Table 2.
Empirical family-wise error rates (FWERs) of SS2, SMR, and SMR-multi and false positive rates of COLOC and COLOC2 for multiple genes
| Locus | Proportion of genes with eQTL association but do not colocalize | FWER of SS2 | FWER of SMR | FWER of SMR-multi | False positive rate of COLOC | False positive rate of COLOC2 |
|---|---|---|---|---|---|---|
| MUC20/MUC4 | 0% | 0.0377 | 0.0010 | 0.0010 | 0.1307 | 0.0088 |
| 20% | 0.0294 | 0.0003 | 0.0002 | 0.1089 | 0.0023 | |
| 40% | 0.0297 | 0.0002 | 0.0001 | 0.0854 | 0.0027 | |
| 60% | 0.0300 | 9.00 × 10−5 | 5.00 × 10−5 | 0.0606 | 0.0034 | |
| 80% | 0.0317 | 8.00 × 10−5 | 4.00 × 10−5 | 0.0351 | 0.0040 | |
| 100% | 0.0346 | 6.00 × 10−5 | 5.00 × 10−5 | 0.0043 | 0.0044 | |
| SLC6A14 | 0% | 0.0054 | 0.0008 | 0.0008 | 0.1626 | 0.0003 |
| 20% | 0.0016 | 0.0008 | 0.0004 | 0.1360 | 0.0049 | |
| 40% | 0.0011 | 0.0004 | 0.0002 | 0.1103 | 0.0056 | |
| 60% | 0.0010 | 0.0003 | 0.0002 | 0.0831 | 0.0070 | |
| 80% | 0.0008 | 0.0002 | 0.0001 | 0.0542 | 0.0080 | |
| 100% | 0.0007 | 0.0001 | 9.00 × 10−5 | 0.0234 | 0.0089 |
The height of the GWAS peak is set at 5.06 on the −log10p scale such that 10% power is achieved to detect the GWAS association at significance level of 10−8. In total, 600 genes are simulated based on the LD pattern at the MUC20/MUC4 locus or the SLC6A14 locus, respectively. Each row corresponds to a different proportion of genes that have eQTL association (0%, 20%, 40%, 60%, 80%, and 100%). The eQTL peaks are randomly generated from 6 different intervals (50%–60%, 60%–70%, 70%–80%, 80%–90%, 90%–95%, 95%–100% power is achieved to detect the eQTL association at the significance level of 10−8) with probabilities according to the proportion of the -log10(maximum eQTL p value) within each interval observed at the corresponding locus. None of the eQTL peak colocalizes with the GWAS peak for FWER evaluation. SMR and Multi-SNP-based SMR test (SMR-multi) are conducted under the default setting such that a SNP is picked only if the eQTL p value is less than 5 × 10−8. COLOC2 is conducted by using the algorithm implemented in GWAS-PW, where the posterior probability is calculated based on the likelihood of all gene-by-tissue pairs. In total, 105 replications are simulated to evaluate FWER of 0.05 and the false positive rates by applying the 0.8 threshold (as recommended by Dobbyn et al.14) for the colocalization posterior probability. The empirical FWER (or false positive rates for COLOC and COLOC2) is calculated by counting the proportion of 105 replications where at least one gene has a false colocalization claim.