## 4 Discussion
Furthermore, on the same training set we performed a cluster analysis, in order to identify the positive or negative contribution of different feature subsets for classification purposes. The cluster analysis highlighted the correlation among some feature subsets and the realization of either false-positive or false-negative cases. Indeed, we observed that false negatives were afferent to features such as small T1b and T1c tumors, low grading (G1 or G2), negative kief7 and absent in situ component; instead, false positives were related to features as T1c and T2 tumors, kief7 positive, medium-high grading G3 or G2 and present during the in situ component. Finally, we observed that the performance of the best Logistic Regression model, as well as the performances of the other ones, were lower on the hold-out test set. Even though the best model in terms of accuracy and specificity resulted the RF classifier on a subset of eight features, the only model with a sensitivity still greater than 68% was the Logistic Regression algorithm, which had the same result as the best model of the hold-out training set. The state-of-the-art model is characterized by many works, which propose non-sentinel lymph nodes status predictive models based on features of different nature [33; 34; 35; 36; 37]. On the contrary, there are a low number of studies whose aim was the development of a sentinel lymph nodes status predictive model through the analysis of histological features [20; 38; 39; 40; 41]. Thus far, the nomogram developed by the researchers of Memorial Sloan-Kettering Cancer Center (MSKCC) (a, b, c) is the most widely used model to predict the likelihood of SLN metastasis. The baseline model (a) reached an AUC value of 75.4%. In subsequent validation studies, comparable performances were achieved (b, c). However, these models were evaluated on cohorts of non-clinically negative patients and therefore different from the sample object of our study. The model developed in [41] for prediction of sentinel lymph nodes metastasis reached an AUC value equal to 88.3% by considering some histological features, such as tumor size, and lymph vascular invasion in ER-positive and HER2-negative (ER+/HER2\(-\)), but also genetic ones. In our previous work [20], we evaluated the usefulness of the CancerMath tool to predict the sentinel lymph node status for clinically negative patients referred to our institute. In this validation study, by using tumor size, age, histologic type, grading, expression of estrogen receptor, and progesterone receptor ki67 and HER2 on the independent test set, the model showed an accuracy of 53.8%, which is much lower than the accuracy value achieved thanks to the analysis exposed here. The current work differs from the other mentioned research studies because of the use of a machine learning approach for the analysis. Although the model can be further optimized by evaluating other feature selection techniques or classification algorithms on a very extensive experimental database, the only histological features did not allow us to develop a support instrument suitable for actual clinical application. What emerges, and which is important to underline to a public of biomedical data scientists or clinician with a transactional interest field, is that the maximum informative power contained in the only characteristics considered for the prediction of the sentinel lymph node status does not exceed 62-63% on the independent test. For this reason, encouraged by recent studies with improved results in the prediction of the lymph node metastasis probability thanks to the joint use of histopathologic and radiomic features [6; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54], in our future works we will also involve radiomic features extracted from first-level radiological examinations, such as ultrasound and mammography.