Table 1 Multivariate regression models results in the development data and models’ performance in the validation data

Predictors

OR (95% CI)

OR (95% CI)

OR (95% CI)

Beta (95% CI)

Beta (95% CI)

Beta (95% CI)

  (Intercept)

0.5 (0.21, 1.22)

0.28 (0.11, 0.68)

0.48 (0.19, 1.26)

0.16 (-0.16, 0.47)

0.24 (-0.05, 0.54)

0.2 (-0.09, 0.50)

 Age (years)

1.01 (1.00, 1.02)

1.01 (1.01, 1.02)

1.01 (1.00, 1.02)

0.07 (0.02, 0.11)

0.09 (0.05, 0.14)

0.06 (0.02, 0.10)

 Gender (ref. female)

male

1.14 (0.97, 1.34)

1.18 (1.00, 1.39)

1.18 (0.99, 1.41)

0.08 (0.00, 0.15)

0.08 (0.02, 0.15)

0.1 (0.03, 0.17)

 Degen. disease (ref. disc herniation)

stenosis

0.61 (0.47, 0.77)

0.63 (0.49, 0.81)

0.77 (0.59, 0.99)

-0.21 (-0.31, -0.10)

-0.15 (-0.25, -0.05)

-0.18 (-0.28, -0.08)

disc herniation & stenosis

0.78 (0.60, 1.02)

0.74 (0.56, 0.97)

0.89 (0.67, 1.19)

-0.12 (-0.24, -0.00)

-0.15 (-0.26, -0.04)

-0.12 (-0.23, -0.01)

 Previous surgeries (ref. no)

yes

0.67 (0.55, 0.82)

0.78 (0.63, 0.96)

0.67 (0.54, 0.83)

-0.24 (-0.33, -0.15)

-0.13 (-0.22, -0.05)

-0.24 (-0.33, -0.16)

 Treatment duration (ref. < 3 months)

3–12 months

0.95 (0.79, 1.15)

0.85 (0.70, 1.02)

0.94 (0.77, 1.15)

-0.06 (-0.15, 0.02)

-0.05 (-0.13, 0.02)

-0.04 (-0.12, 0.03)

 > 12 months

1 (0.79, 1.26)

0.89 (0.70, 1.13)

0.99 (0.77, 1.27)

-0.03 (-0.14, 0.07)

-0.06 (-0.16, 0.04)

-0.05 (-0.14, 0.05)

 BMI (ref. normal)

overweight

1.13 (0.93, 1.38)

1.13 (0.92, 1.38)

0.95 (0.77, 1.18)

0.04 (-0.05, 0.12)

0.01 (-0.07, 0.09)

-0.04 (-0.12, 0.05)

obese

1 (0.80, 1.24)

1.02 (0.82, 1.28)

1.04 (0.82, 1.32)

-0.06 (-0.16, 0.04)

-0.08 (-0.17, 0.01)

-0.01 (-0.10, 0.08)

 Current smoker (ref. no)

yes

0.6 (0.47, 0.75)

0.67 (0.52, 0.84)

0.56 (0.44, 0.72)

-0.24 (-0.34, -0.13)

-0.21 (-0.31, -0.11)

-0.27 (-0.37, -0.17)

 Morbidity (ref. ASA1)

ASA2

0.72 (0.58, 0.88)

0.73 (0.59, 0.89)

0.61 (0.48, 0.76)

-0.14 (-0.23, -0.05)

-0.12 (-0.21, -0.04)

-0.16 (-0.24, -0.07)

ASA3/4

0.57 (0.43, 0.77)

0.67 (0.49, 0.91)

0.55 (0.40, 0.76)

-0.31 (-0.44, -0.18)

-0.18 (-0.31, -0.06)

-0.25 (-0.37, -0.12)

 Baseline COMI

1.24 (1.16, 1.33)

0.91 (0.85, 0.97)

0.95 (0.88, 1.02)

0.32 (0.27, 0.36)

-0.05 (-0.10, -0.01)

-0.03 (-0.08, 0.01)

 Baseline back pain

0.87 (0.83, 0.90)

1.37 (1.31, 1.42)

