Table 2 Alternative estimator results for log-normal, gamma and weibull distributions for n=25
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) | -0.13903 | 0.58026 | 0.28579 | 0.798 | 1.214 | 56.527 | 0.0484 |
Gamma | -0.00070 | 0.53623 | 0.24738 | 0.765 | 1.221 | 43.796 | 0.0453 | |
Weibull | -0.11815 | 0.57319 | 0.25534 | 0.742 | 1.236 | 45.032 | 0.0493 | |
Cox | -1.45570 | 3.85240 | 6.77976 | -1.823 | -1.089 | 114.191 | 0.0522 | |
Log normal σ2=1 | OLS for Ln(y) | -0.14087 | 0.80071 | 0.57158 | 0.715 | 1.303 | 73.856 | 0.0467 |
Gamma | -0.00259 | 0.74803 | 0.47688 | 0.637 | 1.332 | 49.636 | 0.0432 | |
Weibull | -0.02790 | 0.75177 | 0.51067 | 0.635 | 1.333 | 49.889 | 0.0451 | |
Cox | -1.02151 | 3.67692 | 4.79504 | -1.374 | -0.670 | 115.543 | 0.0581 | |
Log normal σ2=1.5 | OLS for Ln(y) | -0.14266 | 0.96247 | 0.85736 | 0.651 | 1.371 | 83.992 | 0.0481 |
Gamma | -0.00667 | 0.90470 | 0.69826 | 0.523 | 1.427 | 48.094 | 0.0440 | |
Weibull | 0.08439 | 0.85470 | 0.76599 | 0.553 | 1.407 | 47.547 | 0.0442 | |
Cox | -0.83058 | 3.61682 | 4.04647 | -1.179 | -0.483 | 116.007 | 0.0544 | |
Log normal σ2=2 | OLS for Ln(y) | -0.14384 | 1.08909 | 1.14315 | 0.597 | 1.429 | 91.184 | 0.0485 |
Gamma | -0.01478 | 1.03115 | 0.91562 | 0.420 | 1.514 | 43.316 | 0.0429 | |
Weibull | 0.19665 | 0.91580 | 1.02132 | 0.484 | 1.470 | 42.107 | 0.0414 | |
Cox | -0.71755 | 3.58418 | 3.63860 | -1.06 | -0.373 | 116.245 | 0.0536 | |
Gamma α=0.5 | OLS for Ln(y) | -0.30508 | 1.10870 | 4.184 | 0.327 | 1.646 | 112.098 | 0.1269 |
Gamma | -0.00608 | 0.93533 | 1.831 | 0.514 | 1.405 | 40.684 | 0.0468 | |
Weibull | 0.22314 | 0.86661 | 2.132 | 0.509 | 1.426 | 41.359 | 0.0455 | |
Cox | -0.70630 | 3.61984 | 3.532 | -1.054 | -0.359 | 116.236 | 0.0534 | |
Gamma α =1 | OLS for Ln(y) | -0.16364 | 0.76291 | 1.424 | 0.626 | 1.380 | 85.253 | 0.0727 |
Gamma | -0.00141 | 0.70474 | 0.854 | 0.687 | 1.289 | 51.104 | 0.0470 | |
Weibull | -0.01889 | 0.70780 | 0.858 | 0.686 | 1.290 | 51.072 | 0.0481 | |
Cox | 1.07902 | 3.67304 | 4.794 | -1.412 | -0.714 | 115.454 | 0.0546 | |
Gamma α =2 | OLS for Ln(y) | -0.14447 | 0.55706 | 0.567 | 0.779 | 1.240 | 62.351 | 0.0545 |
Gamma | -0.00064 | 0.51805 | 0.422 | 0.760 | 1.203 | 45.250 | 0.0461 | |
Weibull | -0.11319 | 0. 54472 | 0.406 | 0.773 | 1.202 | 45.302 | 0.0485 | |
Cox | 1.52397 | 3.95791 | 6.794 | -1.887 | -1.161 | 113.989 | 0.0583 | |
Gamma α =4 | OLS for Ln(y) | -0.13872 | 0.40613 | 0.248 | 0.847 | 1.166 | 42.011 | 0.0479 |
Gamma | -0.00020 | 0.37338 | 0.208 | 0.851 | 1.150 | 32.861 | 0.0431 | |
Weibull | -0.12969 | 0.40265 | 0.200 | 0.840 | 1.151 | 33.311 | 0.0471 | |
Cox | -2.18196 | 4.31535 | 10.402 | -2.572 | -1.792 | 111.303 | 0.0486 | |
Wiebull α=0.5 | OLS for Ln(y) | -0.34517 | 1.36816 | 3.73002 | 0.251 | 1.761 | 119.821 | 0.1253 |
Gamma | -0.02216 | 1.15326 | 1.73985 | 0.296 | 1.600 | 22.472 | 0.0448 | |
Weibull | 0.43461 | 0.95799 | 2.23442 | 0.349 | 1.581 | 22.094 | 0.0408 | |
Cox | -0.51486 | 3.57624 | 2.98777 | -0.948 | -0.082 | 116.549 | 0.0531 | |
Wiebull α =1 | OLS for Ln(y) | -0.16807 | 0.76539 | 0.93251 | 0.626 | 1.380 | 85.164 | 0.0702 |
Gamma | -0.00210 | 0.70482 | 0.56343 | 0.676 | 1.290 | 51.009 | 0.0492 | |
Weibull | -0.01845 | 0.70757 | 0.55860 | 0.675 | 1.291 | 50.971 | 0.0502 | |
Cox | -1.04789 | 3.75803 | 4.92479 | -1.489 | -0.607 | 115.443 | 0.0526 | |
Wiebull α =5 | OLS for Ln(y) | -0.13691 | 0.20584 | 0.03730 | 0.926 | 1.076 | 4.692 | 0.0526 |
Gamma | -0.00006 | 0.17590 | 0.03153 | 0.930 | 1.068 | 0.040 | 0.0412 | |
Weibull | -0.08524 | 0.18546 | 0.02234 | 0.935 | 1.059 | -2.112 | 0.0470 | |
Cox | -5.24388 | 7.34860 | 40.76941 | -5.785 | -4.703 | 96.674 | 0.0526 | |