Table 3 Alternative estimator results for log-normal, gamma and weibull distributions for n=50
From: Statistical models for the analysis of skewed healthcare cost data: a simulation study
Data | Estimator | MPE | MAPE | MSE(β) | 95% CI | AIC | Prob. H.Lsignif | |
|---|---|---|---|---|---|---|---|---|
Lower | upper | |||||||
Log normal σ2=0.5 | OLS for Ln(y) | -0.06472 | 0.56174 | 0.14414 | 0.901 | 1.109 | 110.247 | 0.0403 |
Gamma | -0.00024 | 0.54325 | 0.12915 | 0.880 | 1.112 | 84.882 | 0.0377 | |
Weibull | -0.11401 | 0.58013 | 0.13512 | 0.865 | 1.119 | 87.987 | 0.0416 | |
Cox | -1.37774 | 3.67486 | 5.99725 | -1.550 | -1.206 | 292.456 | 0.0507 | |
Log normal σ2=1 | OLS for Ln(y) | -0.06560 | 0.77896 | 0.28826 | 0.861 | 1.153 | 144.905 | 0.0375 |
Gamma | -0.00084 | 0.75579 | 0.24681 | 0.809 | 1.169 | 97.178 | 0.0332 | |
Weibull | -0.01498 | 0.75773 | 0.27025 | 0.809 | 1.169 | 97.694 | 0.0344 | |
Cox | -0.96876 | 3.53907 | 4.20450 | -1.135 | -0.803 | 295.126 | 0.0536 | |
Log normal σ2=1.5 | OLS for Ln(y) | -0.06646 | 0.93700 | 0.43240 | 0.830 | 1.188 | 165.178 | 0.0346 |
Gamma | -0.00204 | 0.91116 | 0.35880 | 0.743 | 1.219 | 94.667 | 0.0309 | |
Weibull | 0.10499 | 0.85852 | 0.40537 | 0.766 | 1.206 | 93.005 | 0.0298 | |
Cox | -0.78847 | 3.49213 | 3.52210 | -0.952 | -0.624 | 296.053 | 0.0556 | |
Log normal σ2=2 | OLS for Ln(y) | -0.06989 | 1.10461 | 0.57653 | 0.803 | 1.217 | 179.5625 | 0.0347 |
Gamma | -0.00465 | 1.07701 | 0.46796 | 0.680 | 1.266 | 89.735 | 0.0307 | |
Weibull | 0.23242 | 0.95573 | 0.54049 | 0.730 | 1.238 | 86.227 | 0.0281 | |
Cox | -0.68152 | 3.46853 | 3.14852 | -0.846 | -0.520 | 296.522 | 0.0504 | |
Gamma α=0.5 | OLS for Ln(y) | -0.13425 | 1.01591 | 2.105 | 0.675 | 1.334 | 222.881 | 0.1086 |
Gamma | -0.00197 | 0.94922 | 0.891 | 0.772 | 1.208 | 77.941 | 0.0351 | |
Weibull | 0.24545 | 0.87554 | 1.055 | 0.770 | 1.219 | 79.168 | 0.0346 | |
Cox | -0.70741 | 3.51983 | 3.211 | -0.871 | -0.544 | 296.415 | 0.0531 | |
Gamma α =1 | OLS for Ln(y) | -0.07705 | 0.47464 | 0.702 | 0.813 | 1.190 | 168.791 | 0.0608 |
Gamma | -0.00047 | 0.28527 | 0.426 | 0.847 | 1.144 | 100.154 | 0.0388 | |
Weibull | -0.00937 | 0.28340 | 0.428 | 0.847 | 1.145 | 100.134 | 0.0389 | |
Cox | 1.03789 | 0.33563 | 4.397 | -1.198 | -0.871 | 294.821 | 0.0531 | |
Gamma α =2 | OLS for Ln(y) | -0.06760 | 0.54581 | 0.278 | 0.886 | 1.125 | 122.363 | 0.0498 |
Gamma | -0.00026 | 0.53020 | 0.212 | 0.896 | 1.106 | 87.850 | 0.0438 | |
Weibull | -0.11172 | 0.55696 | 0.201 | 0.893 | 1.106 | 88.214 | 0.0470 | |
Cox | 1.47746 | 3.80179 | 6.397 | -1.648 | -1.307 | 291.826 | 0.0504 | |
Gamma α =4 | OLS for Ln(y) | -0.06486 | 0.39403 | 0.123 | 0.927 | 1.087 | 81.482 | 0.0456 |
Gamma | -0.00003 | 0.38221 | 0.106 | 0.928 | 1.079 | 63.053 | 0.0424 | |
Weibull | -0.13114 | 0.41234 | 0.103 | 0.923 | 1.080 | 64.471 | 0.0471 | |
Cox | -2.09719 | 4.10274 | 9.736 | -2.282 | -1.912 | 286.445 | 0.0496 | |
Wiebull α=0.5 | OLS for Ln(y) | -0.15405 | 1.25405 | 1.89494 | 0.638 | 1.396 | 237.978 | 0.1004 |
Gamma | -0.00678 | 1.16471 | 0.84376 | 0.652 | 1.304 | 43.032 | 0.0352 | |
Weibull | 0.47033 | 0.96587 | 1.14195 | 0.690 | 1.296 | 41.454 | 0.0333 | |
Cox | -0.50825 | 3.47052 | 2.60197 | -0.754 | -0.264 | 297.097 | 0.0504 | |
Wiebull α =1 | OLS for Ln(y) | -0.07916 | 0.74709 | 0.47373 | 0.819 | 1.199 | 168.664 | 0.0625 |
Gamma | -0.00076 | 0.72112 | 0.28681 | 0.845 | 1.147 | 99.360 | 0.0416 | |
Weibull | -0.00859 | 0.72241 | 0.28548 | 0.844 | 1.148 | 99.339 | 0.0418 | |
Cox | -1.02239 | 3.63137 | 4.43438 | -1.272 | -0.776 | 294.819 | 0.0521 | |
Wiebull α =5 | OLS for Ln(y) | -0.06425 | 0.18584 | 0.01895 | 0.964 | 1.040 | 7.720 | 0.051 |
Gamma | -0.00003 | 0.18068 | 0.01658 | 0.967 | 1.035 | -1.858 | 0.0452 | |
Weibull | -0.08750 | 0.19046 | 0.01142 | 0.969 | 1.029 | -6.490 | 0.0534 | |
Cox | -5.11234 | 6.96179 | 38.13497 | -5.360 | -4.864 | 256.001 | 0.0493 | |