0.89 (0.86, 0.93)

-0.21 (-0.25, -0.16)

0.5 (0.46, 0.54)

-0.16 (-0.19, -0.12)

 Baseline leg pain

1.02 (0.98, 1.07)

0.99 (0.95, 1.04)

1.44 (1.37, 1.53)

0.03 (-0.02, 0.07)

-0.02 (-0.06, 0.02)

0.48 (0.44, 0.52)

 Extent of surgery (ref. 1)

2

1.13 (0.69, 1.86)

0.99 (0.59, 1.66)

1 (0.58, 1.69)

0.09 (-0.13, 0.31)

0.06 (-0.16, 0.27)

0.06 (-0.15, 0.27)

3

1.37 (0.80, 2.34)

1.13 (0.65, 1.96)

1.21 (0.67, 2.14)

0.09 (-0.15, 0.33)

0.09 (-0.14, 0.31)

0.08 (-0.15, 0.30)

 ≥ 4

1.01 (0.49, 2.04)

0.91 (0.44, 1.87)

0.75 (0.35, 1.57)

-0.01 (-0.32, 0.31)

0.01 (-0.29, 0.30)

-0.03 (-0.33, 0.27)

 Surgical measures (ref. decompression)

decompression & fusion

1.98 (1.21, 3.28)

1.45 (0.89, 2.39)

1.81 (1.06, 3.13)

0.37 (0.16, 0.58)

0.28 (0.08, 0.48)

0.33 (0.13, 0.53)

 Surgeon (ref. specialized spine)

board certified neuro

1.14 (0.94, 1.39)

1.1 (0.90, 1.34)

0.94 (0.76, 1.16)

0.03 (-0.05, 0.12)

0.02 (-0.06, 0.10)

0 (-0.08, 0.08)

board certified ortho

1.12 (0.50, 2.61)

1.09 (0.47, 2.54)

1.58 (0.63, 4.60)

-0.04 (-0.40, 0.32)

-0.01 (-0.34, 0.33)

0.16 (-0.18, 0.50)

neuro in training

0.95 (0.76, 1.19)

0.85 (0.67, 1.07)

0.87 (0.68, 1.11)

-0.04 (-0.14, 0.06)

-0.01 (-0.11, 0.08)

-0.03 (-0.12, 0.07)

ortho in training

0.87 (0.38, 2.00)

0.53 (0.22, 1.23)

0.86 (0.36, 2.17)

-0.14 (-0.51, 0.23)

-0.21 (-0.56, 0.15)

-0.01 (-0.36, 0.35)

other

1.13 (0.69, 1.87)

1.3 (0.78, 2.21)

0.87 (0.52, 1.50)

0.01 (-0.21, 0.23)

0.06 (-0.15, 0.27)

0.02 (-0.19, 0.23)

 Operation time (ref. < 1)

1–2

0.88 (0.73, 1.05)

0.95 (0.79, 1.14)

0.92 (0.76, 1.12)

-0.06 (-0.14, 0.02)

-0.03 (-0.11, 0.04)

-0.05 (-0.13, 0.02)

2–3

0.91 (0.62, 1.36)

0.98 (0.66, 1.46)

1.03 (0.67, 1.58)

-0.05 (-0.22, 0.13)

-0.02 (-0.18, 0.15)

0.04 (-0.12, 0.21)

 > 3

0.55 (0.28, 1.05)

0.58 (0.30, 1.11)

0.75 (0.37, 1.51)

-0.33 (-0.61, -0.04)

-0.31 (-0.58, -0.04)

-0.07 (-0.35, 0.20)

 Blood loss (ref. < 100 ml)

100–500 ml

1.19 (0.94, 1.50)

1.29 (1.01, 1.64)

1.22 (0.95, 1.58)

0.09 (-0.02, 0.19)

0.08 (-0.02, 0.17)

0.05 (-0.05, 0.15)

 > 500 ml

0.47 (0.18, 1.12)

0.83 (0.34, 1.97)

0.65 (0.27, 1.59)

-0.18 (-0.55, 0.19)

-0.19 (-0.54, 0.17)

-0.17 (-0.52, 0.18)

