Table 4 Polytomous discrimination index, pairwise c-statistics, and Brier score on the updating data after correction for optimism using bootstrapping

 No updating

0.87 (0.85–0.90)

0.99 (0.98–0.99)

0.92 (0.89–0.94)

0.89 (0.85–0.93)

0.172 (0.155–0.190)

 Intercept recalibration

0.87 (0.84–0.89)

0.99 (0.98–0.99)

0.92 (0.89–0.94)

0.89 (0.85–0.92)

0.165 (0.148–0.183)

 Logistic recalibration

0.88 (0.85–0.90)

0.99 (0.98–>0.99)

0.93 (0.91–0.95)

0.91 (0.88–0.94)

0.158 (0.143–0.173)

 Refitting

0.88 (0.85–0.90)

0.99 (0.99–>0.99)

0.93 (0.91–0.95)

0.91 (0.88–0.94)

0.157 (0.141–0.172)

 Penalized refitting

0.88 (0.85–0.90)

0.99 (0.98–>0.99)

0.93 (0.91–0.95)

0.91 (0.88–0.94)

0.158 (0.142–0.172)

 Refitting + rcs

0.88 (0.86–0.91)

0.99 (0.98–>0.99)

0.93 (0.91–0.95)

0.92 (0.89–0.95)

0.153 (0.137–0.168)

 Extension

0.89 (0.87–0.92)

0.99 (0.99–>0.99)

0.93 (0.92–0.95)

0.93 (0.90–0.95)

0.150 (0.135–0.165)

 Penalized extension

0.89 (0.87–0.92)

0.99 (0.99–>0.99)

0.93 (0.92–0.95)

0.93 (0.90–0.95)

0.150 (0.135–0.165)

 No updating

0.80 (0.77–0.83)

0.95 (0.93–0.97)

0.91 (0.88–0.94)

0.84 (0.79–0.88)

0.286 (0.258–0.314)

 Intercept recalibration

0.80 (0.77–0.83)

0.95 (0.93–0.97)

0.91 (0.88–0.94)

0.84 (0.79–0.88)

0.278 (0.247–0.310)

 Logistic recalibration

0.80 (0.77–0.83)

0.96 (0.94–0.97)

0.93 (0.90–0.95)

0.84 (0.79–0.88)

0.267 (0.243–0.291)

 Refitting

0.80 (0.77–0.83)

0.96 (0.94–0.97)

0.94 (0.92–0.96)

0.84 (0.80–0.88)

0.266 (0.243–0.291)

 Penalized refitting

0.80 (0.77–0.83)

0.96 (0.94–0.97)

0.94 (0.91–0.95)

0.84 (0.79–0.88)

0.265 (0.242–0.289)

 Refitting + rcs

0.82 (0.79–0.85)

0.96 (0.94–0.97)

0.94 (0.92–0.96)

0.85 (0.81–0.89)

0.261 (0.237–0.284)

 Extension

0.81 (0.78–0.84)

0.96 (0.94–0.97)

0.94 (0.92–0.96)

0.84 (0.80–0.88)

0.262 (0.238–0.287)

 Penalized extension

0.81 (0.78–0.84)

0.96 (0.94–0.97)

0.94 (0.92–0.96)

0.84 (0.80–0.88)

0.263 (0.239–0.287)