|  | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 | Model 8 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | Â | X2 | X3 | X4 | X2,X3 | X2,X4 | X3,X4 | X2,X3,X4 | X1,X2,X3,X4 | ||||||||
 |  | PSm | IPTW | PSm | IPTW | PSm | IPTW | PSm | IPTW | PSm | IPTW | PSm | IPTW | PSm | IPTW | PSm | IPTW |
40 | Type I error | 0.062 | 0.041 | 0.059 | 0.051 | 0.058 | 0.040 | 0.060 | 0.047 | 0.053 | 0.036 | 0.048 | 0.045 | 0.053 | 0.044 | 0.052 | 0.047 |
 | Bias | 0.273 | 0.235 | 0.265 | 0.251 | 0.086 | 0.06 | 0.259 | 0.25 | 0.075 | 0.061 | 0.064 | 0.071 | 0.075 | 0.074 | 0.048 | 0.079 |
 | Relative bias | 32.6 | 28.1 | 31.7 | 30 | 10.3 | 7.2 | 31 | 29.9 | 9 | 7.3 | 7.6 | 8.5 | 9 | 8.8 | 5.7 | 9.4 |
 | Variance | 0.809 | 0.508 | 0.872 | 0.566 | 0.862 | 0.551 | 0.874 | 0.573 | 0.843 | 0.56 | 0.907 | 0.634 | 0.904 | 0.644 | 0.903 | 0.683 |
 | MSE | 0.884 | 0.563 | 0.942 | 0.629 | 0.869 | 0.555 | 0.941 | 0.635 | 0.848 | 0.563 | 0.911 | 0.639 | 0.909 | 0.649 | 0.905 | 0.69 |
60 | Type I error | 0.055 | 0.050 | 0.058 | 0.057 | 0.045 | 0.038 | 0.052 | 0.053 | 0.043 | 0.037 | 0.049 | 0.042 | 0.044 | 0.041 | 0.044 | 0.039 |
 | Bias | 0.239 | 0.203 | 0.235 | 0.217 | 0.041 | 0.02 | 0.245 | 0.219 | 0.047 | 0.022 | 0.051 | 0.028 | 0.059 | 0.03 | 0.05 | 0.033 |
 | Relative bias | 28.6 | 24.3 | 28.1 | 25.9 | 4.9 | 2.4 | 29.3 | 26.2 | 5.6 | 2.6 | 6.1 | 3.3 | 7.1 | 3.6 | 6 | 3.9 |
 | Variance | 0.466 | 0.317 | 0.52 | 0.354 | 0.494 | 0.339 | 0.532 | 0.348 | 0.477 | 0.333 | 0.524 | 0.379 | 0.514 | 0.375 | 0.516 | 0.388 |
 | MSE | 0.523 | 0.359 | 0.575 | 0.401 | 0.495 | 0.339 | 0.592 | 0.396 | 0.479 | 0.334 | 0.527 | 0.38 | 0.517 | 0.376 | 0.519 | 0.389 |
100 | Type I error | 0.062 | 0.057 | 0.065 | 0.066 | 0.052 | 0.039 | 0.057 | 0.062 | 0.042 | 0.034 | 0.046 | 0.041 | 0.044 | 0.037 | 0.04 | 0.036 |
 | Bias | 0.209 | 0.193 | 0.212 | 0.203 | 0.029 | 0.013 | 0.215 | 0.203 | 0.029 | 0.013 | 0.028 | 0.016 | 0.028 | 0.016 | 0.025 | 0.016 |
 | Relative bias | 25 | 23.1 | 25.3 | 24.3 | 3.5 | 1.6 | 25.7 | 24.3 | 3.5 | 1.6 | 3.3 | 1.9 | 3.3 | 1.9 | 2.9 | 1.9 |
 | Variance | 0.239 | 0.175 | 0.254 | 0.194 | 0.242 | 0.186 | 0.256 | 0.188 | 0.239 | 0.18 | 0.259 | 0.205 | 0.253 | 0.199 | 0.261 | 0.204 |
 | MSE | 0.282 | 0.212 | 0.299 | 0.235 | 0.243 | 0.186 | 0.302 | 0.23 | 0.24 | 0.18 | 0.259 | 0.205 | 0.254 | 0.2 | 0.262 | 0.204 |
500 | Type I error | 0.148 | 0.155 | 0.150 | 0.162 | 0.051 | 0.045 | 0.146 | 0.157 | 0.046 | 0.040 | 0.046 | 0.042 | 0.045 | 0.037 | 0.042 | 0.037 |
 | Bias | 0.187 | 0.182 | 0.192 | 0.191 | 0.014 | 0.005 | 0.193 | 0.191 | 0.015 | 0.005 | 0.014 | 0.005 | 0.014 | 0.005 | 0.013 | 0.005 |
 | Relative bias | 22.3 | 21.8 | 22.9 | 22.8 | 1.7 | 0.6 | 23.1 | 22.8 | 1.8 | 0.6 | 1.7 | 0.6 | 1.7 | 0.6 | 1.5 | 0.6 |
 | Variance | 0.037 | 0.032 | 0.042 | 0.036 | 0.04 | 0.034 | 0.041 | 0.034 | 0.039 | 0.033 | 0.044 | 0.037 | 0.042 | 0.035 | 0.042 | 0.035 |
 | MSE | 0.072 | 0.066 | 0.079 | 0.072 | 0.04 | 0.034 | 0.078 | 0.071 | 0.039 | 0.033 | 0.044 | 0.037 | 0.042 | 0.035 | 0.042 | 0.035 |