## 3 Results and Discussions

Table 2: Summary of statistical quality of the linear mt-QSAR models (L01-L08) developed using LDA coupled with different feature selection (FS) techniques. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Model Equation**} & \multicolumn{2}{c}{**Sub-Training**} & \multicolumn{1}{c}{**Test**} & \multicolumn{1}{c}{**Validation**} \\ \hline \(\text{Tox}_{j}=\) & \(+1.917\,-\,3.148\,\Delta(\text{Ms})_{stt}\) & TP: 316, TN: 256, & TP: 64, TN: 82, & TP: 120, TN:151, \\  & \(-1.426\,\Delta(\text{MATSY})_{stt}\) & FP: 37, FN: 32, & FP: 8, FN: 7, & FP: 13, FN:64, \\  & \(+1.597\,\Delta(\text{MATSY})_{stt}\) & Se: 90.80, & Se: 90.14, & Se: 65.22, \\  & \(-3.342\,\Delta(\text{C}\)=(\text{O})\(\text{-}[\text{N},\text{aromatic attach}])_{stt}\) & Sp: 87.37, & Sp: 91.11, & Sp: 92.07, \\  & \(+5.001\,\Delta(\text{E1s})_{stt}\) + \(1.464\,\Delta(\text{GATS3m})_{sg}\) & Acc: 89.23, & Acc: 90.68, & Acc: 77.87, \\  & \(+7.486\,\Delta(\text{Dm})_{te}\) + \(0.065\,\Delta(\text{XLOGP2})_{stt}\) & MCC: 0.783, & MCC: 0.811, & MCC: 0.589, \\  & \(-19.523\,\Delta(\text{De})_{co}\) + \(6.573\,\Delta(\text{MATS1e})_{te}\) & AUROC: 0.891 & AUROC: 0.906 & AUROC: 0.784 \\ \hline \hline \end{tabular}  
* From Table 3, it is evident that the model achieves an overall accuracy of approximately 86%, correctly predicting 989 data points. However, the external predictivity towards the validation set remains only moderate. Therefore, to ensure that L08 represents the optimal mt-QSTR model, it was crucial to investigate alternative model development strategies. This involved exploring non-linear modeling approaches, employing the five machine learning techniques (\(k\)NN, RF, SVC, MLP, and GB) along with the six feature selection algorithms (descriptors from L08 model, all descriptors, RFE, RF-importance, SFS, and GA-\(k\)NN) as detailed in the previous section.  
In so doing, 30 non-linear models were developed, and rigorous hyperparameter optimization was performed for each to identify the most suitable model parameters. The performance metrics for these models are summarized in Table 4. While six non-linear models demonstrated superior predictive performance compared to the best linear model (L08) on the sub-training and test sets, this advantage did not translate to improved performance on the independent validation set. This observation suggests a potential for overfitting within the non-linear models, hindering their ability to generalize beyond the training data and thus limiting their ability to surpass the predictive accuracy of the linear model.  
\end{table} 
Table 3: Detailed statistical results of the linear mt-QSTR model L08. As a final resort, we relied on the consensus model generation technique to check if combining predictions from multiple models would improve predictivity towards the validation set. For consensus prediction, we selected the most predictive linear model, L08, and four non-linear models: NL06, NL10, NL16, and NL30 (cf. Table 4), which demonstrated satisfactory predictivity (MCC > 0.5) towards the validation set. Although four consensus models achieved MCC > 0.55 for the validation set (see Table S3), none surpassed the performance of L08 in terms of external predictivity towards the validation set. Therefore, the linear model L08 stood out as the most predictive mt-QSTR model generated for tackling the environmental toxicity of PPCPs. Further support for the model's suitability is provided by the ROC plot (see Figure 2), clearly indicating that the L08 model is not random but a statistically significant classifier. Additionally, inspecting the correlation matrix of its deviation descriptors confirmed that high inter-collinearity (\(R\) > 0.95) did not exist among them. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**FS Technique**} & \multirow{2}{*}{ \begin{tabular}{c} **Machine** \\ **Learning** \\ \end{tabular}