## 2 Materials and Methods
### Validation of the QSAR-MLR Model  
The obtained model must be carefully evaluated and rigorously validated to ensure its reliability. QSARINS provides several tools to assess whether the model complies with the standards established by the Organization for Economic Cooperation and Development (OECD) for the development, validation, acceptance, and use of QSAR models. Adhering to these guidelines enhances confidence in the predictive reliability of the model. According to OECD principles, a valid QSAR-MLR model must satisfy the following criteria [38,39]:  
1. A defined endpoint;
2. An unambiguous algorithm;
3. A defined domain of applicability;
4. Appropriate measures of goodness-of-fit, robustness, and predictability;
5. A mechanistic interpretation, if possible.  
To comply with the 1 st principle, the dissociation equilibrium constant (Kd) between the molecules and the DAT was used as the endpoint. For compliance with the 2 nd principle, molecular descriptors were calculated using Dragon software, while the QSARINS platform was employed to develop the MLR model as we explained in the previous section. This algorithm allows us to correlate the chemical structure descriptors and their binding affinity for DAT.  
The definition of the applicability domain (AD) of the model is considered a critical aspect in chemometric studies and is the 3 rd principle. Only predictions for compounds that fall within the AD may be considered reliable, but not the extrapolations of the models, even if they show robustness and significance. In order to define the AD of the model, the Williams graph/plot was used, so that reliable predictions of the model have leverage values lower than the critical leverage, ranging within \(\pm 3\) standard deviations [40]. Compounds falling outside these ranges were considered outliers. In addition, the Insubria graph (generated by QSARINS) was utilized to assess further the reliability of predictions. This graphical tool is particularly useful for visualizing the position of molecules with unknown experimental responses and comparing them with those in the prediction set, helping to evaluate the confidence in their predicted values.  
Following the 4 th principle, the goodness of the fit was evaluated using the coefficient of determination R2 and its modified form R2 adj; the latter accounts for the number of descriptors in the model and penalizes the inclusion of non-informative variables. To evaluate the robustness of the model, several internal validation strategies were employed. First,  
Figure 2: Molecular structures of compounds used in the prediction set.  
the Q\({}^{2}\)_LOO metric was used, applying _Leave-One-Out_ (_LOO_) cross-validation, where each compound in the dataset is sequentially excluded, and the model is recalculated to predict the excluded compound. Additionally, QSARINS provides a more rigorous validation approach, _Leave-Many-Out_ (_LMO_) cross-validation, which was also applied. In this method, between 5% and 30% of the dataset was randomly excluded in each iteration, allowing us to examine the model's stability and predictive behavior under more challenging conditions. To ensure that the model is not the result of a casual correlation, a randomization test (_Y-scrambling_) was performed [41]. In this procedure, the response values (K\({}_{\text{d}}\)) are randomly shuffled, breaking any real association with the molecular descriptors. A valid model is expected to show a significant drop in performance under these conditions, confirming that the original model's predictive power is not because of chance.  
To further confirm the predictive capability of the model, an external validation was carried out. The external set included several widely used reference radiopharmaceuticals, which were excluded from model training and used solely to assess predictability. The affinity values of these compounds (see Figure 2) were predicted using the final MLR model equation, providing an independent evaluation of the model's generalization ability.