Table 5 Alternative estimator results for log-normal, gamma and weibull distributions for n=500
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) | -0.00617 | 0.55823 | 0.01166 | 0.991 | 1.011 | 1075.552 | 0.0438 |
Gamma | -0.000002 | 0.55662 | 0.01079 | 0.989 | 1.011 | 830.756 | 0.0405 | |
Weibull | -0.11093 | 0.59335 | 0.01155 | 0.987 | 1.011 | 870.429 | 0.0538 | |
Cox | -1.31086 | 3.10119 | 5.36566 | -1.326 | -1.296 | 5157.713 | 0.0490 | |
Log normal σ2=1 | OLS for Ln(y) | -0.00625 | 0.76743 | 0.02331 | 0.987 | 1.015 | 1422.125 | 0.0444 |
Gamma | -0.00002 | 0.76539 | 0.02041 | 0.981 | 1.017 | 953.996 | 0.0380 | |
Weibull | -0.00211 | 0.76577 | 0.02309 | 0.982 | 1.016 | 958.951 | 0.0382 | |
Cox | -0.92086 | 3.01376 | 3.71427 | -0.935 | -0.907 | 5189.630 | 0.0543 | |
Log normal σ2=1.5 | OLS for Ln(y) | -0.00646 | 0.92875 | 0.03497 | 0.985 | 1.019 | 1624.858 | 0.0406 |
Gamma | -0.00004 | 0.92652 | 0.02935 | 0.974 | 1.022 | 945.716 | 0.0338 | |
Weibull | 0.12644 | 0.87192 | 0.03464 | 0.978 | 1.020 | 919.644 | 0.0351 | |
Cox | -0.74999 | 2.98739 | 3.08671 | -0.764 | -0.736 | 5200.723 | 0.0474 | |
Log normal σ2=2 | OLS for Ln(y) | -0.00665 | 1.05164 | 0.04662 | 0.983 | 1.021 | 1768.699 | 0.0407 |
Gamma | -0.00006 | 1.04944 | 0.03788 | 0.966 | 1.028 | 867.320 | 0.0316 | |
Weibull | 0.25187 | 0.93223 | 0.04619 | 0.974 | 1.024 | 813.451 | 0.0371 | |
Cox | -0.64857 | 2.97510 | 2.74186 | -0.663 | -0.635 | 5206.363 | 0.0500 | |
Gamma α=0.5 | OLS for Ln(y) | -0.01173 | 0.97145 | 0.170 | 0.966 | 1.026 | 2218.380 | 0.0814 |
Gamma | -0.00010 | 0.96635 | 0.069 | 0.981 | 1.019 | 745.079 | 0.0395 | |
Weibull | 0.26621 | 0.88808 | 0.082 | 0.979 | 1.018 | 756.009 | 0.0613 | |
Cox | -0.69386 | 3.04111 | 2.896 | -0.999 | -0.388 | 5204.358 | 0.050 | |
Gamma α =1 | OLS for Ln(y) | -0.00739 | 0.73625 | 0.056 | 0.984 | 1.018 | 1669.842 | 0.0582 |
Gamma | -0.00001 | 0.73405 | 0.034 | 0.987 | 1.014 | 960.724 | 0.0431 | |
Weibull | -0.00095 | 0.73423 | 0.034 | 0.987 | 1.014 | 960.723 | 0.0438 | |
Cox | -1.00444 | 3.10634 | 4.035 | -1.019 | -0.990 | 5184.427 | 0.0468 | |
Gamma α =2 | OLS for Ln(y) | -0.00643 | 0.54150 | 0.022 | 0.999 | 1.013 | 1202.164 | 0.0452 |
Gamma | -0.00002 | 0.54021 | 0.017 | 0.992 | 1.011 | 844.867 | 0.0403 | |
Weibull | -0.10982 | 0.56708 | 0.016 | 0.992 | 1.011 | 851.287 | 0.0546 | |
Cox | -1.42736 | 3.23880 | 5.909 | -1.442 | -1.413 | 5148.590 | 0.0461 | |
Gamma α =4 | OLS for Ln(y) | -0.00606 | 0.39091 | 0.010 | 0.993 | 1.007 | 792.221 | 0.0443 |
Gamma | 0.000004 | 0.39006 | 0.008 | 0.993 | 1.007 | 598.026 | 0.0416 | |
Weibull | -0.13200 | 0.42060 | 0.008 | 0.993 | 1.007 | 617.434 | 0.1017 | |
Cox | -2.01502 | 3.48489 | 9.092 | -2.031 | -1.999 | 5086.403 | 0.0486 | |
Wiebull α=0.5 | OLS for Ln(y) | -0.01379 | 1.18150 | 0.15321 | 0.962 | 1.032 | 2362.321 | 0.0606 |
Gamma | -0.00012 | 1.17416 | 0.06475 | 0.965 | 1.025 | 411.304 | 0.0338 | |
Weibull | 0.49762 | 0.97207 | 0.09307 | 0.969 | 1.025 | 384.861 | 0.0693 | |
Cox | -0.49022 | 2.99166 | 2.25145 | -0.563 | -0.421 | 5213.082 | 0.0495 | |
Wiebull α =1 | OLS for Ln(y) | -0.00741 | 0.73714 | 0.03830 | 0.980 | 1.016 | 1669.173 | 0.0530 |
Gamma | -0.00002 | 0.73494 | 0.02327 | 0.984 | 1.012 | 961.400 | 0.0421 | |
Weibull | -0.00082 | 0.73506 | 0.02326 | 0.984 | 1.012 | 961.376 | 0.0418 | |
Cox | -0.99154 | 3.11589 | 4.00036 | -1.066 | -0.922 | 5184.367 | 0.0473 | |
Wiebull α =5 | OLS for Ln(y) | -0.00605 | 0.18346 | 0.00153 | 0.996 | 1.004 | 59.7355 | 0.0453 |
Gamma | -0.000003 | 0.18362 | 0.00138 | 0.997 | 1.003 | -51.535 | 0.0447 | |
Weibull | -0.08896 | 0.19356 | 0.00093 | 0.997 | 1.003 | -101.476 | 0.2244 | |
Cox | -5.00813 | 6.36391 | 36.15827 | -5.029 | -4.987 | 4737.774 | 0.0530 | |