Table 1.
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 i.e. true positives (TP) over 100 simulation runs and a covariate-modulated false discovery rate (cmfdr) cut-off of 0.05
| Model | Independent | Independent, eq. power | Overlapping | Overlapping, corrected |
|---|---|---|---|---|
| Null | ||||
| FDP | – | – | – | – |
| TP | – | – | – | – |
| FP | 0 | 0 | 245.14 (237.9, 252.4) | 0 |
| Positive Pleiotropy A (400 non-null SNPs) | ||||
| FDP | 0.0053 (0.0044, 0.0063) | 0.0030 (0.0024, 0.0037) | 0.39 (0.39, 0.40) | 0.0056 (0.0048, 0.0065) |
| TP | 260.9 (259.6, 262.1) | 283 (282.0, 284.1) | 330.4 (329.5, 331.4) | 243.4 (242.1, 244.7) |
| FP | 1.4 (1.2, 1.7) | 0.9 (0.7, 1.1) | 215.7 (210.1, 221.4) | 1.4 (1.2, 1.6) |
| Positive Pleiotropy + Univariate (400 non-null SNPs) | ||||
| FDP | 0.008 (0.007, 0.009) | 0.005 (0.004, 0.006) | 0.48 (0.48, 0.49) | 0.01 (0.008, 0.01) |
| TP | 233.4 (232.1, 234.7) | 270.4 (269.4, 271.5) | 306.1 (304.7, 307.4) | 209.8 (208.4, 211.2) |
| FP | 2.0 (1.7, 2.2) | 1.3 (1.1, 1.5) | 289.2 (282.4, 296.1) | 2.08 (1.8, 2.4) |
| Positive + Antagonistic Pleiotropy (400 non-null SNPs) | ||||
| FDP | 0.005 (0.005, 0.006) | 0.004 (0.003, 0.005) | 0.46 (0.45, 0.47) | 0.008 (0.007, 0.010) |
| TP | 261.5 (260.4, 262.6) | 290.8 (289.6, 291.9) | 280.9 (280.0, 282.2) | 228.7 (227.3, 230.1) |
| FP | 1.4 (1.2, 1.6) | 1.2 (1.0, 1.4) | 240.1 (233.8, 246.4) | 2.0 (1.7, 2.2) |
| Positive Pleiotropy B (1200 non-null SNPs) | ||||
| FDP | 0.018 (0.008, 0.020) | 0.013 (0.012, 0.014) | 0.32 (0.31, 0.33) | 0.029 (0.027. 0.031) |
| TP | 295.65 (293.01, 298.29) | 425.38 (422.42, 428.34) | 618.30 (615.22, 621.38) | 310.94 (308.22, 313.66) |
| FP | 5.51 (5.05, 5.97) | 5.60 (5.11, 6.09) | 294.64 (288.18, 301.10) | 9.36 (8.70, 10.02) |
| Positive Pleiotropy C (2200 non-null SNPs) | ||||
| FDP | 0.019 (0.017, 0.021) | 0.018 (0.016, 0.020) | 0.36 (0.35, 0.36) | 0.034 (0.032, 0.037) |
| TP | 159.71 (157.63, 161.79) | 243.98 (241.91, 246.04) | 575.33 (570.58, 580.08) | 184.10 (181.68, 186.52) |
| FP | 3.16 (2.80, 3.52) | 4.49 (4.05, 4.92) | 324.94 (317.67, 332.20) | 6.59 (6.08, 7.10) |
Results are presented for six different simulation scenarios: the null model, where both traits are independent from genotype (all SNPs are null); positive pleiotropy A with 400 SNPs that are non-null for both traits; positive pleiotropy plus univariate effects for trait 1, where 200 SNPs were non-null for traits 1 and 2 and 200 SNPs were non-null for trait 1 only; positive plus antagonistic pleiotropy, where 400 SNPs were non-null for both traits 1 and 2, and half of these non-null SNPs have an effect in opposing directions for trait 1 and 2; positive pleiotropy B with 1200 SNPs that are non-null for both traits, 200 with large effects and 1000 with small effects; positive pleiotropy C with 2200 SNPs that are non-null for both traits, 200 with large effects and 2000 with small effects. In all six scenarios d=100,000 SNPs were simulated, the correlation due to overlap is 0.4 and the test statistics for study 2 were used as a covariate for study 1 for the covariate-modulated fdr. For each simulation scenario, we divided the simulated subjects into the following GWAS pairs: Independent, independent GWASs with no overlap (each with n=10,000), Independent eq. power, independent equally-powered GWASs (each with n=12,500 like the GWASs with overlapping subjects), Overlapping, uncorrected overlapping GWAS with (each with n=12,500 including,5000 overlapping, subjects) and Overlapping, corrected, the GWAS with 5,000 overlapping subjects after correction for sample overlap. Data is presented as mean (95% confidence interval)