# Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
## 4 Discussion  
The conventional use of Cmax as the predominant metric for the absorption rate in BE studies has faced growing scrutiny due to its significant limitations in capturing absorption kinetics [11; 12; 13; 14; 15; 16; 17; 18]. In this study, we apply modern machine learning and deep-learning methodologies to examine and contrast the characteristics of the newly proposed metric AS with Cmax in assessing the absorption rate [19; 20; 21]. In pharmacokinetics, the traditional approach to explore the attributes of a PK parameter typically entails establishing its correlations with the bioavailable fraction and absorption rate constant, often assuming a specific kinetic model and using simulations. In this study, rather than relying on simple simulations, we applied ML algorithms, enabling a thorough exploration of all PK parameters concurrently. To further elaborate on the use of AS in describing the absorption rate in BE studies, the ML algorithms allowed for a comparison of AS with the traditional PK parameters and further assessment of the correlations among them. In this scope, the PK parameters of five drugs (nintedanib, methylphenidate, nitrofurantoin, lisdexamfetamine, and theophylline) with varying absorption kinetics were analyzed using three different ML algorithms (PCA, RF, and HCA) and ANNs [22; 23]. To the best of our knowledge, this is the first time this novel metric has been evaluated across a range of diverse absorption kinetics while exploiting the capabilities of three different ML techniques and a deep-learning approach. Figure 9: Variable importance scores for the artificial neural network models developed for lisdexamfetamine, when Tmax is measured on an ordinal scale. The first step of our analysis was to estimate the individual PK parameters (AS, Cmax, Tmax, AUC, and AUCinf) for the five drugs of the study. Then, the three ML approaches were applied in several ways to unveil the characteristics of AS and Cmax towards reflecting the absorption rate. The utilization of PCA, RF, HCA, and ANNs allowed for a comprehensive analysis of the relationships among the PK parameters and demonstrated the suitability of AS in effectively reflecting absorption kinetics. Each algorithm offered unique insights regarding their correlations, enhancing the robustness of our conclusions. PCA analysis identified similarities among the PK parameters, highlighting the opposite behavior of AS to Tmax, as they are positioned in opposite directions relative to the second principal component. Significantly, the vector representing AS is diametrically opposite to Tmax. This indicates that as AS increases, reflecting faster absorption, Tmax decreases. Thus, AS effectively captures changes in absorption kinetics, unlike Cmax, which forms almost a 90-degree angle with Tmax, implying its independence from expressing the kinetic properties of absorption. RF analysis further supported the superiority of AS as an absorption rate metric. By transforming Tmax into its quartiles and using it as the response variable, RF identified AS as the primary contributor to Tmax. This finding was consistent across all drugs studied, with AS showing higher variable importance scores compared to Cmax and other PK parameters. The high prediction accuracy of the RF models underlines the reliability of AS in predicting absorption kinetics. Hierarchical clustering analyses provided additional evidence for the strong character of AS expressing kinetic properties. Finally, the ANNs models validated the findings from PCA, RF, and hierarchical clustering. The ANN models, trained on extensive PK data, demonstrated that AS was the most sensitive parameter for depicting absorption rates. The robustness of the ANN models in identifying AS as the best metric to reflect absorption kinetics unveils its potential utility in BE studies. One point that requires special attention is the choice of drugs for the analysis.