Table 2.
The bias (in percentage to the true value), empirical standard deviation (SD), average standard error (SE), and the CI coverage rate for the estimated ROC curves by DR, IPW and IB estimators.
ROCx (0.1) | ROCx (0.2) | ROCx (0.4) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x = (0,0) | (0,0.5) | (1,0) | (1,0.5) | (0,0) | (0,0.5) | (1,0) | (1,0.5) | (0,0) | (0,0.5) | (1,0) | (1,0.5) | |||
Normal | Bias (%) | DR | 6.8 | 4.4 | 0.0 | -0.1 | 2.8 | 2.0 | 0.3 | -0.0 | 0.9 | 0.6 | -0.1 | -0.1 |
IPW | 6.7 | 4.9 | -0.3 | -0.5 | 3.2 | 2.2 | 0.0 | -0.5 | 0.8 | 0.4 | -0.2 | -0.3 | ||
IB | 6.4 | 4.6 | 0.4 | 0.3 | 2.6 | 2.2 | 0.3 | 0.1 | 0.6 | 0.5 | -0.1 | -0.1 | ||
PR | 6.1 | 4.6 | 1.0 | 0.6 | 3.2 | 2.2 | 0.4 | 0.1 | 1.1 | 0.6 | 0.0 | -0.1 | ||
SD | DR | 0.031 | 0.044 | 0.073 | 0.082 | 0.056 | 0.068 | 0.059 | 0.055 | 0.084 | 0.073 | 0.030 | 0.021 | |
IPW | 0.034 | 0.053 | 0.091 | 0.107 | 0.062 | 0.082 | 0.078 | 0.078 | 0.092 | 0.087 | 0.037 | 0.030 | ||
IB | 0.030 | 0.043 | 0.069 | 0.075 | 0.054 | 0.066 | 0.056 | 0.050 | 0.076 | 0.070 | 0.027 | 0.019 | ||
PR | 0.029 | 0.042 | 0.063 | 0.072 | 0.056 | 0.065 | 0.055 | 0.050 | 0.075 | 0.066 | 0.026 | 0.017 | ||
SE | DR | 0.032 | 0.046 | 0.069 | 0.078 | 0.057 | 0.070 | 0.060 | 0.056 | 0.074 | 0.070 | 0.031 | 0.023 | |
IPW | 0.037 | 0.056 | 0.087 | 0.099 | 0.066 | 0.084 | 0.075 | 0.072 | 0.087 | 0.085 | 0.039 | 0.030 | ||
IB | 0.030 | 0.044 | 0.065 | 0.072 | 0.054 | 0.066 | 0.055 | 0.051 | 0.070 | 0.066 | 0.028 | 0.020 | ||
PR | 0.030 | 0.044 | 0.058 | 0.068 | 0.056 | 0.067 | 0.049 | 0.048 | 0.068 | 0.063 | 0.022 | 0.017 | ||
Coverage (%) | DR | 94.4 | 95.4 | 93.4 | 94.2 | 95.2 | 94.4 | 95.4 | 95.6 | 91.2 | 93.2 | 95.6 | 97.6 | |
IPW | 96.8 | 96.4 | 93.2 | 94.6 | 95.6 | 95.2 | 94.6 | 95.2 | 93.6 | 93.8 | 96.6 | 96.8 | ||
IB | 94.4 | 94.6 | 93.6 | 94.6 | 95.2 | 93.8 | 94.0 | 96.0 | 92.4 | 93.6 | 94.8 | 97.4 | ||
PR | 95.2 | 95.0 | 92.6 | 93.8 | 95.0 | 94.4 | 92.0 | 95.0 | 92.8 | 93.6 | 91.4 | 94.6 | ||
χ 2 | Bias (%) | DR | 3.9 | 3.4 | 4.3 | 4.2 | 1.3 | 1.3 | 1.4 | 0.5 | -0.1 | -0.5 | -0.3 | -0.0 |
IPW | 4.1 | 4.0 | 4.7 | 4.7 | 1.2 | 1.7 | 1.7 | 0.6 | -0.2 | -0.6 | -0.3 | -0.1 | ||
IB | 10.2 | 10.1 | 7.3 | 6.1 | 8.5 | 7.4 | 2.0 | -0.2 | 1.2 | -0.6 | -1.9 | -0.9 | ||
PR | -0.7 | 14.5 | 29.7 | 24.2 | -9.0 | -3.7 | -4.5 | -7.0 | -13.2 | -13.1 | -7.9 | -4.5 | ||
SD | DR | 0.030 | 0.041 | 0.074 | 0.092 | 0.060 | 0.074 | 0.077 | 0.066 | 0.082 | 0.077 | 0.009 | 0.003 | |
IPW | 0.031 | 0.044 | 0.080 | 0.102 | 0.066 | 0.083 | 0.086 | 0.075 | 0.092 | 0.088 | 0.009 | 0.003 | ||
IB | 0.032 | 0.043 | 0.074 | 0.090 | 0.061 | 0.074 | 0.068 | 0.058 | 0.073 | 0.069 | 0.012 | 0.006 | ||
PR | 0.035 | 0.050 | 0.073 | 0.078 | 0.061 | 0.072 | 0.056 | 0.051 | 0.067 | 0.062 | 0.021 | 0.016 | ||
SE | DR | 0.031 | 0.042 | 0.081 | 0.098 | 0.060 | 0.074 | 0.075 | 0.067 | 0.077 | 0.073 | 0.013 | 0.005 | |
IPW | 0.033 | 0.045 | 0.090 | 0.110 | 0.067 | 0.084 | 0.086 | 0.075 | 0.087 | 0.083 | 0.015 | 0.005 | ||
IB | 0.032 | 0.043 | 0.078 | 0.092 | 0.006 | 0.072 | 0.065 | 0.057 | 0.069 | 0.065 | 0.014 | 0.007 | ||
PR | 0.023 | 0.035 | 0.051 | 0.063 | 0.043 | 0.056 | 0.045 | 0.046 | 0.060 | 0.059 | 0.023 | 0.017 | ||
Coverage (%) | DR | 95.0 | 95.4 | 92.6 | 93.2 | 95.2 | 94.8 | 95.0 | 96.2 | 93.4 | 95.4 | 91.3 | - | |
IPW | 94.4 | 94.0 | 94.6 | 93.6 | 94.4 | 93.6 | 96.0 | 97.4 | 93.8 | 93.6 | 95.6 | - | ||
IB | 94.2 | 92.4 | 92.4 | 92.0 | 93.4 | 93.8 | 93.4 | 96.2 | 94.0 | 94.8 | 31.2 | - | ||
PR | 80.4 | 82.6 | 46.0 | 58.4 | 83.4 | 88.6 | 84.2 | 69.4 | 69.4 | 56.0 | 0.0 | - |