Table 2 Machine learning classifiers’ and ensemble models’ performances

Models	Hand and Till’sMulti-AUC			Mean Absolute Error
Models	Arteriosclerosis(cv Banff score)	Arteriolar hyalinosis(ah Banff score)	Interstitial fibrosis tubular atrophy(IFTA Banff score)	Glomerulosclerosis in percentage
Random Forest	0.836	0.774	0.830	5.807
Gradient Boosting Machine	0.807	0.750	0.805	6.486
Extreme Gradient Boosting Tree	0.830	0.767	0.827	5.768
Linear Discriminant Analysis^a	0.761	0.703	0.750	-^a
Model Averaged Neural Network	0.777	0.720	0.757	6.573
Multinomial Logistic Regression^a	0.763	0.706	0.753	-^a
Ensemble Model	0.833	0.773	0.830	5.999

The models used for ordinal scores (multiclass classification) are as follows: random forest, gradient boosting machine, extreme gradient boosting tree, linear discriminant analysis, model averaged neural network, and multinomial logistic regression. The models used for the percentage of glomerulosclerosis (regression) are as follows: random forest, gradient boosting machine, extreme gradient boosting tree, and model averaged neural network. Finally, we created ensemble models; for the ordinal day-zero lesion scores, we averaged the probabilities of the six models; for the percentage of glomerulosclerosis, we used linear regression of the four models we created. For the ordinal day-zero lesion scores, model performances were assessed by Hand and Till’s area under the curve (multi-AUC). For the percentage of glomerulosclerosis, model performances were assessed by mean absolute error (MAE). Ensemble models were selected as virtual biopsy system. Model performances were assessed in 3-times repeated 10-folds cross-validation (30 resamples).
AUC area under the curve (higher the better). MAE mean absolute error (lower the better).
^aLinear discriminant analysis and multinomial logistic regression are not developed for regression but for classification.

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