Table 4.

Multivariate model after introduction of nonlinear term (length of stay in ICU squared) to the model (χ² = 85.0, p < 0.001),^a, ^b and corresponding parametric survival model assuming the generalized gamma distribution. (χ² = 79.0, p < 0.001).^c, ^d

	Cox Regression Model			Parametric Model
Variable	Hazard Ratio	95% Confidence Interval	P	Coefficient	95% Confidence Interval	P
Age (Years)	1.03	1.02, 1.05	<0.001*	−0.0380	−0.0592, −0.0169	<0.001*
ASA Score	1.62	1.31, 1.99	<0.001*	−0.653	−0.954, −0.352	<0.001*
Length of Stay in ICU (days)	1.15	1.09, 1.23	<0.001*	−0.210	−0.303, −0.114	<0.001*
(Length of Stay in ICU)2	0.9978	0.9958, 0.9998	0.028*	0.00334	0.00019, 0.00648	0.038*

ASA = American Society of Anesthesiologists physical status score; ICU = intensive care unit.

Significant differences are indicated by an asterisk.

^aThe likelihood ratio test comparing the Cox regression model to one without the nonlinear term demonstrated significant improvement (p = 0.02). The test for goodness-of-fit for the Cox regression model of Table 4 revealed, for the eight quantiles of risk evaluated, only one significant deviation (p = 0.02), one trend (p = 0.10) with the remainder highly nonsignificant (p ≥ 0.31). If time until surgery is included in the model of Table 4, then in the test for goodness-of-fit, all quantiles are highly insignificant (p ≥ 0.35). If Time Until Surgery is incorporated (χ² = 88.3, p < 0.001), age, ASA and length of stay in ICU remained highly significant (p < 0.001), the square of length of stay in ICU remained significant (p = 0.01), and time until surgery was a trend (p = 0.11). The addition of dementia, depression, or incident postoperative delirium to such a model did not significantly improve the quality of the model with Time Until Surgery as revealed by likelihood ratio tests (cognitive impairment, p = 0.88; depression, p > 0.99; delirium, p = 0.20).

^bLikelihood ratio tests comparing the Cox regression model of Table 4 with one where the eliminated variables from Table 2 were incorporated one at a time in the nonlinear model did not achieve significance (male gender, p = 0.42; cognitive impairment, p = 0.99; postoperative delirium, p = 0.22; depression, p = 0.96; time until surgery, p = 0.07; use of regional anesthesia, p=0.27; number of units of erythrocytes transfused, p = 0.88).

^cThe use of the generalized gamma distribution rather than less general distributions such as the lognormal or Weibull, which are both special cases of the generalized gamma distribution, is justified respectively by a value of κ [95% CI] of 0.746 [0.378, 1.115] different from zero and a value of σ [95% CI] of 1.35 [1.16, 1.58] different from 1.

^dLikelihood ratio tests comparing the parametric survival model of Table 4 with one where the eliminated variables from Table 2 were incorporated one at a time in the nonlinear parametric model of the current table without affecting conclusions (male gender, p = 0.53; cognitive impairment, p = 0.47; incident postoperative delirium, p = 0.19; depression, p = 0.99; time until surgery, p = 0.04; use of regional anesthesia, p=0.50; number of units of erythrocytes transfused, p = 0.88). When time until surgery is explicitly incorporated in the model p = 0.07 for its coefficient, and the likelihood ratio test with the further addition of incident postoperative delirium reveals that the model is not significantly improved (p = 0.16).