## 3 Results
### Population Pharmacokine Model  
Population pharmacokinetic analysis was initially performed separately for each patient group. However, due to the limited number of ICU patients in group B, no model could be derived. Therefore, in order not to waste the information of group B patients, all individuals were pooled into one group to increase the ability to develop a robust pharmacokinetic model, but each patient's individual characteristics (e.g., renal function) were assessed and all available data were used. Furthermore, this pooling was possible because there was no statistically significant difference (\(p\)-value > 0.05) in levetiracetam concentration values between the two groups. A one-compartment model with first order elimination was finally selected as the best model for the description of the levetiracetam concentration--time profiles. The estimates of the pharmacokinetic parameters of this best model are given in Table 2. It is of note that the volume of distribution of the central compartment (V) was 47.19 L and the clearance (CL) was 1.45 L/h. Of all the covariates examined for their influence on the kinetics of levetiracetam, only CKD-EPI eGFR was found to be significant for the clearance of levetiracetam. The coefficient of CKD-EPI eGFR with respect to clearance was 0.25, implying that better renal function (in terms of eGFR) leads to higher clearance of levetiracetam. The residual error model that led to the best results was the proportional error model with b = 0.099. The percentage relative standard errors for all estimated parameters had relatively low values. The significant covariate in the final model was the CKD-EPI eGFR (Wald test \(p\) = 0.00164), which is the Chronic Kidney Disease Epidemiology Collaboration equation, developed in an effort to provide a more precise formula for estimating glomerular filtration rate using serum creatinine, age, sex, and race data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Estimate** & **Standard Error** & **Relative Standard Error (\%)** & \(p\)**-Value** \\ \hline \multicolumn{5}{c}{Fixed effects} \\ \hline V (L) & 47.19 & 5.096 & 10.8 & - \\ \hline Cl (L/h) & 1.45 & 0.221 & 15.2 & - \\ \hline beta\_eGFR & 0.25 & 0.034 & 13.6 & 0.00164 \\ \hline \multicolumn{5}{c}{Random effects} \\ \hline \(\omega\)\_V & 0.184 & 0.037 & 20.1 & - \\ \hline \(\omega\)\_Cl & 0.251 & 0.0454 & 18.1 & - \\ \hline \multicolumn{5}{c}{Error model parameters} \\ \hline b & 0.099 & 0.0124 & 12.5 & - \\ \hline \hline \end{tabular}  
* Key: V, volume of distribution; Cl, clearance; \(\omega\)\_V, between-subject variability value for V; \(\omega\)\_Cl; between-subject variability value for Cl; beta\_eGFR, allometric scaling factor for CKD-EPI eGFR (centered around median) on Cl; b, proportional component of the error model.
* \end{table} 
Table 2: Population parameters of the final pharmacokinetic model of levetiracetam. Figure 1 shows the graphical evaluation of the final model. The visual representation of the predictive power shows that the prediction interval of the developed model includes the experimental concentration data in all cases. Similarly, the good predictive ability of the model is also illustrated in Figure 2, where the population predicted versus observed concentration values are almost linearly correlated (Figure 2a) and the NPDE versus time (Figure 2b) and concentration (Figure 2c) plots show an adequate performance. Additional goodness-of-fit plots are shown in the supplementary material (Figure S1a-c). The shrinkage of the volume and clearance estimates (parameter values were randomly sampled from the conditional distribution) was adequate and equal to 18.3% and \(-\)3.23%, respectively. The relationship between CKD-EPI eGFR and levetiracetam clearance is shown in Figure 3. An almost linear relationship (_levetiracetam clearance = 0.01534-(CKD-EPI eGFR) - 0.21031_) is observed with a correlation coefficient of 0.76.