Table 3:
Simulation results of AUCs, n = 400. Biass and Biasa are Sampling- and Analytic-based AUC estimators, respectively, and MESE is mean estimated standard errors.
| True AUC | Empirical | Beta | Log-Normal | Logit-Normal | Probit-Normal | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bias a | MESE | Bias s | Bias a | MESE | Bias s | Bias a | MESE | Bias s | Bias a | MESE | Bias s | Bias a | MESE | ||
| BNM | 0.500 | 0.000 | 0.0144 | 0.000 | 0.000 | 0.0137 | 0.094 | 0.094 | 0.0351 | 0.000 | −0.001 | 0.0222 | −0.001 | −0.001 | 0.0197 |
| 0.562 | 0.000 | 0.0142 | −0.002 | −0.002 | 0.0135 | 0.079 | 0.078 | 0.0319 | 0.001 | 0.034 | 0.0213 | 0.000 | 0.024 | 0.0192 | |
| 0.623 | 0.000 | 0.0138 | −0.004 | −0.005 | 0.0132 | 0.063 | 0.063 | 0.0288 | 0.001 | 0.064 | 0.0193 | −0.001 | 0.045 | 0.0178 | |
| 0.681 | −0.001 | 0.0132 | −0.007 | −0.007 | 0.0125 | 0.048 | 0.047 | 0.0255 | 0.001 | 0.085 | 0.0163 | −0.002 | 0.062 | 0.0157 | |
| 0.735 | −0.001 | 0.0123 | −0.008 | −0.008 | 0.0116 | 0.035 | 0.035 | 0.0224 | 0.000 | 0.095 | 0.0130 | −0.002 | 0.072 | 0.0132 | |
| 0.784 | −0.001 | 0.0112 | −0.008 | −0.008 | 0.0106 | 0.025 | 0.025 | 0.0193 | 0.000 | 0.098 | 0.0098 | 0.000 | 0.077 | 0.0106 | |
| 0.827 | −0.001 | 0.0101 | −0.008 | −0.009 | 0.0094 | 0.017 | 0.017 | 0.0165 | 0.000 | 0.092 | 0.0071 | 0.000 | 0.075 | 0.0081 | |
| 0.864 | −0.001 | 0.0089 | −0.008 | −0.008 | 0.0081 | 0.010 | 0.010 | 0.0137 | −0.001 | 0.081 | 0.0050 | 0.001 | 0.068 | 0.0059 | |
| 0.896 | −0.001 | 0.0076 | −0.007 | −0.007 | 0.0068 | 0.006 | 0.006 | 0.0114 | 0.000 | 0.068 | 0.0034 | 0.003 | 0.059 | 0.0042 | |
| 0.921 | −0.001 | 0.0065 | −0.006 | −0.006 | 0.0055 | 0.004 | 0.003 | 0.0093 | 0.002 | 0.055 | 0.0022 | 0.004 | 0.048 | 0.0029 | |
| BGM | 0.500 | 0.000 | 0.0144 | 0.000 | 0.000 | 0.0137 | 0.094 | 0.094 | 0.0350 | −0.001 | 0.000 | 0.0221 | 0.000 | 0.000 | 0.0197 |
| 0.565 | 0.000 | 0.0149 | −0.001 | −0.001 | 0.0140 | 0.097 | 0.097 | 0.0363 | 0.003 | 0.044 | 0.0231 | 0.001 | 0.030 | 0.0206 | |
| 0.615 | 0.000 | 0.0150 | −0.002 | −0.002 | 0.0140 | 0.098 | 0.097 | 0.0364 | 0.005 | 0.082 | 0.0221 | 0.002 | 0.057 | 0.0202 | |
