# Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
## 3 Results
### Comparative Performance between AS and Cmax
#### 3.2.4 Artificial Neural Networks  
The analysis continued with the development of two ANNs where the Tmax and AS were considered as continuous response variables. Figure 7 shows the variable importance results for Tmax (Figure 7a) and AS (Figure 7b). The ANN model for Tmax exhibited a relative error of 0.002 for the training set and 0.003 for the test set. Similarly, with the ANN for AS, these relative error values were found to be 0.001 for the training set and 0.004 for the test set. These results suggest a high level of accuracy for both models.  
Figure 6: Hierarchical clustering of the pharmacokinetic variables of the four remaining drugs using single linkage. Each plot shows the dendrogram for (**a**) nintedanib, (**b**) methylphenidate, (**c**) nitrofurantoin, and (**d**) theophylline.  
In Figure 7a, it is obvious that AS is the most important parameter for predicting Tmax, followed closely by Cmax, which also holds significance in predicting Tmax. It is worth noting that AUC and AUCinf exhibit nearly zero importance in predicting Tmax. Meanwhile, Cmax holds more importance in predicting AS, with Tmax being the second most important parameter, having roughly half the importance of Cmax.  
Similar ANN models (for Tmax and AS) were also built for the other four drugs of the study. For space restriction reasons, the variable importance contribution plots for the four drugs and the separate two PK parameters (AS and Tmax) are stacked together in Figure 8. Again, the ANN analyses for all drugs also demonstrated high accuracy, with relative error values for each set ranging from 0.001 to 0.039. It should be underlined that AS was the most important parameter for predicting Tmax in every analysis for each drug. On the contrary, Cmax served as the second or third important PK parameter, indicating the low relationship of Cmax with the kinetic character of Tmax.  
Figure 8: Variable importance scores for the artificial neural network models developed for the remaining four drugs of the study. The panels correspond to the models for (**a**) nintedanib, (**b**) methylphenidate, (**c**) nitrofurantoin, and (**d**) theophylline. The left part of each panel shows the contribution of the pharmacokinetic parameters to Tmax, while the right shows the contribution to AS (both measured on a numerical scale).  
Figure 7: Variable importance scores for two artificial neural network models developed for lisdexamfetamine. The plots show the contribution of the pharmacokinetic parameters to Tmax (**a**) and AS (**b**). Both Tmax and AS were measured on a numerical scale.  
To further study the contribution of all PK parameters to Tmax, the latter was transformed into ordinal scale (see the RF analysis). A new ANN model was developed for lisdexamfetamine, and the variable contribution of the remaining parameters was estimated. Figure 9 shows the variable contribution to Tmax (when considered in the ordinal scale) in the case of lisdexamfetamine. The results are like those mentioned above when utilizing Tmax on a continuous scale. It should be underlined that AS again was found to be the most important factor for predicting Tmax, even if the latter was considered as an ordinal variable.  
Additional results, when Tmax is converted to an ordinal variable, are shown in Figure A3 in the case of nintedanib, methylphenidate, nitrofurantoin, and theophylline. The primary factor to predict AS varied from drug to drug, with either Tmax followed by Cmax or Cmax followed by Tmax being the most important factors.