Fig. 2. Performance metrics of ensemble models across internal and external validation cohorts.

Ensemble models were internally and externally validated on the 3-times repeated 10-folds cross-validation and the external validation cohorts comprising Columbia university from the USA and Sun Yat-sen university from China. For multi-AUC, the full lesion scores were used. For other metrics, such as AUROC and sensitivity, categorical Banff scores (arteriosclerosis [cv Banff score], arteriolar hyalinosis [ah Banff score], and interstitial fibrosis and tubular atrophy [IFTA Banff score]) were dichotomized. Cut-offs were calibrated based on internal validation (cross-validation): 0.582, 0.596, 0.637 for cv, ah, IFTA lesions, respectively. For internal validations, performance was assessed in 30 resamples during cross-validation. For external validations, performance was assessed using 1,000 times bootstrapping. All box plots comprise the median line, the box indicated the interquartile range (IQR), whiskers denote the rest of the data distribution and outliers are denoted by points greater than ±1.5 × IQR. * For sensitivity, specificity, balanced accuracy, accuracy, and AUROC, the Banff lesion scores, cv, ah, and IFTA were dichotomized (scores 0–1 as negative and 2-3 as positive). Banff scores: cv arteriosclerosis, ah arteriolar hyalinosis, IFTA interstitial fibrosis and tubular atrophy. multi-AUC multi-area under the receiver operating characteristic curve, AUROC area under the receiver operating characteristic curve, MAE mean absolute error, RMSE root mean square error. Source data are provided as a Source Data file.