## 1 Introduction
Indeed, if two highly correlated and highly predictive features, \(x_{1}\) and \(x_{2}\), are present in the set of candidate variables, there is a risk that the rank of the two correlated features, which carry a similar information, is underestimated. In fact, it may happen that, in some of the training set resamplings, \(x_{1}\) gets a high importance score, while \(x_{2}\), redundant with respect to \(x_{1}\), gets a low importance score, and the exact opposite might occur (i.e., the importance score is high for \(x_{2}\) and low for \(x_{1}\)) on other occasions. In such a situation, the importance score would be underestimated for both \(x_{1}\) and \(x_{2}\), even if the two features independently bring an important information. The difficulty of performing variable ranking by RFE in presence of highly correlated features was pointed out by the study of [PERSON] et al. [16]. The authors tested in silico the variable ranking obtained by random forest and RFE. They empirically observed that, when highly correlated features were present in the dataset, the importance score of important predictors was poorly estimated by the RFE algorithm. One possible solution to this issue, often adopted in the literature, could be to consider only one representative feature for each group of correlated variables in the candidate list of predictors [17]. If there are no practical reasons on which feature to choose, a possibly objective filtering criterion should be adopted. Commonly, the variable that best explains the outcome in a univariate analysis is selected. However, the variable best performing in the univariate analysis could not be the one best performing in the multivariate analysis. In fact, an a priori choice without considering the joint contribution to outcome prediction of all the candidate predictors can result in a suboptimal feature ranking and thus in suboptimal feature selection and model performance. Moreover, even in the case the chosen feature performs optimally in a multivariate framework, it could poorly generalize in a different dataset. Another option could be to apply a technique for decorrelating the input features, such as the principal component analysis [18]. However, such techniques are suitable to perform dimensionality reduction, not to perform variable ranking or feature selection, and they provide an output set of new features, each obtained from a combination of the original features, whose interpretation is not straightforward. A different approach was proposed in [PERSON] et al. for selecting significant genes in gene expression studies [19]. To deal with highly correlated genes, the authors first identified clusters of highly correlated genes and then applied RFE to rank the identified clusters and select the most important ones for the final model. The classification accuracy of the model obtained with the recursive cluster elimination was higher than that obtained with standard RFE. This suggests that considering the highly correlated features as a group while performing RFE might enhance the variable ranking accuracy. The aim of this work is to propose a new variable ranking method that is able to deal with the presence of highly correlated features and to preserve their interpretation. To offer more detail, the proposed method is a modified version of the RFE-Borda count method that takes into account the correlation between numerical features while performing the ranking, by grouping highly correlated features, as carried out in [19]. The proposed approach is validated on simulated datasets, in which the true variable ranking is known, and compared to the standard RFE-Borda count method that does not consider the correlation between features. After the in-silico validation, the proposed raking method is applied to a case study with real data concerning the development of a predictive model of type 2 diabetes (T2D) onset.