## 2 Materials and Methods
### Experimental Tests: Age Prediction Using Features of Brain Complexity  
Individual age prediction using neuroimaging data is a popular approach for identifying biomarkers supporting brain health [39]. In this context, biomarkers quantifying brain complexity, including the local gyrification index (IGI) and the fractal dimension (FD) of the cerebral gray and white matter, have been proved to have predictive capabilities in age prediction [39; 40; 41]. In a previous paper, we used two public datasets to show that, among others, our implementation of the fractal dimension, using an automated selection of the fractal scale within which the cerebral cortex manifests the highest statistical self-similarity, yielded the most accurate machine learning models for individual age prediction [40]. Figure 1: Schematic representation of the computation of representative SHAP values. SHAP values of training and test folds are computed separately for each round of the outer CV. Then, SHAP values are averaged over the training folds. This procedure is repeated \(K\) times, and SHAP values for the training and test sets are averaged over the \(R\) repetitions (Image adapted from [42]). To prove the utility of computing the SHAP values in repeated nCV, in this study, we considered two regression tasks and one classification task for age prediction using features of brain complexity extracted from MRI data [40]. In particular, we used the high-resolution public and international T\({}_{1}\)-weighted datasets of healthy children and adolescents (Nathan Kline Institute (NKI)--Rockland Sample Pediatric Multimodal Imaging Test-Retest Sample--NKI2 dataset [43; 44]) and adults (International Consortium for Brain Mapping (ICBM) dataset [45]). Briefly, the NKI2 dataset comprises MRI examinations of 73 healthy pediatric subjects aged 6 to 17 years (43 males and 30 females, age \(11.8\pm 3.1\) years, mean \(\pm\) standard deviation). The ICBM dataset comprises MRI examinations of 86 healthy adult and elderly subjects ranging from 19 to 85 years (41 males and 45 females, age \(44.2\pm 17.1\) years). For classification purposes, we also considered a dichotomous task defined as the prediction of a young group vs. an elder group in the ICBM dataset. The young group consisted of subjects with an age \(\leq\) 30 years (25 subjects--9 males and 16 females, \(22.6\pm 3.3\) years), and the elder group of subjects with an age \(\geq\) 56 years (28 subjects--11 males and 17 females, \(64.9\pm 8.2\) years). The extraction of features of brain complexity from MRI data has been described in detail previously [40]. Briefly, a completely automated cortical reconstruction of each subject's structural \(T_{1}\)-weighted MRI scan was performed by employing the FreeSurfer image analysis suite ([[http://surfer.nnm.mgh.harvard.edu/](http://surfer.nnm.mgh.harvard.edu/)]([http://surfer.nnm.mgh.harvard.edu/](http://surfer.nnm.mgh.harvard.edu/)), accessed on 29 May 2022) [46], a dedicated brain segmentation software program [47; 48; 49; 50; 51]. This includes removal of non-brain tissue using a hybrid watershed/surface deformation procedure, automated Talairach transformation, segmentation of the subcortical white matter and deep gray matter volumetric structures, intensity normalization, tessellation of the gray/white matter boundary, automated topology correction [53], and surface deformation following intensity gradients to optimally place the gray/white and gray/cerebrospinal fluid borders at the location where the greatest shift in intensity defines the transition to the other tissue class. The local cortical gyrification IGI was computed following a surface-based approach [54]. Briefly, in each vertex, a spherical region of interest is delineated on an outer envelope (\(ROI_{O}\)) that tightly wraps the pial cortical surface, and its corresponding region of interest on the pial cortical surface (\(ROI_{P}\)) is identified using a matching algorithm based on geodesic constraints.