Table 3 Measures of model performance

ICNARC model

N = 23,269

N = 7,396

N = 7,994

N = 7,879

c index (95% CI)

0.848 (0.843, 0.853)

0.846 (0.837, 0.855)

0.852 (0.843, 0.861)

0.845 (0.836, 0.854)

Hosmer-Lemeshow test

 Chi-squared (P-value)

18.8 (0.043)

3.5 (0.97)

12.7 (0.24)

10.8 (0.37)

Cox calibration regression

 Intercept (95% CI)

-0.02 (-0.06, 0.02)

-0.02 (-0.07, 0.06)

-0.01 (-0.08, 0.06)

-0.05 (-0.12, 0.02)

 Slope (95% CI)

1.02 (0.99, 1.05)

1.02 (0.96, 1.07)

1.04 (0.98, 1.09)

1.01 (0.96, 1.06)

 Chi-squared (P-value)

5.3 (0.070)

0.5 (0.78)

2.9 (0.24)

3.6 (0.17)

Brier’s score

0.140

0.143

0.137

0.139

 Sum-of-squares R²

0.331

0.331

0.338

0.325

Shapiro’s R

0.652

0.646

0.656

0.653

 Entropy-based R²

0.296

0.295

0.303

0.290

APACHE II

N = 22,700

N = 7,277

N = 7,992

N = 7,431

c index (95% CI)

0.806 (0.800, 0.812)

0.793 (0.782, 0.804)

0.808 (0.798, 0.818)

0.817 (0.807, 0.827)

Hosmer-Lemeshow test

 Chi-squared (P-value)

214 (<0.001)

44.9 (<0.001)

85.1 (<0.001)

120 (<0.001)

Cox calibration regression

 Intercept (95% CI)

-0.26 (-0.30, -0.23)

-0.18 (-0.24, -0.12)

-0.27 (-0.33, -0.21)

-0.34 (-0.40, -0.28)

 Slope (95% CI)

0.91 (0.89, 0.94)

0.88 (0.83, 0.93)

0.92 (0.87, 0.97)

0.95 (0.90, 1.00)

 Chi-squared (P-value)

208 (<0.001)

39.2 (<0.001)

77.1 (<0.001)

117 (<0.001)

Brier’s score

0.157

0.165

0.156

0.151

 Sum-of-squares R²

0.244

0.234

0.246

0.250

Shapiro’s R

0.621

0.608

0.623

0.631

 Entropy-based R²

0.214

0.200

0.217

0.224