Table 1. Type I error comparison among MURAT, SKAT, and Maity's method at moderate significance levels, α=0.05, 0.01, and 0.001.
| K=2 | ||||||
|---|---|---|---|---|---|---|
| ρe=0 | ρe=0.1 | |||||
| α | MURAT | Maity | SKAT | MURAT | Maity | SKAT |
| 5 × 10−2 | 5.17 × 10−2 | 5.17 × 10−2 | 4.76 × 10−2 | 5.12 × 10−2 | 5.10 × 10−2 | 4.81 × 10−2 |
| 1 × 10−2 | 0.90 × 10−2 | 0.94 × 10−2 | 0.94 × 10−2 | 0.97 × 10−2 | 0.99 × 10−2 | 0.95 × 10−2 |
| 1 × 10−3 | 1.01 × 10−3 | 1.30 × 10−3 | 0.90 × 10−3 | 1.10 × 10−3 | 1.10 × 10−3 | 1.20 × 10−3 |
| ρe=0.4 |
ρe=0.7 |
|||||
| 5 × 10−2 | 4.99 × 10−2 | 4.80 × 10−2 | 4.78 × 10−2 | 5.01 × 10−2 | 4.78 × 10−2 | 4.41 × 10−2 |
| 1 × 10−2 | 1.02 × 10−2 | 0.91 × 10−2 | 0.98 × 10−2 | 0.98 × 10−2 | 0.93 × 10−2 | 0.97 × 10−2 |
| 1 × 10−3 | 1.02 × 10−3 | 0.70 × 10−3 | 1.40 × 10−3 | 1.10 × 10−3 | 0.80 × 10−3 | 1.30 × 10−3 |
| K=3 | ||||||
|---|---|---|---|---|---|---|
| ρe=0 | ρe=0.1 | |||||
| α | MURAT | Maity | SKAT | MURAT | Maity | SKAT |
| 5 × 10−2 | 5.08 × 10−2 | 4.83 × 10−2 | 4.79 × 10−2 | 5.12 × 10−2 | 4.62 × 10−2 | 4.91 × 10−2 |
| 1 × 10−2 | 1.03 × 10−2 | 0.90 × 10−2 | 1.02 × 10−2 | 1.06 × 10−2 | 0.98 × 10−2 | 0.91 × 10−2 |
| 1 × 10−3 | 1.00 × 10−3 | 0.90 × 10−3 | 0.60 × 10−3 | 1.30 × 10−3 | 0.80 × 10−3 | 1.20 × 10−3 |
| ρe=0.4 |
ρe=0.7 |
|||||
| 5 × 10−2 | 5.06 × 10−2 | 4.69 × 10−2 | 4.65 × 10−2 | 5.08 × 10−2 | 4.67 × 10−2 | 4.05 × 10−2 |
| 1 × 10−2 | 1.02 × 10−2 | 0.93 × 10−2 | 0.93 × 10−2 | 1.04 × 10−2 | 0.99 × 10−2 | 0.86 × 10−2 |
| 1 × 10−3 | 1.20 × 10−3 | 0.90 × 10−3 | 1.40 × 10−3 | 1.10 × 10−3 | 1.00 × 10−3 | 1.40 × 10−3 |
Abbreviations: MURAT, Multivariate Rare-Variant Association Test; SKAT, sequence kernel association test.
The simulations are based on 10 000 simulated data sets. The results for SKAT are based on adjusted P-values, which are defined as K times the minimum of univariate-based P-values obtained via SKAT.