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

Table 2 Performance comparisons for various estimators

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

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.

ISSN: 1471-2288