## 2 Materials and Methods
The final selection of Random Forest over competing models was the result of experimental evaluation. Table 3 shows the performance (MAPE and MAE) of individual candidates for the baseline models obtained by 5-fold cross-validation and then averaged for all three prediction tasks: 1 st, 4 th, and 7 th days after surgery. The baseline models were taken with default parameters, since the amount of data at our disposal did not allow hyperparameter optimization. All experimental results were obtained using the Scikit learn package [32], LightGBM package [33], and XGBoost package [34]. In order to get a clearer picture of the selected basic algorithms, we list some of the most important default parameters: Lasso (alpha = 1, max_iter = 1000), ExtraTrees (n_estimators = 100, criterion = gini, max_features = sqrt), RandomForest (n_estimators = 100, criterion = gini, max_features = sqrt), LightGBM (boosting_type = gbdt, n_estimators = 100, num_leaves = 31), SVM (kernel = linear, C = 1, tol = 0.001), SVM (kernel = rbf, C = 1, tol = 0.001, gamma = scale), AdaBoost (n_estimators = 50, leakage_rate = 1), KNN (n_neighbors = 5, metric = minkowski, p = 2), MLP (hidden_layer_size = {7,3,2}, activation = relu, solver = Adam, max_iter = 200), MLP (hidden_layer_size = {3,2}, activation = relu, solver = Adam, max_iter = 200), Ridge (alpha = 1, solver = auto), XGBoost (see [34]), LogisticRegression (penalty = l2, solver = lbfgs, max_iter = 100). The light ocher yellow indicates nine models that were included in the final architecture. The omission of the MLP models was primarily motivated by the large number of free parameters compared to the available length of the training sets. Additionally,

our results confirmed the already noted fact (see [35; 36] that despite the significant progress in the application of deep neural networks for tabular data, they are still outperformed by tree-based models on many standard benchmarks. The last row of Table 3 shows the corresponding performance of the meta-model for the selected nine base regressors: Lasso, Extra Tree, Random Forest, SVM Linear, KNN, Ridge Regression, XGBoost, SVM RBF, and LogisticReg. As expected, the meta-model gave better results for both performances (MAPE and MAE) compared to any base model. To minimize the risk of overfitting we wish to highlight the taken measures:

* Selection of base regressors dominantly employing ensemble methods
* Selection of Random Forest as the final regressor
* Nested cross-validation (see Algorithm 2), ensuring the training of stacked regressor \(H_{R}\), in an additional L-fold cross-validation. It is well known that nested cross-validation minimizes the amount of information leakage between the training and validation sets [37]. Table 4 shows the performance of the proposed meta-model, along with the performances of three standard models (Functional segments, Juhl-Frost, Nakahara), obtained with 5-fold cross-validation. In order to quantitatively measure the gain of the meta-model, we introduced the values \(Gain\_MAPE\), i.e., \(Gain\_MAE\) defined as the ratio of the respective performances of the compared model M with the meta-model:

\[Gain\_MAPE=\frac{J_{MAPE}(M)}{J_{MAPE}(\textit{meta model})}, \tag{9}\]

\[Gain\_MAE=\frac{J_{MAE}(M)}{J_{MAPE}(\textit{meta model})}, \tag{10}\]

From Table 4, we concluded that our meta-model gave significantly more accurate results for ppoEFV1[%] than traditional calculations. By analyzing the gains, we can conclude the following:

1. The proposed meta-model in the first postoperative day gave a gain of more than three times compared to any traditional method, both for MAPE and MAE criteria (average Gain_MAPE = 3.84, average Gain_MAE = 3.51). Among traditional prediction methods, [PERSON]'s model performed best, compared to which the meta-model has Gain_MAPE = 3.43, i.e., Gain_MAE = 3.14.