Table 1 Empirical type I error rates of various tests at the significance level of 0.05 for a quantitative trait with an error distribution (Distr), a number of independent SNVs (#SNVs), and with two covariates
Distr#SNVsSKATSKAT-OSPU(1)SPU(2)SPU(3)SPU(4)SPU(Embedded Image)aSPUaSPUr
Embedded Image80.0440.0530.0480.0500.0550.0550.0590.0570.055
320.0640.0580.0650.0630.0510.0610.0560.0630.056
640.0500.0470.0470.0530.0490.0550.0540.0470.052
1280.0440.0410.0490.0520.0510.0530.0470.0470.053
1920.0310.0320.0490.0390.0480.0530.0540.0490.048
2560.0190.0310.0510.0250.0400.0350.0370.0410.033
Embedded Image80.0760.0720.0510.0420.0470.0430.0470.0480.046
320.1130.1050.0500.0460.0500.0550.0520.0450.042
640.1320.1090.0390.0340.0390.0490.0510.0400.047
1280.1140.1050.0480.0270.0450.0420.0570.0480.047
1920.1040.1010.0650.0190.0320.0320.0500.0440.048
2560.0870.0740.0420.0070.0130.0220.0430.0260.062
Embedded Image80.0820.0810.0520.0480.0510.0490.0500.0490.031
320.1900.1860.0600.0640.0510.0620.0780.0610.040
640.2890.2680.0430.0360.0330.0360.1000.0620.042
1280.3100.2760.0380.0250.0270.0280.0850.0500.033
1920.2690.2510.0360.0110.0150.0190.0540.0310.032
2560.3100.2820.0360.0060.0130.0160.0640.0370.036
Embedded Image80.1070.0930.0560.0650.0630.0620.0610.0670.053
320.1600.1370.0520.0410.0520.0530.0610.0520.047
640.1650.1440.0520.0380.0370.0430.0570.0450.038
1280.1760.1470.0530.0300.0490.0500.0590.0480.052
1920.1730.1420.0450.0120.0290.0350.0490.0330.050
2560.1510.1150.0430.0070.0250.0270.0470.0390.050
Embedded Image80.1130.1030.0630.0560.0590.0590.0610.0580.057
320.2090.1970.0430.0430.0580.0600.0750.0580.051
640.2760.2590.0450.0380.0400.0440.0620.0530.059
1280.2770.2510.0520.0320.0390.0440.0690.0450.064
1920.2690.2410.0330.0130.0220.0250.0540.0260.063
2560.2870.2490.0350.0100.0190.0230.0510.0340.056
Embedded Image contaminated Embedded Image80.3710.3160.1770.3330.3270.3400.3370.2900.060
320.2260.1870.0780.1390.1360.1430.1550.1210.054
640.1470.1200.0580.0770.0830.0840.0830.0800.055
1280.0890.0890.0610.0480.0540.0540.0690.0680.060
1920.0600.0550.0490.0350.0490.0400.0550.0500.039
2560.0450.0410.0410.0270.0450.0350.0600.0400.047
Embedded Image contaminated Embedded Image80.6050.5820.3650.5630.5660.5720.5640.5160.061
320.4770.4440.1180.2010.2090.2110.2300.1740.054
640.3490.2980.0890.0960.1170.1180.1420.1040.057
1280.1780.1550.0670.0430.0560.0540.0860.0640.060
1920.1420.1310.0470.0330.0460.0400.0510.0440.041
2560.1120.0990.0400.0200.0430.0340.0680.0370.048