## 4 Discussion
Apart from the findings offered by the two machine learning approaches, there is also a fundamental theoretical reason for considering a parameter as a measure of the absorption rate. This essential issue refers to the units of measurement. A parameter that is used to express the \"rate\" of a process should represent the change of a measure (e.g., distance, concentration, etc.) over time. In the case of absorption, since we are not able to know the absolute quantities after oral administration of a drug, an appropriate measure of absorption rate should have units of _concentration per time_. That means that this measure should be the ratio of the change in drug concentration values divided by the relevant change in time (Equation (3)). \[\text{Rate of absorption}=\frac{\text{Change in drug concentration}}{\text{Change in time}} \tag{3}\]  
It becomes evident that all other metrics proposed in the literature do not exhibit the appropriate units. The several expressions of areas under the curve (AUCt, AUCp, AUCinf) refer to surfaces and have units of _concentration-time_. Therefore, these measures should be used to reflect several aspects of the extent of absorption. It should not be disregarded that AUCp has been proposed as a measure to express early \"exposure\" and not the rate of absorption. Besides Cmax, which is traditionally used in BE studies as an indirect metric for absorption rate, there is only one concentration measurement. As a result, in principle, it cannot be used to express the rate. Even though Cmax is currently used worldwide to indirectly reflect absorption rate, the machine learning findings presented in this study disputed this fact, showing that there is a small direct relationship with Tmax(Figures 2 and 4). The ratio Cmax/AUC has been proposed as an alternative to Cmax, aiming to exclude the influence of absorption extent by dividing with AUCt; however, Cmax/AUC lacks appropriate units because it is the fraction _concentration/(concentration time) = time_-1. The concept of \"intercept\" on the axis of the relative concentration values has also been proposed [17; 18]. In this case, the absorption rate metric is determined by dividing the initial concentrations of the drug in the two formulations by the time point [17]. A different approach to the \"intercept\" concept was the \"Modified Intercept\" metric, which utilized the limit of the quotient C/t when t\(\rightarrow\)0 (i.e., the intercept on the axis of concentration) [18]. However, these approaches assume first-order kinetics, a one-compartment model, and are based on complex estimation methods since they require log transformation, application of linear regression analysis, back extrapolation to time zero, and estimation of the intercept. Finally, Tmax, which has been considered an appropriate measure to express the rate of bioequivalence, has not been used because it is on a discrete scale and lacks appropriate measurement units [24]. Tmax has units of time, and therefore it cannot, in principle, be used to express the absorption rate. The simplest approach to fulfilling the requirements of Equation (3) is through the use of Cmax/Tmax, which refers to the slope formed between the (Tmax, Cmax) coordinates, namely, the tangent of the angle \(\angle\)(_Cmax-0-Tmax_) (Figure 1a). In order to avoid using a metric that relies on a single measurement (since both Cmax and Tmax come from the same measurement), an alternative approach is introduced in this study that is termed \"average slope\". The latter is calculated as the average of all slopes between subsequent time points up to Tmax (Figure 1b). AS or Cmax/Tmax have the appropriate concentration/time units and express rate of change. As mentioned above, one of the benefits of using AS instead of Cmax/Tmax is that AS estimation is based on many points and is easy to figure out by using a model-independent approach. Another advantage of using AS is that it can be thought of as a generalization of Cmax/Tmax, as shown in Equations (4)-(8).