## 4 Discussion
In this context, the weighted average slope (AS\({}_{\text{w}}\)) (Equation (9)) can be defined by appropriately modifying AS (i.e., Equation (2)):  
\[\text{AS}_{\text{w}}=\frac{\sum_{\text{i}=1}^{\text{n}-1}\left(\frac{\text{T max}-\text{t}}{\text{Tmax}}\times\text{slope}_{\text{i}}\right)}{\text{n}-1}= \frac{\sum_{\text{i}=1}^{\text{n}-1}\left(\frac{\text{Tmax}-\text{t}}{\text{ Tmax}}\times\frac{\text{C}_{\text{i}+1}-\text{C}_{\text{i}}}{\text{t}_{ \text{i}+1}-\text{t}_{\text{i}}}\right)}}{\text{n}-1} \tag{9}\]  
The unitless weighting factor (Tmax \(-\) T\({}_{\text{i}}\))/Tmax places more weight on earlier time points where the effect of absorption is predominant, and therefore AS\({}_{\text{w}}\) can express more purely the absorption process. As in the case of AS, the estimation of AS\({}_{\text{w}}\) is model-independent, and no assumptions are required for its calculation. Even though more studies are required to examine all properties of AS and AS\({}_{\text{w}}\), it is a regulatory criterion to select between AS and AS\({}_{\text{w}}\); namely, if we need a metric placing emphasis on all points up to Tmax (i.e., AS) or a metric (i.e., AS\({}_{\text{w}}\)) that is influenced more by the early time points, which are more indicative of absorption. The current study used simulated data to investigate different absorption rates (slow, typical, and fast) and sampling schemes (sparse, typical, and dense). A special emphasis was placed on the sampling schedule (Table 2) since the appropriate identification of Tmax depends on the appropriateness of the sampling schedule around Cmax. Even though the utilized sampling scheme is generally termed \"sparse\", \"typical\", and \"dense\", they were different among the conditions tested; in other words, they were appropriately set to fit in the absorption kinetic scenario (see Table 2). It should be noted that, for the sake of this research, the donepezil population PK model developed in the previous study [23] was utilized to generate several two \(\times\) two crossover simulated BE datasets. The use of simulated datasets allowed us to verify earlier findings and investigate the influence of absorption rate on each metric. This method has the advantage of preserving all donepezil PK parameters at the same level as the original dataset while only the absorption rate constant is changed. As a result, the impact of the absorption rate could be identified and analyzed in the machine learning analysis. Setting the absorption rate constant at \"0.5\(\times\)\" and \"2\(\times\)\" of the initial estimate is considered a reasonable choice for slower and quicker absorption, respectively (Figure 5). Slower or quicker absorption kinetics than those described above would not provide any advantage or alter the results. Furthermore, the use of simulated conditions for the actual data (i.e., the \"1\(\times\)\" scenario) allowed the findings acquired from the original dataset to be validated. It is worth mentioning that the random forest analysis implemented in this study was carried out in a way to explore the PK parameters' contribution to Tmax, namely, in the opposite way of what was done in the previous study. Overall, in this study, AS is introduced as a new metric for characterizing the absorption rate. AS has several advantages over the traditionally used Cmax and the previously proposed Cmax/Tmax. These advantages are briefly outlined below:  
(a) AS satisfies the fundamental theoretical reason for considering a parameter as a measure of absorption rate; namely, AS has units of _concentration/time_ in contrast to all other measures proposed in the literature, which have meaningless units. (b) The machine learning methods applied in this study showed that AS succeeds in reflecting the \"absorption rate\", while Cmax and other existing metrics fail. (c) AS can be estimated quite simply using a model-independent approach (Equation (2)), as in the case of AUCt, without any assumptions.