| 0.655 | −0.001 | 0.0149 | −0.005 | −0.005 | 0.0138 | 0.095 | 0.096 | 0.0363 | 0.006 | 0.108 | 0.0202 | 0.002 | 0.077 | 0.0192 | |
| 0.714 | 0.000 | 0.0145 | −0.008 | −0.008 | 0.0133 | 0.091 | 0.091 | 0.0352 | 0.008 | 0.139 | 0.0153 | 0.003 | 0.104 | 0.0162 | |
| 0.778 | −0.001 | 0.0137 | −0.014 | −0.014 | 0.0125 | 0.081 | 0.080 | 0.0329 | 0.008 | 0.147 | 0.0092 | 0.004 | 0.118 | 0.0115 | |
| 0.808 | −0.001 | 0.0131 | −0.016 | −0.016 | 0.0119 | 0.073 | 0.073 | 0.0312 | 0.011 | 0.141 | 0.0066 | 0.006 | 0.118 | 0.0090 | |
| 0.848 | −0.001 | 0.0121 | −0.019 | −0.019 | 0.0108 | 0.062 | 0.062 | 0.0283 | 0.014 | 0.124 | 0.0037 | 0.010 | 0.109 | 0.0057 | |
| 0.900 | −0.001 | 0.0103 | −0.022 | −0.022 | 0.0089 | 0.044 | 0.044 | 0.0234 | 0.021 | 0.089 | 0.0015 | 0.015 | 0.083 | 0.0025 | |
| 0.938 | −0.001 | 0.0084 | −0.021 | −0.021 | 0.0068 | 0.029 | 0.028 | 0.0185 | 0.025 | 0.057 | 0.0006 | 0.018 | 0.055 | 0.0011 | |
| BMN | 0.503 | 0.001 | 0.0144 | 0.002 | 0.001 | 0.0137 | 0.096 | 0.095 | 0.0350 | 0.002 | 0.004 | 0.0223 | 0.002 | 0.003 | 0.0198 |
| 0.553 | 0.002 | 0.0154 | 0.015 | 0.016 | 0.0145 | 0.103 | 0.104 | 0.0379 | 0.020 | 0.075 | 0.0263 | 0.014 | 0.049 | 0.0228 | |
| 0.603 | 0.000 | 0.0159 | 0.014 | 0.014 | 0.0147 | 0.112 | 0.111 | 0.0403 | 0.023 | 0.127 | 0.0251 | 0.015 | 0.085 | 0.0230 | |
| 0.654 | 0.000 | 0.0161 | 0.008 | 0.008 | 0.0145 | 0.115 | 0.113 | 0.0411 | 0.023 | 0.162 | 0.0205 | 0.014 | 0.115 | 0.0209 | |
| 0.704 | 0.001 | 0.0158 | −0.001 | −0.001 | 0.0140 | 0.117 | 0.116 | 0.0413 | 0.021 | 0.175 | 0.0150 | 0.012 | 0.132 | 0.0172 | |
| 0.754 | −0.001 | 0.0151 | −0.012 | −0.012 | 0.0133 | 0.107 | 0.107 | 0.0395 | 0.017 | 0.167 | 0.0103 | 0.008 | 0.133 | 0.0132 | |
| 0.804 | 0.000 | 0.0140 | −0.020 | −0.021 | 0.0123 | 0.094 | 0.094 | 0.0360 | 0.014 | 0.146 | 0.0064 | 0.007 | 0.123 | 0.0091 | |
| 0.855 | −0.001 | 0.0122 | −0.026 | −0.027 | 0.0108 | 0.072 | 0.072 | 0.0304 | 0.012 | 0.114 | 0.0039 | 0.006 | 0.101 | 0.0057 | |
| 0.905 | −0.001 | 0.0096 | −0.024 | −0.025 | 0.0083 | 0.043 | 0.043 | 0.0225 | 0.009 | 0.076 | 0.0021 | 0.006 | 0.069 | 0.0031 | |
| 0.955 | −0.001 | 0.0046 | −0.005 | −0.005 | 0.0035 | 0.001 | 0.000 | 0.0062 | 0.004 | 0.033 | 0.0011 | 0.005 | 0.030 | 0.0014 | |