Table 4.
Empirical type I error of binary traits using the linear weighted kernel on all variants in human genetic association.
| α | uSKAT | CI_lower | CI_upper | aSKAT | CI_lower | CI_upper | SKAT | CI_lower | CI_upper |
|---|---|---|---|---|---|---|---|---|---|
| n = 50 | |||||||||
| 5.00E−02 | 1.61E−02 | 1.54E−02 | 1.66E−02 | 1.47E−02 | 1.42E−02 | 1.52E−02 | 6.46E−02 | 6.33E−02 | 6.59E−02 |
| 1.00E−02 | 1.08E−03 | 9.94E−04 | 1.16E−03 | 1.28E−03 | 1.19E−03 | 1.38E−03 | 1.26E−02 | 1.20E−02 | 1.31E−02 |
| 1.00E−03 | 5.42E−05 | 4.92E−05 | 5.90E−05 | 7.95E−05 | 7.22E−05 | 8.63E−05 | 9.38E−04 | 8.24E−04 | 1.06E−03 |
| 1.00E−04 | 9.90E−06 | 8.00E−06 | 1.18E−05 | 1.21E−05 | 9.90E−06 | 1.43E−05 | 7.90E−05 | 5.33E−05 | 1.15E−04 |
| 2.50E−06 | 2.60E−06 | 1.60E−06 | 3.70E−06 | 2.50E−06 | 1.60E−06 | 3.50E−06 | 1.10E−06 | 5.00E−07 | 1.80E−06 |
| n = 100 | |||||||||
| 5.00E−02 | 2.22E−02 | 2.12E−02 | 2.31E−02 | 2.16E−02 | 2.06E−02 | 2.25E−02 | 5.97E−02 | 5.79E−02 | 6.13E−02 |
| 1.00E−02 | 1.83E−03 | 1.61E−03 | 2.07E−03 | 2.07E−03 | 1.83E−03 | 2.32E−03 | 1.22E−02 | 1.15E−02 | 1.28E−02 |
| 1.00E−03 | 4.49E−05 | 2.48E−05 | 7.72E−05 | 6.85E−05 | 4.21E−05 | 1.11E−04 | 1.01E−03 | 8.63E−04 | 1.17E−03 |
| 1.00E−04 | 1.30E−06 | 7.00E−07 | 2.00E−06 | 1.70E−06 | 9.00E−07 | 2.80E−06 | 7.79E−05 | 5.07E−05 | 1.14E−04 |
| 2.50E−06 | 1.00E−07 | 0.00E+00 | 3.00E−07 | 1.00E−07 | 0.00E+00 | 3.00E−07 | 3.40E−06 | 1.00E−07 | 9.40E−06 |
| n = 200 | |||||||||
| 5.00E−02 | 3.31E−02 | 3.18E−02 | 3.46E−02 | 3.29E−02 | 3.16E−02 | 3.44E−02 | 5.59E−02 | 5.41E−02 | 5.78E−02 |
| 1.00E−02 | 3.83E−03 | 3.40E−03 | 4.25E−03 | 4.09E−03 | 3.64E−03 | 4.51E−03 | 1.13E−02 | 1.05E−02 | 1.20E−02 |
| 1.00E−03 | 1.09E−04 | 7.63E−05 | 1.51E−04 | 1.47E−04 | 1.06E−04 | 2.02E−04 | 1.03E−03 | 8.67E−04 | 1.21E−03 |
| 1.00E−04 | 1.30E−06 | 5.00E−07 | 2.40E−06 | 2.20E−06 | 1.10E−06 | 3.70E−06 | 7.50E−05 | 4.74E−05 | 1.13E−04 |
| 2.50E−06 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 2.70E−06 | 3.00E−07 | 7.00E−06 |
The total sample size is denoted by n, α is the nominal significance level. 107 replicates are used. uSKAT is the original SKAT without small sample size adjustment. aSKAT is the proposed adjusted SKAT. SKAT is the SKAT with small sample size adjustment using bootstrapping. CI_lower and CI_upper are the lower and upper endpoint of the bootstrapped 95% confidence interval of the estimated type I error. Bold face indicates the confidence interval is above α.