# Average Slope vs. Cmax: Which Truly Reflects the Drug-Absorption Rate?
## 1 Introduction  
Bioequivalence (BE) testing plays a crucial role in pharmaceutical development and regulatory approval processes. Its primary objective is to establish that two drugs, namely the Test (T) product and the Reference (R) product, containing identical active ingredients, exhibit equivalent in vivo performance [1, 2]. This assessment is vital to ensure that both formulations produce similar therapeutic effects. Upon statistical analysis, if the pharmacokinetic (PK) characteristics of the T product closely resemble those of the reference R product, they are deemed pharmacokinetics equivalent, implying therapeutic equivalence as well [3, 4]. According to official guidelines, bioequivalence between a T and R product is accepted if they share the same active moiety and show no significant differences in their time-concentration profiles when administered at equivalent molar doses under comparable experimental conditions, covering both the absorption rate and extent [4]. To streamline BE assessments and ensure consistency, health authorities worldwide have established comprehensive guidelines, primarily focusing on PK considerations. These guidelines delineate essential PK parameters for evaluation, outline statistical methods foranalysis, and recommend appropriate clinical trial designs to more accurately estimate PK parameters [3].  
The traditional metrics used in BE studies to assess absorption kinetics include the maximum plasma concentration (Cmax) to represent the absorption rate and the area under the concentration-time curve from time zero to the last quantifiable concentration (AUC) to illustrate the extent of absorption. Supplementary PK parameters such as AUC extrapolated to infinity (AUCinf) and time (Tmax) to reach Cmax are utilized as secondary endpoints [4; 5; 6; 7; 8; 9; 10]. Despite the widespread acceptance of AUC as a robust metric for the absorption extent, there is skepticism about relying exclusively on Cmax as a metric for absorption-rate assessment. Critiques regarding the adequacy of Cmax in capturing absorption kinetics comprehensively have prompted investigations into alternative metrics, including average slope (AS), Cmax/AUC ratio, Tmax, and partial AUCs, to tackle the limitations of Cmax [10; 11; 12; 13; 14; 15; 16; 17; 18]. Nevertheless, Cmax continues to be widely utilized in BE studies, unable to capture absorption kinetics comprehensively.  
Recent studies integrating machine-learning (ML) methodologies into BE assessment have sought to address these challenges and redefine the evaluation of absorption kinetics. These studies have introduced novel metrics such as AS for characterizing absorption rates and use ML algorithms to unveil their potential [19; 20; 21]. ML techniques enable the development of models using PK data, facilitate automated decision-making processes using data inputs, offer the ability to indicate relationships among PK parameters, and identify novel metrics for characterizing absorption kinetics effectively [22; 23]. Through the integration of population PK modeling, a recent in silico study demonstrated the sensitivity of AS in reflecting changes in the absorption rate [21].  
The objective of this study is to compare the characteristics of AS and Cmax in expressing the absorption rate of drugs. In this context, an extensive investigation is performed on five drugs with different absorption and disposition kinetics.