Model Development and Assessment
The PPK model was constructed based on the dataset composed of 240 serial plasma samples. A two-compartment model with linear elimination and first-order absorption provided the most robust fit for nemonoxacin PK profiles. The base model was finally adjusted to account for the effects of delayed gastric emptying by introducing absorption lag time (ALAG) according to a recent study [13]. The inter-individual variability (IIV) for ALAG was excluded from the model as it is too short to be estimated appropriately. Before the inclusion of any covariates, the IIV in the base model parameters was moderate, 39.6% for CL, 18.7% for central compartment volume (V1), and 22.8% for peripheral compartment volume (V2).
The full PK model simultaneously included the covariates possibly affecting PK variability in the building process. The effect of CrCl on CL was found to be the most significant (ΔOFV = -40.471, compared with the base model). The effects of age on CL (ΔOFV = -7.027, P<0.01) and TBW on V1 (ΔOFV = -7.309, P<0.01) were significant in the objective function. These statistically significant covariates were retained in the final model. However, other clinical indicators such as sex, body weight, BMI, eGFR, and albumin were eliminated due to the nonsignificant contribution to ΔOFV or severe multicollinearity between variables. The full PK model successfully converged with an acceptable condition number 386 (the ratio of the largest eigenvalue of the correlation matrix to the smallest one), indicating that the model was stable and not ill-conditioned. The model equations for CL and V1 are presented below:
CL =\(\mathrm{\ (}{\frac{\mathrm{\text{age}}}{\mathrm{45.5}}\mathrm{)}}^{\mathrm{0.326}}\mathrm{\ \times\ (}{\frac{\mathrm{\text{CrCl}}}{\mathrm{57.45}}\mathrm{)}}^{\mathrm{0.443}}\)\(\mathrm{\times\ }\mathrm{\text{TVCL\ }}\mathrm{\times\ }\mathrm{e}^{\mathrm{\eta}_{\mathrm{1}}}\)
V1 =\(\mathrm{\ (}{\frac{\mathrm{\text{TBW}}}{\mathrm{37.25}}\mathrm{)}}^{\mathrm{0.672}}\)\(\mathrm{\times\ }\mathrm{TVV1\ }\mathrm{\times\ }\mathrm{e}^{\mathrm{\eta}_{\mathrm{2}}}\)
where TVCL and TVV1 are the population mean values for CL and V1, respectively. The IIV of CL (η 1) was reduced from 39.6% to 11.3% after including the covariates, while the IIV of V1 (η 2) was declined from 18.7% to 14.5%. All PK parameters demonstrated acceptable precision, with relative standard error (RSE) < 25%. The η-shrinkage was obtained with a fairly small scatter, 3.2% for CL, 11.2% for V1, and 18.3% for V2. The parameter estimates of the full model were presented in Table 3.
Figure 1 presents the full model’s diagnostics, which confirmed satisfactory goodness-of-fit between the observed and predicted concentration values. The figure also illustrated conditional weighted residuals (CWRDES) against predicted concentration and time postdose. There were equally spread residuals around the horizontal line without showing any peculiar trends, indicating a reasonable fit to the data. To evaluate the model stability and confidence intervals of the final parameter estimates, VPC and bootstrapping approaches were used. VPC was shown in Figure 2 by plotting the median and 90% prediction intervals which were consistent with the observed plasma concentration data. The original datasets were overlapped with the 95% CIs from 1000 bootstrapping analysis runs and were closely similar to median values, proving that the final model was stable (Table 3).