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Table 2 Performance comparisons for various estimators

From: A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and new Zealand intensive care adult patient data-base, 2008–2009

Performance index BIC R^2 R^2 CCC CCC MAE MAE RMSE RMSE Residual Normality Residual vs
Model Determination set Determination data-set (n = 86740) Validation data-set (n = 21678) Validation data-set Determination data-set Determination Validation Determination Validation P-P plot Q-Q plot fitted
OLS: raw scale 509801.4 0.19 0.18 0.313 0.308 2.4 2.4 4.6 4.5 No + ve skew No
OLS: log scale 216183.2 0.18 0.18 0.293 0.290 2.4 2.4 4.6 4.5 Yes + ve skew Yes
LMM (log scale) 210285.8 0.22 0.20 0.334 0.328 2.3 2.3 4.5 4.5 Yes + ve skew Yes
(Raw scale) 507492.8  
Treatment effects regression (log scale) 244883.2 0.18 0.17 0.296 0.294 2.4 2.4 4.6 4.5 Yes + ve skew Yes
(Raw scale) 539291.4  
GLM: family(Poisson), link(log) 479143.3 0.19 0.18 0.321 0.314 2.4 2.4 4.5 4.5 No + ve skew No
GLM: family(negbin), link(log) 375021.6 0.19 0.18 0.322 0.316 2.4 2.4 4.5 4.5 No + ve skew No
GLM: family(gamma), link(log) 355449.9 0.19 0.18 0.322 0.317 2.4 2.4 4.6 4.5 No + ve skew# No
GLM: 365186.1 0.19 0.18 0.322 0.317 2.4 2.4 4.6 4.6 No + ve skew# No
family(inverse Gaussian), link(log)  
EEE: Not estimable 0.19 0.18 0.320 0.316 2.4 2.4 4.6 4.6 No + ve skew# No
Log-skew- t regression 213465.5 0.18 0.17 0.285 0.283 2.4 2.4 4.6 4.6 Yes neg skew# No
(Raw scale) 349461.3  
Log-skew-normal regression 214216.4 0.18 0.17 0.317 0.273 2.6 2.4 4.6 4.6 No neg skew# No
(Raw scale) 436227.8  
FMM: raw scale 329774.9 0.18 0.18 0.151 0.149 2.2 2.2 5.0 5.0 No + ve skew# Yes
  1. LLM; Linear mixed model (random coefficient model). CCC; concordance correlation coefficient. Negbin; negative binomial. P-P plot; standardized normal probability plot. Q-Q plot; plot of the quantiles of the residuals against the quantiles of the normal distribution . +ve skew#; marked positive skew. neg skew#; marked negative skew. Residuals vs fitted; increase spread of residuals with increment of fitted values (predicted length of stay). MAE; mean absolute error. RMSE; root mean square error. FMM; finite mixture model. R2, CCC,MAE and RMSE were computed on the back-transformed “day” scale (for the linear mixed model, OLS-log, “treatreg” log-skew-t and log-skew-normal regression) using the Duan smearing estimate.