## 2 Methods
### Associations Between Brain Age Gap and Psychometrics  
In the final analysis stage, we examined correlations between brain age gap (BAG) estimates and cognitive performance. We applied behavioural partial least squares (PLS), a multivariate technique commonly used in neuroimaging to assess brain-behaviour relationships [40; 41; 42; 43]. This analysis was conducted separately for each of the two BAG profiles and each cognitive test, resulting in 16 Behavioural PLS analyses (2 BAG profiles \(\times\) 8 cognitive tests).  
Behavioural PLS decomposed the covariance between network-specific BAG estimates and cognitive scores into latent variables (LVs) using singular value decomposition (SVD). Each LV captured a distinct pattern of covariance between brain age gaps and cognitive performance across participants.  
To assess the significance of the overall brain-cognition correlations, we performed a permutation test wherein we randomly shuffled data across participants and tested for stability of correlations based on the original data. This produced a vector of overall correlations, with dimensionality determined by the number of cognitive scores. We performed a bootstrap test to evaluate the robustness of individual networks' contributions to the identified overall correlations. In each bootstrap iteration, we resampled participants with replacements while preserving the correspondence between each participant's BAG and cognitive scores. Behavioural PLS then computed bootstrap ratio values, defined as the ratio of original network saliences to the standard error of the bootstrap distribution. These values are equivalent to z-scores. In our study, we used the terms of bootstrap ratio values and z-scores interchangeably. We applied 10,000 iterations for both permutation and bootstrap tests and focused on the first LV, which accounted for the largest proportion of variance in the brain-cognition covariances.  
For each PLS analysis, we reported three key results: (i) a vector of overall correlations, with each value representing the association between BAG and a cognitive variable within a given test; (ii) a \(p\)-value assessing the statistical significance of these correlations across the entire dataset; and (iii) a vector of network-specific z-scores, indicating the robustness of networks' contribution to the observed brain-cognition overall correlations, as defined in (i). Larger absolute z-scores reflected more potent effects, and we focused on networks with z-scores greater than \(\pm 2\), approximately corresponding to a 95% confidence interval.  
We note that PLS analysis yields several metrics for interpreting brain-behaviour relationships. First, it provides a global significance value for each identified latent variable (LV), which represents the strength of the overall multivariate correlation between the combined imaging features and behavioural scores. The individual correlation values between the cognitive scores and the LV's brain scores indicate the effect size concerning specific behavioural outcomes. For the imaging data, the contribution of individual fMRI networks to the LV is quantified using Z-scores, which are computed as bootstrap ratio values. These ratios are derived by dividing the original salience of each network by the standard deviation of its bootstrap distribution, thereby providing a measure of effect size for each network's involvement in the identified pattern.  
Interpretation of individual correlations between BAG and cognitive scores required considering overall correlations and z-scores together. Positive brain-cognition associations were reflected either by both a positive overall correlation and z-score or by both values being negative. Conversely, negative brain-cognition associations occurred when one metric (correlation or z-score) was positive and the other was negative.