## 5 Conclusions  
The concept of \"average slope\" is introduced in this study as a metric to express the absorption rate that can be used as a primary endpoint in BE studies. Two machine learning methods, principal component analysis and random forest models, were applied to actual and simulated bioequivalence data in order to uncover the properties of AS and show that AS expresses the appropriate properties for characterizing absorption rate. Several absorption kinetics (slow, typical, fast) and sampling schemes (sparse, typical, dense) were simulated in order to investigate many different conditions and their impact on the performance of all pharmacokinetic parameters. The two machine learning algorithms, applied to all these scenarios, proved the desired properties of AS to characterize absorption rate while showing the non-desired performances of other metrics currently used (i.e., Cmax) or have been proposed in the literature (e.g., Cmax/AUC, AUCCp). AS meets the fundamental theoretical reason for adopting a parameter as a measure of absorption rate; notably, AS has _concentration/time_ units, as opposed to all other measures offered in the literature, which have meaningless units. This study also provides a model-independent estimation method for AS, as well as a theoretical justification for its suitability to express absorption rate. The estimation of AS does not require any assumptions, models, or transformations and is as simple as that of AUCT, which is widely used in pharmacokinetics and bioequivalence studies. In addition, a modified version of AS, the so-termed weighted AS, is introduced and can be used to place emphasis on early time points, where the C-t profile describes more clearly the absorption process. Overall, the modern machine learning technique, used within pharmacokinetics and bioequivalence assessment, enabled the exploration of an old problem and the provision of a solution. This research received no external funding. Not applicable. The author would like to thank Verisfield UK Ltd. for providing the C-t data used in this computational study. The author declares no conflict of interest. Figure 13: Principal component analysis for the pharmacokinetic parameters estimated from the simulated bioequivalence studies when a typical sampling schedule (see Table 2) was utilized. The results refer to the three simulated conditions of slow 0.5\(\times\) (**a**), typical 1\(\times\) (**b**), and fast 2\(\times\) absorption (**c**). The terms 0.5\(\times\), 1\(\times\), and 2\(\times\) refer to the number of times the absorption rate constant used in simulations is greater or less than the one observed in actual data. Left panel: Biplot of the two principal components displaying the individual scores and the loadings (blue lines). Right panel: Loading values in the case of the first and second principal components (PC1 and PC2). A description of the pharmacokinetic parameters is provided in Table 1.  
**Figure A4. ** Principal component analysis for the pharmacokinetic parameters estimated from the simulated bioequivalence studies when a dense sampling schedule (see Table 2) was utilized. The results refer to the three simulated conditions of slow 0.5\(\times\) (**a**), typical 1\(\times\) (**b**), and fast 2\(\times\) absorption (**c**). The terms 0.5\(\times\), 1\(\times\), and 2\(\times\) refer to the number of times the absorption rate constant used in simulations is greater or less than the one observed in actual data. Left panel: Biplot of the two principal components displaying the individual scores and the loadings (blue lines). Right panel: Loading values in the case of the first and second principal components (PC1 and PC2). A description of the pharmacokinetic parameters is provided in Table 1.  
**Table A1. ** Median and quartile values of the Tmax estimates. (A) The upper panel shows the median Tmax values for the calculation of partial AUC (i.e., AUCp) in the case of simulated datasets referring to slow, typical, and fast absorption.