Table 6 Alternative estimator results for log-normal, gamma and weibull distributions for n=1000
From: Statistical models for the analysis of skewed healthcare cost data: a simulation study
Data | Estimator | MPE | MPAE | MSE(β) | 95% CI | AIC | Prob. H.Lsignif | |
|---|---|---|---|---|---|---|---|---|
Lower | upper | |||||||
Log normal σ2=0.5 | OLS for Ln(y) | -0.00311 | 0.55282 | 0.00586 | 0.996 | 1.006 | 2147.649 | 0.0488 |
Gamma | -0.00001 | 0.55202 | 0.00543 | 0.994 | 1.006 | 1642.073 | 0.0436 | |
Weibull | -0.10959 | 0.58828 | 0.00583 | 0.994 | 1.006 | 1722.864 | 0.0701 | |
Cox | -1.30433 | 3.10889 | 5.32271 | -1.312 | -1.296 | 11694.099 | 0.0467 | |
Log normal σ2=1 | OLS for Ln(y) | -0.00326 | 0.77307 | 0.01172 | 0.995 | 1.009 | 2840.796 | 0.0488 |
Gamma | -0.00001 | 0.77202 | 0.01028 | 0.990 | 1.008 | 1924.378 | 0.0419 | |
Weibull | -0.00120 | 0.77225 | 0.01166 | 0.990 | 1.008 | 1934.411 | 0.0417 | |
Cox | -0.91650 | 3.02844 | 3.68525 | -0.923 | -0.909 | 11757.613 | 0.0467 | |
Log normal σ2=1.5 | OLS for Ln(y) | -0.00339 | 0.92803 | 0.01759 | 0.994 | 1.010 | 3246.261 | 0.0477 |
Gamma | -0.00002 | 0.92689 | 0.01477 | 0.986 | 1.010 | 1893.638 | 0.0393 | |
Weibull | 0.12788 | 0.87225 | 0.01749 | 0.988 | 1.010 | 1839.946 | 0.0433 | |
Cox | -0.74664 | 3.00457 | 3.06286 | -0.754 | -0.740 | 11779.664 | 0.0479 | |
Log normal σ2=2 | OLS for Ln(y) | -0.00351 | 1.05067 | 0.02344 | 0.993 | 1.013 | 3533.943 | 0.0463 |
Gamma | -0.00002 | 1.04957 | 0.01904 | 0.981 | 1.013 | 1738.981 | 0.0354 | |
Weibull | 0.25118 | 0.92331 | 0.02331 | 0.987 | 1.011 | 1607.688 | 0.0480 | |
Cox | -0.64582 | 2.99362 | 2.72102 | -0.653 | -0.639 | 11790.872 | 0.0543 | |
Gamma α=0.5 | OLS for Ln(y) | -0.00551 | 0.96948 | 0.085 | 0.978 | 1.007 | 4435.972 | 0.0845 |
Gamma | -0.00001 | 0.96709 | 0.034 | 0.989 | 1.008 | 1487.309 | 0.0417 | |
Weibull | 0.26721 | 0.88856 | 0.041 | 0.989 | 1.007 | 1508.951 | 0.0931 | |
Cox | -0.69278 | 3.06113 | 2.881 | -0.700 | -0.686 | 11786.66 | 0.0505 | |
Gamma α =1 | OLS for Ln(y) | -0.00374 | 0.73620 | 0.028 | 0.992 | 1.009 | 3337.268 | 0.0540 |
Gamma | -0.000001 | 0.73511 | 0.017 | 0.993 | 1.006 | 1919.125 | 0.0420 | |
Weibull | -0.00042 | 0.73519 | 0.017 | 0.993 | 1.006 | 1919.131 | 0.0417 | |
Cox | -1.00124 | 3.1238 | 4.015 | -1.008 | -0.994 | 11747.09 | 0.0529 | |
Gamma α =2 | OLS for Ln(y) | -0.00318 | 0.54246 | 0.011 | 0.995 | 1.006 | 2401.279 | 0.0481 |
Gamma | -0.00001 | 0.54183 | 0.009 | 0.995 | 1.005 | 1691.20 | 0.0447 | |
Weibull | -0.10998 | 0.56877 | 0.008 | 0.995 | 1.005 | 1704.418 | 0.0785 | |
Cox | -1.42245 | 3.24810 | 5.882 | -1.430 | -1.415 | 11675.63 | 0.0533 | |
Gamma α =4 | OLS for Ln(y) | -0.00305 | 0.39286 | 0.005 | 0.996 | 1.003 | 1581.076 | 0.0455 |
Gamma | -0.000004 | 0.39244 | 0.004 | 0.997 | 1.003 | 1203.85 | 0.0435 | |
Weibull | -0.13273 | 0.42318 | 0.004 | 0.997 | 1.004 | 1243.481 | 0.2093 | |
Cox | -2.00825 | 3. 48492 | 9.047 | -2.016 | -2.000 | 11551.56 | 0.0518 | |
Wiebull α=0.5 | OLS for Ln(y) | -0.00654 | 1.17692 | 0.07707 | 0.978 | 1.014 | 4722.98 | 0.0643 |
Gamma | -0.00004 | 1.17347 | 0.03245 | 0.980 | 1.012 | 819.453 | 0.0378 | |
Weibull | 0.49853 | 0.97136 | 0.04682 | 0.983 | 1.011 | 765.204 | 0.1416 | |
Cox | -0.48930 | 3.01307 | 2.23645 | -0.543 | -0.439 | 11804.08 | 0.0492 | |
Wiebull α =1 | OLS for Ln(y) | -0.00361 | 0.73627 | 0.01926 | 0.989 | 1.007 | 3336.686 | 0.0560 |
Gamma | -0.00001 | 0.73520 | 0.01171 | 0.991 | 1.006 | 1919.109 | 0.0426 | |
Weibull | -0.00042 | 0.73527 | 0.01170 | 0.991 | 1.005 | 1919.06 | 0.0432 | |
Cox | -0.99001 | 3.13384 | 3.98134 | -1.044 | -0.940 | 11746.65 | 0.0509 | |
Wiebull α =5 | OLS for Ln(y) | -0.00301 | 0.18367 | 0.00077 | 0.998 | 1.002 | 117.810 | 0.0397 |
Gamma | -0.000001 | 0.18377 | 0.00069 | 0.998 | 1.002 | -105.433 | 0.0393 | |
Weibull | -0.08904 | 0.19371 | 0.00047 | 0.998 | 1.002 | -205.982 | 0.6238 | |
Cox | -5.00343 | 6.35876 | 36.0715 | -5.014 | -4.992 | 10855.17 | 0.0485 | |