## 2 Materials and Methods
### Machine Learning  
A supervised ML approach was employed to predict the likelihood of developing breast cancer based on the risk factors collected. These risk factors, serving as features, were used to train several ML classifiers, including decision tree, support vector machine (SVM), naive Bayes, ECOC, discriminant analysis, linear models, ensemble of trees, artificial neural networks (ANNs), and k-nearest neighbors (KNNs). Among these, the ensemble of decision trees emerged as the best performer. This model was chosen not only for its superior performance but also for its ability to handle missing values effectively and to combine multiple weak learners into a stronger predictive model, which is particularly advantageous given the nature of the dataset. The training process used a 10-fold cross-validation scheme to partition the data into training and validation sets. To optimize the performance of the best model, we employed the MATLAB automatic hyperparameter optimization feature. This process automatically tuned the parameters of the ensemble of decision tree models to find the optimal configuration for our dataset. The optimization procedure selected the AdaBoostM1 method, configured with 11 as the number of trees and a learning rate of 0.42. The number of trees and the learning rate were determined as the most effective parameters to balance the trade-off between model complexity and performance. The ensemble method, AdaBoost, enhanced the performance of these decision trees by iteratively focusing on difficult-to-classify instances, thus improving the overall accuracy of the model. AdaBoost's capability to combine weak learners into a strongclassifier and its inherent robustness against overfitting made it the preferred choice for this study. For completeness, it is important to mention that other classifiers, including artificial neural networks with missing data imputation, were also used, but their results were inferior. To evaluate the classifier performance and to determine the optimal threshold for predictions, the receiver operating characteristic (ROC) curve was employed. It plots the true positive rate (sensitivity) on the Y-axis against the false positive rate (1--specificity) on the X-axis across different threshold values. The curve provides a comprehensive overview of the trade-off between sensitivity and specificity at various thresholds. Based on the optimal working point of the ROC curve, a binary classifier was derived. The ROC curve was utilized to assess the classifier performance with the area under the curve (AUC) figure of merit and to determine an \"optimal\" prediction threshold that maximizes the accuracy. At this optimal threshold, the sensitivity, specificity, and accuracy of the classifier were calculated. The sensitivity, representing the true positive rate, and specificity, representing the true negative rate, were derived directly from the confusion matrix at this threshold. The accuracy was computed as the proportion of true results (both true positives and true negatives) relative to the total number of cases examined. To further assess the performance of the model, particularly in the context of imbalanced classes, the precision-recall (PR) curve was employed. The PR curve plots the precision (the proportion of true positive results relative to all positive predictions) against the recall (the proportion of true positive results relative to all actual positives) at various threshold levels. The F1 score, which is the harmonic mean of the precision and recall, was calculated at specific thresholds to provide a balanced measure of the model's accuracy. The F1 score offers insight into how well the model balances the trade-off between precision and recall, especially when the goal is to minimize both false positives and false negatives. To ensure a robust and unbiased classification, the features were normalized to a range of 0-1 using min-max normalization on the training dataset [43; 44; 45]. The same normalization parameters were then applied to the validation set samples.