## 3 Results
### Relationships among the PK Variables
#### 3.1.2 Random Forest Analysis  
To determine the contribution of PK characteristics to each potential absorption rate metric (Cmax, Cmax/AUC, and Cmax/Tmax), a random forest classifier was used. Before applying RF, it was necessary to have the response variable in the ordinal scale. Thus, the continuous scale variables Cmax, Cmax/AUC, and Cmax/Tmax were transformed into ordinal scales. The most rationale approach was to split each variable into its quartiles. Then, four groups were initially created with an equal number of observations within each one of them, allowing balanced representation of all attributes (very high, high, medium, and low value of the variable). Other groupings, with two-, three-, and five- classes were also investigated. The categorization results obtained from the 4-group sorting were at least as good as those obtained from the 3-group. Other types (e.g., two or five groups) resulted in inferior categorization. Thus, the 4-group classification was finally selected. The quartile values of the three variables (Cmax, Cmax/AUC, and Cmax/Tmax) are listed in Table 1.  
Application of the RF algorithm to the three response variables separately is shown in Figure 3. The variable importance plot for Cmax (Figure 3a) reveals that AUC (50.1%) contributes mostly to Cmax values, followed by lambda (34.6%), and lastly by the kinetic term Tmax (15.3%). A similar pattern was observed for Cmax/AUC (Figure 3b). However, a completely different performance was detected for Cmax/Tmax (Figure 3c), where Tmax contributes the most (36.5%), followed by AUC (34.1%) and lambda (29.4%). To express how many of the predictions of a random forest classifier were correct and when they were incorrect (i.e., when the RF classifier becomes \"confused\"), a confusion matrix was created for each case. In all cases, the developed RF models were able to correctly classify more than 70% of observations (74.2%, 72.6%, 76.1% for Cmax, Cmax/AUC, and Cmax/Tmax, respectively), which shows that the models are good at making predictions. The confusion matrix plots are not shown due to space limitations.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Correlation Coefficient**} \\ \hline  & **AUCinf** & **AUC** & **Cmax** & **Tmax** & **Cmax/AUC** & **Cmax/Tmax** & **Lambda** \\ \hline AUCinf & 1.000 & 0.986 & 0.588 & 0.106 & \(-\)0.432 & 0.209 & \(-\)0.478 \\ \hline AUC & 0.986 & 1.000 & 0.632 & 0.114 & \(-\)0.425 & 0.236 & \(-\)0.375 \\ \hline Cmax & 0.588 & 0.632 & 1.000 & \(-\)0.142 & 0.38 & 0.617 & \(-\)Figure 14 presents additional results where both AUC and AUCinf are analyzed (i.e., not only AUC as done before) for their contributions to Cmax, Cmax/AUC, and Cmax/Tmax. Again, in this case, similar results were obtained. AUC and AUCinf were the major contributors to Cmax, accounting together for 67.4%, while the contribution of Tmax was only 9.93% (Figure 14a). A similar pattern was also observed for Cmax/AUC (Figure 14b). However, the performance of Cmax/Tmax (Figure 14c) was radically different, compared to the two previous PK metrics, with Tmax contributing the most (38.1%) and the other three factors contributing approximately equally (around 20% each).