## 3 Interpretability Analysis in the Prediction of Cardiovascular Diseases
### Performance Evaluation Methods
In the first step, the data are divided by rules using the attribute that best separates the data according to the values of the target attribute. This process continues until the data are completely split. It uses the GINI index as a splitting criterion. The rules can be expressed in the form of a tree, which is the most common method to represent the result obtained by RPART. In the second stage, to avoid overfitting, the algorithm performs a pruning of the tree considering a complexity regularization factor. RPART has some known limitations, such as attribute selection being biased to allow more cutpoints [42]. This means that attributes with a larger value range or more categories are selected. Ctree is a decision tree creation algorithm that does not have this drawback. It is based on a statistical inference framework and selects the attributes by applying a statistical test to select the best attribute with which to split the data. Both algorithms behaved similarly, like linear partitioning algorithms: adding features did not improve the quality of the solutions. The curve corresponding to the use of all features always appeared below the curves with fewer features. The one with the highest value was the one with the least number of features. If relevant features in the nodes were chosen poorly, then the mistake was propagated to the decision of the class. This finding supports the importance of correctly choosing features to be used when solving a classification task. Figure 4: Comparison of classifier performance (accuracy). Blue, all features; green, best 66% of features; red, best 33% of features. Figure 5: Comparison of classifier performance (AUC). Blue, all features; green, best 66% of features; red, best 33% of features. The behavior with the depth level of the best classification tree was expected. As the depth of the tree increased, i.e., its complexity, its behavior improved. The level of complexity was inversely associated with the ability to interpret the model: the more complex the model, the less interpretable. In Figure 6 when the depth of the tree increased, the AUC grew to a maximum level; although the complexity continued growing, it no longer improved the performance. An interesting result was the Pareto front structure that appeared between complexity and performance, regardless of the number of features used. If it is assumed that complexity makes the classification model less interpretable, then a design decision must always be made between them. In this case, for the problem of classifying cardiovascular diseases, the price was small and the saturation of complexity occurred  
Figure 6: Variation in the performance (AUC) with the tree depth and the percentage of features used. Up, recursive partitioning and regression trees (RPART); Down, conditional inference trees (Ctree). when a depth of three was reached. For problems with many more instances, a Pareto front with a smoother curve with depth saturation was to be expected. Depending on the problem and the technique, the curves corresponding to the amount of features were reversed. In Figures 7-9, the variation in AUC was 0.06 for RPART when increasing the tree depth from two to three, and had a lower value, approximately 0.05 for Ctree. The expert analyst must determine if they want to have a more precise or more interpretable model. This is a design decision similar to finding the elbow point in a clustering problem in which precision must be balanced with the number of clusters obtained. The figure below shows the trees' best accuracy corresponding to RPART with different numbers of features for a maximum depth of six. The differences between the methods were minimal: in accuracy, it was about 0.07. With 100% and 66% of the features, the depth of the tree increased (25 and 19 nodes and nine and six features, respectively). The algorithm tries to exploit all the available information.