## 4 Discussion  
The purpose of this study was to introduce \"average slope\" as a new metric characterizing the \"rate\" of absorption and explore its properties compared to other metrics using ML approaches. The advantages of using AS, as an absorption metric are proven through a stepwise procedure of applying machine learning approaches. In order to tackle  
Figure 8: Variable importance scores and confusion matrices, in the case of simulated data, using Tmax as the response variable. The three separate random forest models developed correspond to sparse (**a**), typical (**b**), and dense (**c**) sampling schemes. The descriptors used for random forest models refer to the average slope (AS) ratio and other pharmacokinetic parameters listed in Table 1. The quartiles of the Tmax distribution were used to define its four categories. the challenge of defining a new absorption rate measure, this study exploits tools from the fields of machine learning and population pharmacokinetic modeling. Initially, the analysis was performed on actual data from a BE study of donepezil in 26 healthy volunteers. Additionally, using a previously developed population pharmacokinetic model [23], simulated two \(\times\) two crossover BE datasets were generated for combinations of three sampling schemes (sparse, typical, and dense) with different absorption kinetics (slow, typical, and fast). This way of analysis allowed exploring the properties of the newly proposed parameter (average slope) along with the other PK parameters under several scenarios. The study path was planned to be similar to a \"screening process\", with each exploration stage revealing some aspects of the PK metrics, allowing the optimal absorption metric to be determined gradually. The scenarios provided a progressive strategy to exclude PK parameters from their usage as absorption rate measures. A summarized view of the main findings is shown in Table 4. The application of PCA to the actual data allowed the identification of AS (followed by Cmax and Tmax) as the most desired behavior because it performs almost oppositely to Tmax (Figure 2). This attribute is desired since it shows that AS reflects the kinetic character of absorption; as the AS increases, Tmax occurs at earlier time points. Based on the PCA results, other PK metrics (like AUCp and Cmax/AUC) could probably reflect the kinetic behavior, but to a lesser extent. However, according to the findings from the RF model (Figure 4), it became obvious that Cmax/AUC, which has been proposed as a possible indirect measure of absorption, contributes to a low extent to Tmax. In the same RF model, AUCp appears to exert a relatively high contribution, and it is the second most important after AS (or Cmax/Tmax). Thus, the initial application of the two machine learning techniques to the actual BE data filtered out the PK metrics for expressing the absorption rate. Up to this point, the potential PK measures could be: primarily AS (or Cmax/Tmax) and secondarily AUCp. All other parameters should be omitted since they did not find a way to express the desired properties. The next step was to use simulated data to look into more possible situations. To simulate situations with different absorption kinetics (slow, typical, fast) and sampling procedures (sparse, typical, dense), a population pharmacokinetic model from a previous study was used [23]. For the case of different absorption kinetics, all donepezil parameters