## 4 Discussion  
As evidenced in a recent simulation study [16], the presence of highly correlated features can negatively affect the performance of the RFE algorithm. A common approach to deal with this issue is to exclude a priori the highly correlated features before the development of the model, by choosing one representative feature for each group of correlated variables. However, 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, a suboptimal feature selection and model performance. To solve the issues that an a priori feature filtering might bring, in this paper we proposed a new ranking algorithm that handles the highly correlated features within the ranking procedure. The algorithm is a modified version of the RFE-Borda count method in which highly correlated features are grouped during the RFE procedure. This ensures that all the features are considered for model development. Then, if a pair of highly correlated features are selected for the final model, e.g., \(x_{1}\) and \(x_{2}\), the model developer can decide a posteriori which feature to remove, by comparing the multivariate model with \(x_{1}\) vs. the multivariate model with \(x_{2}\), in terms of prediction performance. This would be a better choice than the one made a priori, because it takes into account the presence of all the other variables relevant for the prediction. Moreover, it allows performing variable importance ranking in an unbiased way. The idea of grouping the correlated features while performing the RFE is not totally new. A similar approach, called recursive cluster elimination, was indeed adopted by [PERSON] et al. [19] for selecting significant genes in gene expression studies using the SVM model. [PERSON] et al. showed that the clustering of highly correlated features allowed to improve the final model performance, suggesting that a better feature ranking and feature selection was obtained. However, to the best of our knowledge, the method by [PERSON] et al. was never validated in terms of variable ranking performance. Moreover, an issue of the method by [PERSON] et al. is that, after the ranking of clusters and the selection of the most important ones, all the highly correlated features in the selected clusters are included in the final model, thus maintaining a certain level of redundancy in the model. In this paper, the proposed algorithm was validated on simulated datasets in which the true variable ranking is known. Results showed that the proposed algorithm provides \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**Estimated Coefficient (Standard Error)**} \\ \cline{2-5}  & **Approach 1** & **Approach 2** & **Approach 3** & **Approach 4** \\ \hline age & 0.40 & 0.23 & 0.43 & - \\  & (0.36) & (0.35) & (0.36) & - \\ depriv & 0.38 & 0.40 & 0.40 & 0.36 \\  & (0.20) & (0.20) & (0.20) & (0.20) \\ htn & 0.26 & 0.29 & 0.26 & 0.28 \\  & (1.30) & (0.11) & (0.11) & (0.11) \\ sex & - & - & - & \(-\)0.21 \\ \hline C-index & 0.75 & 0.75 & 0.75 & 0.75 \\
5-fold CV & (0.02) & (0.03) & (0.02) & (0.02) \\ C-index test & 0.74 & 0.74 & 0.74 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(Cont.\)better ranking performance compared to the standard RFE-Borda count method that does not consider the correlation between features. This result was confirmed on 12 different simulation scenarios, in which we varied the noise level on the outcome, the proportion of noise variables in the training set, the number of training set samples, and the fraction of censored data. In all the tested scenarios, the proposed algorithm outperformed the standard RFE-Borda count method, proving its good performance even in challenging scenarios with high noise, small sample sizes, and high censoring fractions.