.92E-03) | 5.92E-03 (4.97E-03, 6.88E-03) | 6.03E-03 (5.07E-03,7.00E-03) | ||
| TP | 268.55 (267.90, 269.90) | 268.52 (267.18, 269.86) | 268.59 (267.18, 269.86) | ||
| FP | 1.62 (1.36, 1.88) | 1.61 (1.35, 1.87) | 1.64 (1.37, 1.91) | ||
| 500 | 0.04 | ||||
| FDP | 5.32E-03 (4.41E-03,6.22E-03) | 5.58E-03 (4.58E-03,6.59E-03) | 4.77E-03 (3.81E-03,5.73E-03) | ||
| TP | 262.75 (261.58,263.92) | 266.3 (264.99, 267.61) | 260.47 (259.05, 261.61) | ||
| FP | 1.41 (1.17, 1.65) | 1.5 (1.23, 1.77,) | 1.25 (1.00, 1.50) | ||
| 1000 | 0.08 | ||||
| FDP | 5.83E-03 (4.87E-03, 6.78E-03) | 8.02E-03 (6.81E-03, 9.23E-03) | 5.69E-03 (4.76E-03,6.63E-03) | ||
| TP | 263.43 (262.08, 264.78) | 271.85 (270.59, 273.11) | 258.92 (257.57, 260.27) | ||
| FP | 1.55 (1.29, 1.81) | 2.21 (1.87, 2.55) | 1.49 (1.24, 1.74) | ||
| 1500 | 0.12 | ||||
| FDP | 5.25E-03 (4.44E-03, 6.06E-03) | 1.21E-02 (1.08E-03, 1.34E-02) | 6.00E-03 (5.08E-03, 6.92E-03) | ||
| TP | 263.67 (262.43, 264.91) | 277.11 (275.82, 278.40) | 257.79 (256.51, 259.07) | ||
| FP | 1.4 (1.18, 1.62) | 3.4 (3.02, 3.78) | 1.56 (1.32, 1.80) | ||
| 2000 | 0.16 | ||||
| FDP | 4.42E-03 (3.61E-03, 5.22E-03) | 1.77E-02 (1.61E-02, 1.92E-02) | 4.06E-03 (3.26E-03, 4.86E-03) | ||
| TP | 255.16 (253.98, 256.34) | 274.18 (273.10, 275.26) | 248.52 (247.27, 249.77) | ||
| FP | 1.14 (0.93, 1.35) | 4.96 (4.51, 5.41) | 1.02 (0.82, 1.22) | ||
| 2500 | 0.20 | ||||
| FDP | 5.03E-03 (4.16E-03,5.90E-03) | 3.64E-02 (3.38E-02, 3.91E-02) | 5.20E-03 (4.28E-03, 6.12E-03) | ||
| TP | 258.84 (257.51, 260.17) | 288.47 (287.29, 289.65) | 249.59 (248.22, 250.96) | ||
| FP | 1.31 (1.08, 1.54) | 10.98 (10.15, 11.81) | 1.31 (1.08, 1.54) | ||
| 3000 | 0.24 | ||||
| FDP | 5.08E-03 (4.18E-03, 5.97E-03) | 7.08E-02 (6.74E-02,7.42E-02) | 6.32E-03 (5.41E-03, 7.22E.03) | ||
| TP | 261.65 (260.32, 262.98) | 300.52 (299.39, 301.65) | 250.14 (248.75, 251.53) | ||
| FP | 1.34 (1.10, 1.58) | 23.03 (21.83, 24.23) | 1.6 (1.37, 1.83) | ||
| 3500 | 0.28 | ||||
| FDP | 4.24E-03 (3.52E-03, 4.96E-03) | 1.25E-01 (1.21E-01, 1.30E-01) | 5.57E-03 (4.74E-03, 6.40E-03) | ||
| TP | 268.5 (267.37, 269.63) | 315.07 (314.00, 316.14) | 256.42 (255.08, 257.76) | ||
| FP | 1.15 (0.95, 1.35) | 45.42 (43.46, 47.38) | 1.44 (1.23, 1.65) | ||
| 4000 | 0.32 | ||||
| FDP | 3.62E-03 (2.84E-03, 4.41E-03) | 1.98E-01 (1.93E-01, 2.03E-01) | 4.74E-03 (3.91E-03, 5.56E-03) | ||
| TP | 262.39 (261.27, 263.51) | 316.5 (315.46, 317.54) | 249.16 (247.94, 250.38) | ||
| FP | 0.96 (0.75, 1.17) | 78.65 (76.05, 81.25) | 1.19 (0.98, 1.40) | ||
| 4500 | 0.36 | ||||
| FDP | 4.81E-03 (3.99E-03, 5.63E-03) | 2.89E-01 (2.83E-01, 2.94E-01) | 5.49E-03 (4.54E-03, 6.44E-03) | ||
| TP | 259.29 (258.16, 260.42) | 319.99 (319.04, 320.94) | 245.16 (243.92, 246.40) | ||
| FP | 1.26 (1.04, 1.48) | 130.41 (127.08, 133.74) | 1.36 (1.12, 1.60) | ||
| 5000 | 0.40 | ||||
| FDP | 5.44E-03 (4.57E-03, 6.31E-03) | 3.98E-01 (3.92E-01, 4.04E-01) | 6.79E-03 (5.78E-03, 7.80E-03) | ||
| TP | 262.26 (261.02, 263.50) | 334.25 (333.28, 335.22) | 245.02 (243.66, 246.38) | ||
| FP | 1.44 (1.21, 1.67) | 222.52 (216.73, 228.31) | 1.68 (1.43, 1.93) |
Here d=100,000 SNPs were simulated, of which 400 were non-null in both study 1 and study 2, i.e., the positive pleiotropy senario. The test statistics for study 2 were used as a covariate for study 1 for the covariate-modulated fdr. For each simulation, we divided the simulated subjects into the following GWAS pairs: Independent, independent GWASs with no overlap (each with n=10,000), Overlapping, uncorrected, overlapping GWAS with (each with including between 0 and 5000 overlapping subjects) and Overlapping, corrected, the GWAS with overlapping subjects after correction for sample overlap. Data is presented as mean (95% confidence interval)
#, number overlapping. ρ, correlation due to overlap