Table 5

Results of the updating methods14 30 for the Brock model.2 Variances of logistic regression models’ coefficients were adjusted with the use of the Huber-White robust variance estimator.34 The reference groups are the same as in McWilliams et al.2 For each model, the c-statistic, the Brier score and the Akaike information criterion (AIC) were calculated

Updating methodsDiscrimination (c-statistic)Overall performance (Brier score)Relative goodness of fit (AIC)
Method 1: No adjustment0.905 (0.882, 0.928)0.0231385
Method 2: Recalibration0.905 (0.882, 0.928)0.0221333
α −0.54 (−0.71, 0.36)
Method 3: Recalibration0.905 (0.882, 0.928)0.0221335
α −0.59 (−0.81, −0.36)
Embedded Image 0.97 (0.88, 1.06)
Method 4: Revision0.907 (0.885, 0.930)0.0211317
α −1.0 (−1.48, −0.52)
Embedded Image 0.85 (0.75, 0.96)
Embedded Image
Embedded Image −0.34 (−0.69, 0.01)
Embedded Image
Embedded Image −0.28 (−0.65, 0.09)
Embedded Image
Embedded Image
Embedded Image
Embedded Image
Embedded Image 0.81 (0.40, 1.21)
Method 5: Revision0.901 (0.879–0.924)0.0221324
α −6.92 (−7.5, −6.35)
Embedded Image 0.04 (0, 0.07)
Embedded Image 0.19 (−0.17, 0.55)
Embedded Image 0.16 (−0.24, 0.55)
Embedded Image −0.06 (−0.42, 0.31)
Embedded Image −4.50 (−5.12, −3.87)
Embedded Image −0.19 (−0.93, 0.54)
Embedded Image 0.01 (−0.61, 0.64)
Embedded Image 0.70 (0.33, 1.07)
Embedded Image −0.15 (−0.28, −0.02)
Embedded Image 1.46 (1.08, 1.83)
Method 6: Extension0.914 (0.892, 0.936)0.0211288
α −1.88 (−2.48, −1.29)
Embedded Image 0.83 (0.72, 0.94)
Embedded Image
Embedded Image
Embedded Image
Embedded Image −0.35 (−0.72, 0.03)
Embedded Image
Embedded Image
Embedded Image
Embedded Image −0.10 (−0.23, 0.04)
Embedded Image 0.85 (0.45, 1.25)
Embedded Image
Embedded Image 0.38 (0.22, 0.54)
Embedded Image
Embedded Image
Method 7: Extension0.910 (0.888, 0.931)0.0221383
α −7.98 (−10.27, −5.68)
Embedded Image 0.03 (0, 0.07)
Embedded Image 0.34 (−0.04, 0.71)
Embedded Image 0.15 (−0.25, 0.54)
Embedded Image −0.10 (−0.46, 0.27)
Embedded Image 0.10 (0.06, 0.13)
Embedded Image −0.14 (−0.85, 0.58)
Embedded Image 0.20 (−0.47, 0.87)
Embedded Image 0.75 (0.37, 1.12)
Embedded Image −0.18 (−0.31, −0.04)
Embedded Image 2.07 (1.65, 2.48)
Embedded Image
Embedded Image 0.35 (0.20, 0.50)
Embedded Image
Embedded Image
Method 8: Extension0.909 (0.887, 0.931)0.0221388
α −7.99 (−10.41, −5.56)
Embedded Image 0.03 (0, 0.07)
Embedded Image 0.32 (−0.06, 0.69)
Embedded Image 0.14 (−0.25, 0.54)
Embedded Image −0.10 (−0.48, 0.28)
Embedded Image 0.10 (0.06, 0.13)
Embedded Image −0.13 (−0.85, 0.59)
Embedded Image 0.23 (−0.43, 0.89)
Embedded Image 0.75 (0.38, 1.12)
Embedded Image −0.18 (−0.31, −0.04)
Embedded Image 2.07 (1.65, 2.49)
Embedded Image 0.001 (−0.21, 0.21)
Embedded Image 0.36 (0.20, 0.51)
Embedded Image 0.03 (−0.33, 0.40)
Embedded Image −0.33 (−1.32, 0.66)
  • In methods 6–8, we used the data set presented in online supplementary table S2. The references for those covariates are always yes versus no. As in McWilliams et al,2 age was centred on 62 years, nodule size was centred on 4 mm and nodule count was calculated as ({nodule size/10} 0.5 −1.58113883).

  • Pack-year and body mass index (BMI) covariates were normalised. They had a non-linear relationship with lung cancer and were transformed using a fractional polynomial.36 After transformation, BMI was ((BMI−27.64)/4.8)+3 and pack-year was ((pack-year−57.32)/25.01)+1.1.