## 4 Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Step** & **Action** & **Order of Preference** & **Parameters with Non-Desired** \\  & & & **Characteristics** \\ \hline \hline \multicolumn{4}{c}{Actual dataset} \\ \hline
1 & PCA & AS or Cmax/Tmax \textgreater{} Cmax/AUCt \textgreater{} AUCp or Cavg & Cmax, Cmax/Cavg, lambda, AUCt, AUCinf \\ \hline
2 & RF & AS or Cmax/Tmax \textgreater{} AUCp & AUCt, Cmax/AUC, Cmax, lambda \\ \hline
3 & Overall & Best performance: & \\  & & AS or Cmax/Tmax and afterwards AUCp & \\ \hline \multicolumn{4}{c}{Simulated datasets} \\ \hline
4 & PCA & AS or Cmax/Tmax \textgreater{} Cmax/AUC & AUCt, AUCinf, Cmax, AUCp, lambda \\ \hline
5 & RF & AS or Cmax/Tmax & AUCt, Cmax, AUCp, Cmax/AUC, lambda \\ \hline
6 & Overall & Best performance: & \\  & & AS or Cmax/Tmax & \\ \hline \multicolumn{4}{c}{Overall findings from steps 1–3 and 4–6} \\ \hline \hline
7 & Overall from the entire & Best performance: & \\  & analysis & AS or Cmax/Tmax & All other parameters tested \\ \hline \hline \end{tabular} Key: PCA, Principal Component Analysis; RF, Random Forest.  
\end{table} 
Table 4: The stepwise process of analysis allowed screening the pharmacokinetic parameters with the desired behavior. Within each step of the analysis, the pharmacokinetic parameters are listed in the order of preference (\(>\)). (as well as the estimated between- and within-variabilities) were kept identical to those found from the population pharmacokinetic analysis, while only the absorption rate constant changed. The latter aimed to isolate the impact of the absorption rate from the other aspects of the PK performance (e.g., distribution and elimination properties). Furthermore, the use of sampling schemes with different sampling frequencies (Table 2) allowed us to investigate how sensitive to errors (due to the sampling schedule) the calculations of the PK parameters are, particularly for Cmax/Tmax, Tmax, and Cmax, which are based on a single time point measurement. Since for ML, a large number of cases is preferred, the simulated number of subjects was set equal to 1000 per study. Application of PCA to the simulated data verified the findings observed above in the case of actual data. The opposite performance of AS (or Cmax/Tmax) compared to Tmax was consistent for all the different scenarios studied. For AUCp, a variable performance was observed; in some cases, such as the simulated \"typical\" case (Figure 6b), the results were similar to those from the actual data, and AUCp showed a desired performance. However, the behavior of AUCp was not desired for the cases of sparse (Figure 6a) or dense (Figure 6c) sampling schemes. On the contrary, the ratio Cmax/AUC expressed a nice performance in all these scenarios. In the subsequent step, the application of RF models to the simulated data further clarified these findings. In particular, it was shown that the major contributor to Tmax is always AS (or Cmax/Tmax). The next most important contributors (but with a much lower contribution compared to AS or Cmax/Tmax) were either Cmax or Cmax/AUC. However, Cmax/AUC showed low importance for Tmax when sparse sampling schemes were utilized. Besides, Cmax has already been excluded from the PCA analysis, whether in the actual or simulated data (Table 4). It is also worth noting that the partial AUC (i.e., AUCp) until the median Tmax of R, which is currently used as an early exposure metric in regulatory guidelines [2; 3], fails to characterize the kinetic manner of absorption. The latter can be derived from the PCA analysis applied to the simulated data. The moderate-to-low contribution of AUCp to Tmax observed in the RF models further adds to its undesirable character. Overall, it appears that only AS (or Cmax/Tmax) exhibits the desired performance in all cases for either the PCA or RF models (Table 4). AS and Cmax/Tmax appear superior to all other PK parameters in terms of reflecting absorption rate. For \"slow\" absorption kinetics (Figures A3a and A4a), AS shows slightly better behavior compared to Cmax/Tmax.