# Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
## 4 Discussion
This multifaceted approach not only validated the superior of performance of AS, compared to Cmax under varied conditions, but also demonstrated the potential of advanced analytics in pharmacokinetic research. Despite the limitations of Cmax as a metric for the absorption rate being recognized since its early use, it has been traditionally used in BE studies for more than 40 years. In pharmacokinetics, the conventional method for examining the properties of a pharmacokinetic prevalence involves identifying its relationships with the bioavailable fraction and absorption rate constant, assuming a specific type of kinetics (e.g., a one-compartment model with first-order absorption and elimination) and utilizing simple simulations. All contributions in the field of BE toward finding an appropriate metric for absorption have used pharmacokinetic modeling approaches. In the 1980s, when the foundations of this field were established, simple pharmacokinetic modeling was applied. Later, during the 2000s and 2010s, more sophisticated mechanistic models were used. However, in all these cases, there was a need to use certain pharmacokinetic models and rely on specific assumptions. In this study, we utilize modern machine-learning techniques to address an old problem from a fresh perspective. Several variations of three ML methods (PCA, RF, and hierarchical clustering) were used, as well as many types of artificial neural networks, to identify the relationships between the PK parameters. For the first time, ML algorithms are applied instead of simple simulation exercises, and all pharmacokinetic features are explored together. This is the first research work where such a variety of methods is used to unveil the relationships among the PK characteristics, and it is certainly the first time that ANNs are utilized. Each of the methods used offers different capabilities, and together they allow for the investigation of various properties of the PK characteristics (particularly AS and Cmax). The combinatorial use of all these methods allows for verifying the findings and obtaining reliable conclusions about the superiority of AS over Cmax. Finally, and perhaps most importantly, it should be emphasized that AS exhibits the ideal physical properties (i.e., units) since it is expressed in terms of concentration change over time, and its calculation does not rely on any assumptions or models. The estimation of AS can be easily conducted directly from the C-t data, even by a pocket calculator, without any assumptions. Our findings suggest that AS is a superior metric for capturing absorption rates across various drug profiles and providing a robust alternative to Cmax in pharmacokinetics. AS not only correlates strongly with Tmax but also offers practical advantages in terms of calculation and interpretability. The ease of calculating AS, along with its appropriate units and properties, makes it a feasible metric for widespread adoption in BE studies. Also, it is important to underline that the calculation of AS does not rely on any assumptions,but it can be done through a simple non-compartmental approach. The strong (negative) correlation of AS with Tmax, suggests that it can reliably reflect the clinical outcomes associated with absorption kinetics. This correlation is crucial for ensuring that any new metric used in BE studies maintains the strict standards required for regulatory approval and therapeutic equivalence. On the contrary, Cmax exhibits properties related more to the extent of absorption, rather than the rate. In all case studies, for the five drugs with different kinetics, and the four machine-/deep-learning algorithms, AS was significantly superior to Cmax in reflecting absorption rate. These results are in line with the previous literature findings suggesting that Cmax is not an adequate metric for expressing absorption rate [10, 11, 12, 13, 14, 15, 16, 17, 18]. However, in this study we applied modern methodologies, like the three ML algorithms and ANN, allowing us to extensively explore all properties of Cmax.