## 4 Discussion  
The objective of this study was to explore the relationships among the PK parameters used in BE assessment and identify the most appropriate metric for characterizing absorption rate. This task was accomplished using two machine learning algorithms (PCA and RF) and the use of actual BE data from 26 healthy volunteers, as well as three simulated BE  
Figure 7: Variable importance scores for the feature parameters for the simulated bioequivalence studies. The response variable was either Cmax (**a**), Cmax/AUC (**b**), or Cmax/Tmax (**c**). Three levels of the simulated absorption rate constant were assumed: 0.5x, 1x, and 2x. Thus, in total, nine Random Forest models were developed. studies. To the best of knowledge, this is the first study that utilizes machine learning in the field of bioequivalence assessment. Over the last few years, it has been agreed that AUC indicates the extent of exposure, whereas Cmax (the maximum plasma concentration or peak exposure) and Tmax refer to absorption rate-dependent characteristics [1; 2; 4]. Even though there are no doubts about the use of AUC as a measure of the extent of absorption, the choice of Cmax as a metric for the rate of absorption has raised many concerns [6; 11; 12; 14; 16; 17]. First of all, it has to be reminded why Cmax was preferred over other PK metrics, e.g., Tmax, partial AUC areas, or mean residence time for reflecting the kinetic aspects of absorption. The requirement to evaluate \"rate\" in bioequivalence tests using indirect metrics comes from the ambiguity about whether such testing is meant to ensure pharmaceutical quality (in terms of drug release characteristics) as well as clinical safety and efficacy [12]. Thirty years ago, scientists using simple simulations demonstrated the danger of evaluating the performance of several indirect rate measures using a fixed universal acceptability interval for bioequivalence [12]. However, because rate, as indicated by a rate constant, cannot be accurately assessed using indirect metrics and may have little clinical relevance, regulatory guidelines supported the use of Cmax as an empirical index of safety and efficacy. However, Cmax inherently carries two problems: first, the fact that concentration measurements are only taken at discrete time intervals complicates the direct determination of Cmax (as well as Tmax). Secondly, and most importantly, Cmax is known to be greatly influenced by the extent of absorption. Hence, Cmax should be better used to measure high drug exposure rather than absorption rate. This implies that the ineffective use of Cmax as an indirect parameter for absorption rate contributes to the unpredictable and uncertain outcome of BE studies [11]. In this context, Tmax and the ratio Cmax/AUC have been proposed as possible alternatives to Cmax for assessing the absorption rate characteristics of immediate-release formulations [14]. Studies comparing the absorption rates of two drug formulations have shown that Tmax and the Cmax/AUC ratio share similar features [14]. This observation provided a compelling justification for using the observed Cmax/AUC ratio as a measure of absorption rate rather than Tmax because Cmax/AUC was easier to handle statistically and could be measured with more precision than Tmax [14; 18]. Even though the limitations of Cmax as an absorption rate metric have been acknowledged since its initial adoption, the use of Cmax in BE studies has been traditionally used for more than 30 years. In this study, the modern tool of machine learning is used to address an old problem from another perspective. Two ML methods, principal component analysis and random forest, are used to identify the relationships between the PK parameters. The underlying meaning of this task was to unveil the relationships among all possible pharmacokinetic measures used in bioequivalence studies. In general, in bioequivalence testing, pharmacokinetic parameters are calculated to express two characteristics: extent and rate of absorption.