Fig. 3

Mean differences and root mean squared differences (RMSD) between c-statistics computed by data resampling techniques and the independently validated (IV) c-statistic for the model estimators ML, FL, and RR for the simulation settings with 50 observations, an event fraction of 0.25, and either no or strong effects. The Monte Carlo standard errors of the mean difference and of the root mean squared difference were smaller than 0.008 and 0.007, respectively, for all scenarios. ML, maximum likelihood; FL, Firth’s logistic regression; RR, ridge regression. LOO, leave-one-out cross-validation; LPO, leave-pair-out cross-validation; 5-fold, 5-fold cross-validation; enhBT, enhanced bootstrap; .632+, .632+ bootstrap; app, apparent estimate