 Complications (ref. no)

yes

0.83 (0.65, 1.05)

0.73 (0.57, 0.94)

0.78 (0.61, 1.01)

-0.05 (-0.16, 0.06)

-0.05 (-0.15, 0.05)

-0.08 (-0.18, 0.02)

  (log) Hospital stay (days)

0.78 (0.66, 0.92)

0.88 (0.75, 1.05)

0.78 (0.65, 0.93)

-0.07 (-0.12, -0.03)

-0.04 (-0.08, -0.00)

-0.05 (-0.09, -0.01)

 Follow-up (ref. 3 months)

12 months

0.99 (0.61, 1.60)

0.93 (0.57, 1.53)

1.02 (0.61, 1.68)

-0.02 (-0.23, 0.19)

-0.07 (-0.28, 0.13)

0.01 (-0.19, 0.21)

24 months

1.1 (0.72, 1.68)

1.13 (0.73, 1.73)

1.28 (0.81, 1.98)

0.14 (-0.04, 0.33)

-0.01 (-0.19, 0.17)

0.11 (-0.07, 0.28)

Development performance (N = 2691)

 Nagelkerke R²

0.10

0.17

0.17

 Null deviance (df = 2690) / Residual deviance (df = 2657)

3669 / 3456

3723 / 3359

3424 / 3077

 AUC (95% CI)

0.65 (0.63, 0.67)

0.69 (0.67, 0.71)

0.70 (0.68, 0.72)

 Sensitivity / Specificity (optimal cut-off)

0.66 / 0.56 (0.56)

0.75 / 0.51 (0.49)

0.72 / 0.56 (0.65)

 F-test

F(33,2657) = 13.35, p < 0.001

F(33,2657) = 24.11, p < 0.001

F(33,2657) = 23.62, p < 0.001

 R² / adjusted R²

0.142 / 0.132

0.230 / 0.221

0.227 / 0.217

 RMSE

2.84

2.90

3.24

 Calibration intercept (95% CI)

0.01 (-0.06, 0.09)

0.02 (-0.09, 0.12)

0.02 (-0.05, 0.08)

0.10 (-0.28, 0.48)

0.00 (-0.25, 0.26)

-0.03 (-0.48, 0.41)

 Calibration slope (95% CI)

0.97 (0.85, 1.09)

0.97 (0.78, 1.16)

0.97 (0.88, 1.07)

0.97 (0.86, 1.08)

1.00 (0.90, 1.09)

1.01 (0.90, 1.12)

 Calibration-in-the-large

 < 0.01

 < 0.01

 < 0.01

 > -0.01

0.00

 < 0.01

 E/O

1.00

1.00

1.00

 Brier score

0.23

0.22

0.19

 ECI

0.03

0.15

0.02

 Pearson’s r (observed vs. predicted)

0.38

0.48

0.48

Validation performance (N = 1616)

 AUC (95% CI)

0.63 (0.61, 0.66)

0.72 (0.69, 0.74)

0.68 (0.65, 0.71)

 Sensitivity / Specificity (optimal cut-off)

0.51 / 0.70 (0.61)

0.53 / 0.77 (0.61)

0.76 / 0.49 (0.63)

 R²

0.156

0.276

0.219

 RMSE

2.93

3.00

3.33

 Calibration intercept (95% CI)

0.09 (-0.06, 0.24)

0.02 (-0.11, 0.14)

0.08 (-0.03, 0.18)

0.18 (-0.23, 0.59)

0.15 (-0.18, 0.48)

0.49 (0.28, 0.69)

 Calibration slope (95% CI)

0.84 (0.59, 1.10)

1.03 (0.81, 1.26)

0.89 (0.74, 1.04)

1.02 (0.90, 1.15)

1.09 (0.97, 1.21)

0.94 (0.89, 0.99)

 Calibration-in-the-large

 < 0.01

0.04

0.01

0.25

0.35

0.28

 E/O

1.00

0.93

0.99

 Brier score

0.23

0.21

0.19

 ECI

0.10

0.33

0.10

 Pearson’s r (observed vs. predicted)

0.40

0.53

0.47